机器学习–课程笔记–01

Introduction

推荐书目

• Tom. M. Mitchell -- Machine Learning

  • Mitchell是machine learning的开创者
  • 全书偏向理论，基本的方法。

• Bishop -- Pattern Recognition and Machine Learning

  • 基于贝叶斯理论，统计学

• Trevor Hastie -- The elements of statistical learning: Data Ming,inference and prediction

  • 频率主义，统计学

• Russell -- Aritificial Intelligence : A Modern Approach

  • 从AI的侧面介绍一小部分ML

• Aplaydin -- Introduction to Machine Learning

  • 内容简单精炼，观点正确丰富
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• 李航 -- 统计学方法

• Mohri -- Foundations of Machine Learning

  • 偏向理论，可以知道所以然

学科概述

什么可以成为学科？

可以成为体系的东西，具有一系列:

• 方法
• 理论

• 工具

机器学习的缘起

• 是AI和计算科学的分支

比较好的期刊

• Machine Learning

• Journal of Machine Learning Research

  • This is free!

定义

机器学习是研究智能体的:

• 增长知识
• 提高性能
• 学习学习

的一般原理和计算模型的学科。

使用计算模型来表示机器学习的方法和结果

什么叫学习

学习是一种递归的概念，是一种广泛存在于自然界的现象，普遍，普通。

• 学无止境
• Meta-learning 元学习，学习学习的方法

• 理论创新 -- 滴水穿石都可以是学习

增长知识

知道了原来所不知道的东西。

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例如给出离散的数列对<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-75" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:26px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-76" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-77" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">f<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span><span class="mo" id="MathJax-Span-78" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">[</span><span class="mi" id="MathJax-Span-79" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-80" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">]</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>，其中<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-81" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:130px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-82" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-83" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-84" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">∈</span><span class="mo" id="MathJax-Span-85" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">{</span><span class="msubsup" id="MathJax-Span-86" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:16.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-87" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mn" id="MathJax-Span-88" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">0</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-89" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="msubsup" id="MathJax-Span-90" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:16.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-91" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mn" id="MathJax-Span-92" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">1</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-93" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="mo" id="MathJax-Span-94" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-95" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-96" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-97" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="msubsup" id="MathJax-Span-98" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:17.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-99" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x </span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mi" id="MathJax-Span-100" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">n</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-101" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">}</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>,将这个<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-102" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:26px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-103" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-104" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">f<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span><span class="mo" id="MathJax-Span-105" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">[</span><span class="mi" id="MathJax-Span-106" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-107" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">]</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>拟合成函数<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-108" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:34px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-109" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-110" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-111" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="munderover" id="MathJax-Span-112" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:12.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-113" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">f<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-40.3px; left:4.2px"><span class="mo" id="MathJax-Span-114" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">^</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-115" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">(</span><span class="mi" id="MathJax-Span-116" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-117" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">)</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:22.6px"></span></span></nobr>，那么对于一个新的<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-118" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:130px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-119" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-120" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-121" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">∉</span><span class="mo" id="MathJax-Span-122" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">{</span><span class="msubsup" id="MathJax-Span-123" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:16.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-124" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mn" id="MathJax-Span-125" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">0</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-126" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="msubsup" id="MathJax-Span-127" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:16.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-128" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mn" id="MathJax-Span-129" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">1</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-130" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="mo" id="MathJax-Span-131" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-132" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-133" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">.</span><span class="mo" id="MathJax-Span-134" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static; font-family:MathJax_Main">,</span><span class="msubsup" id="MathJax-Span-135" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 2.7px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:17.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-136" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-31.6px; left:9px"><span class="mi" id="MathJax-Span-137" style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">n</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span></span><span class="mo" id="MathJax-Span-138" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">}</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>，这个新的<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-139" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:34px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-140" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-141" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-142" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="munderover" id="MathJax-Span-143" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:12.2px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mi" id="MathJax-Span-144" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">f<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-40.3px; left:4.2px"><span class="mo" id="MathJax-Span-145" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">^</span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span></span></span></span><span class="mo" id="MathJax-Span-146" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">(</span><span class="mi" id="MathJax-Span-147" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">x</span><span class="mo" id="MathJax-Span-148" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Main">)</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-5.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:22.6px"></span></span></nobr>就是新的知识，这就达到了增长知识的目的。

提高性能

如上图所示，为一个产生式系统。对于一种特征，某一种结果<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-149" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:7px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-150" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-151" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">r</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-1.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:9.3px"></span></span></nobr>发生的概率是<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-152" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:8px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-153" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-154" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">p</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:12.3px"></span></span></nobr>，那对于存储知识库的硬件来说，将概率越大的结果放到更容易访问的空间，便可以更快速的访问，达到提高性能的作用。

学习学习

还是和上图中的产生式系统一样，其推断引擎最为复杂，那么可以使用一个新的产生式系统实现这个产生式系统的推理引擎。

学习元规则的过程，mata-learning

机器学习的一般结构

机器学习和CS的关系

改变了计算机交互的范型<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-155" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:67px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-156" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-157" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">p</span><span class="mi" id="MathJax-Span-158" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">a</span><span class="mi" id="MathJax-Span-159" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">r</span><span class="mi" id="MathJax-Span-160" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">a</span><span class="mi" id="MathJax-Span-161" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">d<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:0px"></span></span><span class="mi" id="MathJax-Span-162" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">i</span><span class="mi" id="MathJax-Span-163" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">g<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:0px"></span></span><span class="mi" id="MathJax-Span-164" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">m</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.3px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:16.6px"></span></span></nobr>,从之前的Human --> Computer, 到Human --> ML --> Computer

机器学习和人工智能的关系

有关系，但是究竟是<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-165" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:69px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-166" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-167" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">M<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1.3px"></span></span><span class="mi" id="MathJax-Span-168" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">L</span><span class="mo" id="MathJax-Span-169" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">⊂</span><span class="mi" id="MathJax-Span-170" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">A</span><span class="mi" id="MathJax-Span-171" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">I<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-1.6px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:14.2px"></span></span></nobr>还是<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-172" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:69px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-173" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-174" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">A</span><span class="mi" id="MathJax-Span-175" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">I<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1px"></span></span><span class="mo" id="MathJax-Span-176" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Main">⊂</span><span class="mi" id="MathJax-Span-177" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 4.5px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">M<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1.3px"></span></span><span class="mi" id="MathJax-Span-178" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">L</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-1.6px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:14.2px"></span></span></nobr>目前没有定论

ML的分类方式

• 知识表示
• 应用领域
• 学习策略

• 映射类型

  • 

• 反馈类型

  • Supervised
  • unsupervised
  • reinforcement
  • semi-supervised

机器学习的基本问题

• 可学习型

  • 用命题逻辑表示数域里的问题，是不可能的
  • 必须有多项式复杂度

• 可行性

  • 可计算的
  • 有效的
  • 可靠的<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-179" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:60px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-180" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-181" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-182" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-183" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">不</span></span></span></span><span class="texatom" id="MathJax-Span-184" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-185" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-186" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">能</span></span></span></span><span class="texatom" id="MathJax-Span-187" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-188" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-189" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">不</span></span></span></span><span class="texatom" id="MathJax-Span-190" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-191" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-192" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">可</span></span></span></span><span class="texatom" id="MathJax-Span-193" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-194" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-195" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">控</span></span></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>

• 适用性

  • 是否一定要机器学习？

    • 灵活稳健<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-196" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:29px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-197" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-198" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">M<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1.3px"></span></span><span class="mi" id="MathJax-Span-199" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">L</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-1px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:13.1px"></span></span></nobr>和可靠有效<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-200" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:79px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-35px; left:0px"><span class="mrow" id="MathJax-Span-201" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mi" id="MathJax-Span-202" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">N<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1.4px"></span></span><span class="mi" id="MathJax-Span-203" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">o</span><span class="mi" id="MathJax-Span-204" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">n</span><span class="mo" id="MathJax-Span-205" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 3.6px; display:inline; position:static; font-family:MathJax_Main">−</span><span class="mi" id="MathJax-Span-206" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px 0px 0px 3.6px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">M<span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; height:1px; width:1.3px"></span></span><span class="mi" id="MathJax-Span-207" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static; font-family:MathJax_Math; font-style:italic">L</span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:35px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-1.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:13.2px"></span></span></nobr>的抉择
    • 是否存在通用的学习器
    • 任何问题都存在最优的学习器，任何学习器有最优的问题。<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-208" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:288px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-209" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-210" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-211" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-212" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">所</span></span></span></span><span class="texatom" id="MathJax-Span-213" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-214" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-215" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">以</span></span></span></span><span class="texatom" id="MathJax-Span-216" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-217" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-218" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">，</span></span></span></span><span class="texatom" id="MathJax-Span-219" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-220" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-221" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">看</span></span></span></span><span class="texatom" id="MathJax-Span-222" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-223" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-224" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">论</span></span></span></span><span class="texatom" id="MathJax-Span-225" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-226" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-227" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">文</span></span></span></span><span class="texatom" id="MathJax-Span-228" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-229" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-230" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">的</span></span></span></span><span class="texatom" id="MathJax-Span-231" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-232" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-233" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">时</span></span></span></span><span class="texatom" id="MathJax-Span-234" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-235" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-236" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">候</span></span></span></span><span class="texatom" id="MathJax-Span-237" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-238" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-239" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">，</span></span></span></span><span class="texatom" id="MathJax-Span-240" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-241" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-242" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">实</span></span></span></span><span class="texatom" id="MathJax-Span-243" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-244" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-245" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">验</span></span></span></span><span class="texatom" id="MathJax-Span-246" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-247" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-248" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">数</span></span></span></span><span class="texatom" id="MathJax-Span-249" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-250" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-251" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">据</span></span></span></span><span class="texatom" id="MathJax-Span-252" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-253" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-254" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">往</span></span></span></span><span class="texatom" id="MathJax-Span-255" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-256" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-257" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">往</span></span></span></span><span class="texatom" id="MathJax-Span-258" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-259" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-260" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">是</span></span></span></span><span class="texatom" id="MathJax-Span-261" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-262" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-263" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">给</span></span></span></span><span class="texatom" id="MathJax-Span-264" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-265" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-266" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">定</span></span></span></span><span class="texatom" id="MathJax-Span-267" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-268" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-269" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">了</span></span></span></span><span class="texatom" id="MathJax-Span-270" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-271" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-272" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">的</span></span></span></span><span class="texatom" id="MathJax-Span-273" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-274" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-275" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">。</span></span></span></span><span class="texatom" id="MathJax-Span-276" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-277" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-278" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">：</span></span></span></span><span class="texatom" id="MathJax-Span-279" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-280" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-281" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">）</span></span></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>

• 三个ML的教训

  • Rashomon<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-282" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:84px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-283" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-284" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-285" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-286" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">好</span></span></span></span><span class="texatom" id="MathJax-Span-287" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-288" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-289" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">模</span></span></span></span><span class="texatom" id="MathJax-Span-290" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-291" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-292" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">型</span></span></span></span><span class="texatom" id="MathJax-Span-293" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-294" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-295" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">的</span></span></span></span><span class="texatom" id="MathJax-Span-296" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-297" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-298" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">多</span></span></span></span><span class="texatom" id="MathJax-Span-299" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-300" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-301" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">样</span></span></span></span><span class="texatom" id="MathJax-Span-302" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-303" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-304" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">性</span></span></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>
  • Occam<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-305" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:120px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-306" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-307" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-308" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-309" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">简</span></span></span></span><span class="texatom" id="MathJax-Span-310" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-311" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-312" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">单</span></span></span></span><span class="texatom" id="MathJax-Span-313" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-314" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-315" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">性</span></span></span></span><span class="texatom" id="MathJax-Span-316" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-317" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-318" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">和</span></span></span></span><span class="texatom" id="MathJax-Span-319" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-320" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-321" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">精</span></span></span></span><span class="texatom" id="MathJax-Span-322" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-323" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-324" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">确</span></span></span></span><span class="texatom" id="MathJax-Span-325" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-326" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-327" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">性</span></span></span></span><span class="texatom" id="MathJax-Span-328" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-329" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-330" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">的</span></span></span></span><span class="texatom" id="MathJax-Span-331" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-332" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-333" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">冲</span></span></span></span><span class="texatom" id="MathJax-Span-334" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-335" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-336" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">突</span></span></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>
  • Bellman<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-337" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:16px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:relative; width:48px; height:0px"><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:absolute; top:-34px; left:0px"><span class="mrow" id="MathJax-Span-338" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="texatom" id="MathJax-Span-339" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-340" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-341" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">维</span></span></span></span><span class="texatom" id="MathJax-Span-342" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-343" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-344" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">数</span></span></span></span><span class="texatom" id="MathJax-Span-345" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-346" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-347" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">灾</span></span></span></span><span class="texatom" id="MathJax-Span-348" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mrow" id="MathJax-Span-349" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span class="mo" id="MathJax-Span-350" style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline; position:static"><span style="border:0px; outline:0px; font-size:12px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; position:static; font-family:STIXGeneral,'Arial Unicode MS',serif">难</span></span></span></span></span><span style="border:0px; outline:0px; vertical-align:0px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; width:0px; height:34px"></span></span></span><span style="border-width:0px; border-left-style:solid; outline:0px; vertical-align:-4.2px; background-color:transparent; margin:0px; padding:0px; display:inline-block; position:static; overflow:hidden; width:0px; height:18.2px"></span></span></nobr>

• 欠拟合和过拟合的问题。

  • 训练的多了容易把样本中不是特征的东西也学习过来

ML的理论基础

• 数学
• 统计学
• 信息论
• 计算理论

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