Tom. M. Mitchell -- Machine Learning
Bishop -- Pattern Recognition and Machine Learning
Trevor Hastie -- The elements of statistical learning: Data Ming,inference and prediction
Russell -- Aritificial Intelligence : A Modern Approach
Aplaydin -- Introduction to Machine Learning
Mohri -- Foundations of Machine Learning
偏向理论,可以知道所以然
可以成为体系的东西,具有一系列:
工具
是AI和计算科学的分支
Journal of Machine Learning Research
This is free!
机器学习是研究智能体的:
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
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。
理论创新 -- 滴水穿石都可以是学习
知道了原来所不知道的东西。
回归问题<nobr style="border:0px; padding:0px; margin:0px; max-width:none; max-height:none; vertical-align:0px"><span class="math" id="MathJax-Span-67" 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:24px; 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-68" 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-69" 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-70" 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-71" 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">拟</span></span></span></span><span class="texatom" id="MathJax-Span-72" 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-73" 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-74" 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">合</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>
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。
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。
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
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
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
可学习型
可行性
适用性
是否一定要机器学习?
三个ML的教训
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