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<h1 id="&#x6700;&#x63A5;&#x8FD1;&#x4EBA;&#x7C7B;&#x601D;&#x7EF4;&#x7684;&#x5206;&#x7C7B;&#x7B97;&#x6CD5;-&#x51B3;&#x7B56;&#x6811;">&#x6700;&#x63A5;&#x8FD1;&#x4EBA;&#x7C7B;&#x601D;&#x7EF4;&#x7684;&#x5206;&#x7C7B;&#x7B97;&#x6CD5;-&#x51B3;&#x7B56;&#x6811;</h1>
<h2 id="&#x4EC0;&#x4E48;&#x662F;&#x51B3;&#x7B56;&#x6811;">&#x4EC0;&#x4E48;&#x662F;&#x51B3;&#x7B56;&#x6811;</h2>
<p>&#x51B3;&#x7B56;&#x6811;&#x8BF4;&#x767D;&#x4E86;&#x5C31;&#x662F;&#x4E00;&#x68F5;&#x80FD;&#x591F;&#x66FF;&#x6211;&#x4EEC;&#x505A;&#x51B3;&#x7B56;&#x7684;&#x6811;&#xFF0C;&#x6216;&#x8005;&#x8BF4;&#x662F;&#x6211;&#x4EEC;&#x4EBA;&#x7684;&#x8111;&#x56DE;&#x8DEF;&#x7684;&#x4E00;&#x79CD;&#x8868;&#x73B0;&#x5F62;&#x5F0F;&#x3002;&#x6BD4;&#x5982;&#x6211;&#x770B;&#x5230;&#x4E00;&#x4E2A;&#x4EBA;&#xFF0C;&#x7136;&#x540E;&#x6211;&#x4F1A;&#x601D;&#x8003;&#x8FD9;&#x4E2A;&#x7537;&#x4EBA;&#x6709;&#x6CA1;&#x6709;&#x4E70;&#x8F66;&#x3002;&#x90A3;&#x6211;&#x7684;&#x8111;&#x56DE;&#x8DEF;&#x53EF;&#x80FD;&#x662F;&#x8FD9;&#x6837;&#x7684;&#xFF1A;</p>
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<p>&#x5176;&#x5B9E;&#x8FD9;&#x6837;&#x4E00;&#x79CD;&#x8111;&#x56DE;&#x8DEF;&#x7684;&#x5F62;&#x5F0F;&#x5C31;&#x662F;&#x6211;&#x4EEC;&#x6240;&#x8BF4;&#x7684;&#x51B3;&#x7B56;&#x6811;&#x3002;&#x6240;&#x4EE5;&#x4ECE;&#x56FE;&#x4E2D;&#x80FD;&#x770B;&#x51FA;&#x51B3;&#x7B56;&#x6811;&#x662F;&#x4E00;&#x4E2A;&#x7C7B;&#x4F3C;&#x4E8E;&#x4EBA;&#x4EEC;&#x51B3;&#x7B56;&#x8FC7;&#x7A0B;&#x7684;&#x6811;&#x7ED3;&#x6784;&#xFF0C;&#x4ECE;&#x6839;&#x8282;&#x70B9;&#x5F00;&#x59CB;&#xFF0C;&#x6BCF;&#x4E2A;&#x5206;&#x679D;&#x4EE3;&#x8868;&#x4E00;&#x4E2A;&#x65B0;&#x7684;&#x51B3;&#x7B56;&#x4E8B;&#x4EF6;&#xFF0C;&#x4F1A;&#x751F;&#x6210;&#x4E24;&#x4E2A;&#x6216;&#x591A;&#x4E2A;&#x5206;&#x679D;&#xFF0C;&#x6BCF;&#x4E2A;&#x53F6;&#x5B50;&#x4EE3;&#x8868;&#x4E00;&#x4E2A;&#x6700;&#x7EC8;&#x5224;&#x5B9A;&#x6240;&#x5C5E;&#x7684;&#x7C7B;&#x522B;&#x3002;&#x5F88;&#x660E;&#x663E;&#xFF0C;&#x5982;&#x679C;&#x6211;&#x73B0;&#x5728;&#x5DF2;&#x7ECF;&#x6784;&#x9020;&#x597D;&#x4E86;&#x4E00;&#x9897;&#x51B3;&#x7B56;&#x6811;&#x7684;&#x8BDD;&#xFF0C;&#x73B0;&#x5728;&#x6211;&#x5F97;&#x5230;&#x4E00;&#x6761;&#x6570;&#x636E;(&#x7537;&#xFF0C; 29)&#xFF0C;&#x6211;&#x5C31;&#x4F1A;&#x8BA4;&#x4E3A;&#x8FD9;&#x4E2A;&#x4EBA;&#x6CA1;&#x6709;&#x4E70;&#x8FC7;&#x8F66;&#x3002;&#x6240;&#x4EE5;&#x5462;&#xFF0C;&#x5173;&#x952E;&#x95EE;&#x9898;&#x5C31;&#x662F;&#x600E;&#x6837;&#x6765;&#x6784;&#x9020;&#x51B3;&#x7B56;&#x6811;&#x4E86;&#x3002;</p>
<p>&#x6784;&#x9020;&#x51B3;&#x7B56;&#x6811;&#x65F6;&#x4F1A;&#x9075;&#x5FAA;&#x4E00;&#x4E2A;&#x6307;&#x6807;&#xFF0C;&#x6709;&#x7684;&#x662F;&#x6309;&#x7167;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#x6765;&#x6784;&#x5EFA;&#xFF0C;&#x8FD9;&#x79CD;&#x53EB;<strong>ID3&#x7B97;&#x6CD5;</strong>&#xFF0C;&#x6709;&#x7684;&#x662F;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6BD4;</strong>&#x6765;&#x6784;&#x5EFA;&#xFF0C;&#x8FD9;&#x79CD;&#x53EB;<strong>C4.5</strong>&#x7B97;&#x6CD5;&#xFF0C;&#x6709;&#x7684;&#x662F;&#x6309;&#x7167;<strong>&#x57FA;&#x5C3C;&#x7CFB;&#x6570;</strong>&#x6765;&#x6784;&#x5EFA;&#x7684;&#xFF0C;&#x8FD9;&#x79CD;&#x53EB;<strong>CART</strong>&#x7B97;&#x6CD5;&#x3002;&#x5728;&#x8FD9;&#x91CC;&#x4E3B;&#x8981;&#x4ECB;&#x7ECD;&#x4E00;&#x4E0B;<strong>ID3&#x7B97;&#x6CD5;</strong>&#x3002;</p>
<h2 id="id3&#x7B97;&#x6CD5;">ID3&#x7B97;&#x6CD5;</h2>
<p>&#x6574;&#x4E2A;<strong>ID3&#x7B97;&#x6CD5;</strong>&#x5176;&#x5B9E;&#x4E3B;&#x8981;&#x5C31;&#x662F;&#x56F4;&#x7ED5;&#x7740;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#x6765;&#x7684;&#xFF0C;&#x6240;&#x4EE5;&#x8981;&#x5F04;&#x6E05;&#x695A;<strong>ID3&#x7B97;&#x6CD5;</strong>&#x7684;&#x6D41;&#x7A0B;&#xFF0C;&#x9996;&#x5148;&#x8981;&#x5F04;&#x6E05;&#x695A;&#x4EC0;&#x4E48;&#x662F;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#xFF0C;&#x4F46;&#x8981;&#x5F04;&#x6E05;&#x695A;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x4E4B;&#x524D;&#x6709;&#x4E2A;&#x6982;&#x5FF5;&#x5FC5;&#x987B;&#x8981;&#x61C2;&#xFF0C;&#x5C31;&#x662F;<strong>&#x71B5;</strong>&#x3002;&#x6240;&#x4EE5;&#x5148;&#x770B;&#x770B;&#x4EC0;&#x4E48;&#x662F;&#x71B5;&#x3002;</p>
<h3 id="&#x71B5;&#x3001;&#x6761;&#x4EF6;&#x71B5;&#x3001;&#x4FE1;&#x606F;&#x589E;&#x76CA;">&#x71B5;&#x3001;&#x6761;&#x4EF6;&#x71B5;&#x3001;&#x4FE1;&#x606F;&#x589E;&#x76CA;</h3>
<p>&#x5728;&#x4FE1;&#x606F;&#x8BBA;&#x548C;&#x6982;&#x7387;&#x7EDF;&#x8BA1;&#x4E2D;&#x5462;&#xFF0C;&#x4E3A;&#x4E86;&#x8868;&#x793A;&#x67D0;&#x4E2A;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#xFF0C;&#x5C31;&#x501F;&#x7528;&#x4E86;&#x70ED;&#x529B;&#x5B66;&#x7684;&#x4E00;&#x4E2A;&#x6982;&#x5FF5;&#x53EB;<strong>&#x71B5;</strong>&#x3002;&#x5982;&#x679C;&#x5047;&#x8BBE; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span> &#x662F;&#x4E00;&#x4E2A;&#x6709;&#x9650;&#x4E2A;&#x53D6;&#x503C;&#x7684;&#x79BB;&#x6563;&#x578B;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x8BDD;&#xFF0C;&#x5F88;&#x663E;&#x7136;&#x5B83;&#x7684;&#x6982;&#x7387;&#x5206;&#x5E03;&#x6216;&#x8005;&#x5206;&#x5E03;&#x5F8B;&#x5C31;&#x662F;&#x8FD9;&#x6837;&#x7684;&#xFF1A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi><mo>(</mo><mi>X</mi><mo>=</mo><msub><mi>x</mi><mi>i</mi></msub><mo>)</mo><mo>=</mo><msub><mi>p</mi><mi>i</mi></msub><mo separator="true">,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>n</mi></mrow><annotation encoding="application/x-tex">P(X=x_i)=p_i, i=1,2,...,n</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="mrel">=</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">)</span><span class="mrel">=</span><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathit">i</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">n</span></span></span></span>&#x3002;</p>
<p>&#x6709;&#x4E86;&#x6982;&#x7387;&#x5206;&#x5E03;&#x540E;&#xFF0C;&#x5219;&#x8FD9;&#x4E2A;&#x968F;&#x673A;&#x53D8;&#x91CF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span> &#x7684;&#x71B5;&#x7684;&#x8BA1;&#x7B97;&#x516C;&#x5F0F;&#x5C31;&#x662F;&#xFF08;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi><mi>S</mi></mrow><annotation encoding="application/x-tex">PS</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mord mathit" style="margin-right:0.05764em;">S</span></span></span></span>&#xFF1A;&#x8FD9;&#x91CC;&#x7684; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>l</mi><mi>o</mi><mi>g</mi></mrow><annotation encoding="application/x-tex">log</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.8888799999999999em;vertical-align:-0.19444em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">o</span><span class="mord mathit" style="margin-right:0.03588em;">g</span></span></span></span> &#x662F;&#x4EE5; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>2</mn></mrow><annotation encoding="application/x-tex">2</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">2</span></span></span></span> &#x4E3A;&#x5E95;&#xFF09;&#xFF1A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>H</mi><mo>(</mo><mi>X</mi><mo>)</mo><mo>=</mo><mo>&#x2212;</mo><msubsup><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>p</mi><mi>i</mi></msub><mi>l</mi><mi>o</mi><mi>g</mi><msub><mi>p</mi><mi>i</mi></msub></mrow><annotation encoding="application/x-tex">H(X)=-\sum_{i=1}^np_ilogp_i</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1.0500099999999999em;vertical-align:-0.30001em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord">&#x2212;</span><span class="mop"><span class="mop op-symbol small-op" style="top:-0.0000050000000000050004em;">&#x2211;</span><span class="msupsub"><span class="vlist"><span style="top:0.30001em;margin-left:0em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mrel mtight">=</span><span class="mord mathrm mtight">1</span></span></span></span><span style="top:-0.364em;margin-right:0.05em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle uncramped mtight"><span class="mord mathit mtight">n</span></span></span><span
<p>&#x4ECE;&#x8FD9;&#x4E2A;&#x516C;&#x5F0F;&#x4E5F;&#x53EF;&#x4EE5;&#x770B;&#x51FA;&#xFF0C;&#x5982;&#x679C;&#x6211;&#x6982;&#x7387;&#x662F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span></span></span></span> &#x6216;&#x8005;&#x662F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span></span></span></span> &#x7684;&#x65F6;&#x5019;&#xFF0C;&#x6211;&#x7684;&#x71B5;&#x5C31;&#x662F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>0</mn></mrow><annotation encoding="application/x-tex">0</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span></span></span></span> &#x3002;&#xFF08;&#x56E0;&#x4E3A;&#x8FD9;&#x79CD;&#x60C5;&#x51B5;&#x4E0B;&#x6211;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x662F;&#x6700;&#x4F4E;&#x7684;&#xFF09;&#xFF0C;&#x90A3;&#x5982;&#x679C;&#x6211;&#x7684;&#x6982;&#x7387;&#x662F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>0</mn><mi mathvariant="normal">.</mi><mn>5</mn></mrow><annotation encoding="application/x-tex">0.5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">0</span><span class="mord mathrm">.</span><span class="mord mathrm">5</span></span></span></span> &#x4E5F;&#x5C31;&#x662F;&#x4E94;&#x4E94;&#x5F00;&#x7684;&#x65F6;&#x5019;&#xFF0C;&#x6211;&#x7684;&#x71B5;&#x662F;&#x6700;&#x5927;&#x4E5F;&#x5C31;&#x662F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span></span></span></span> &#x3002;&#xFF08;&#x5C31;&#x50CF;&#x6254;&#x786C;&#x5E01;&#xFF0C;&#x4F60;&#x6C38;&#x8FDC;&#x90FD;&#x731C;&#x4E0D;&#x900F;&#x4F60;&#x4E0B;&#x6B21;&#x6254;&#x5230;&#x7684;&#x662F;&#x6B63;&#x9762;&#x8FD8;&#x662F;&#x53CD;&#x9762;&#xFF0C;&#x6240;&#x4EE5;&#x5B83;&#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x975E;&#x5E38;&#x9AD8;&#xFF09;&#x3002;&#x6240;&#x4EE5;&#x5462;&#xFF0C;<strong>&#x71B5;&#x8D8A;&#x5927;&#xFF0C;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x5C31;&#x8D8A;&#x9AD8;</strong>&#x3002;</p>
<p>&#x5728;&#x6211;&#x4EEC;&#x5B9E;&#x9645;&#x60C5;&#x51B5;&#x4E0B;&#xFF0C;&#x6211;&#x4EEC;&#x8981;&#x7814;&#x7A76;&#x7684;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x57FA;&#x672C;&#x4E0A;&#x90FD;&#x662F;&#x591A;&#x968F;&#x673A;&#x53D8;&#x91CF;&#x7684;&#x60C5;&#x51B5;&#xFF0C;&#x6240;&#x4EE5;&#x5047;&#x8BBE;&#x6709;&#x968F;&#x4FBF;&#x91CF;(X,Y)&#xFF0C;&#x90A3;&#x4E48;&#x5B83;&#x7684;&#x8054;&#x5408;&#x6982;&#x7387;&#x5206;&#x5E03;&#x662F;&#x8FD9;&#x6837;&#x7684;&#xFF1A;</p>
<p><span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>P</mi><mo>(</mo><mi>X</mi><mo>=</mo><msub><mi>x</mi><mi>i</mi></msub><mo separator="true">,</mo><mi>Y</mi><mo>=</mo><msub><mi>y</mi><mi>j</mi></msub><mo>)</mo><mo>=</mo><msub><mi>p</mi><mrow><mi>i</mi><mi>j</mi></mrow></msub><mo separator="true">,</mo><mi>i</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>n</mi><mo separator="true">;</mo><mi>j</mi><mo>=</mo><mn>1</mn><mo separator="true">,</mo><mn>2</mn><mo separator="true">,</mo><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mi mathvariant="normal">.</mi><mo separator="true">,</mo><mi>m</mi></mrow><annotation encoding="application/x-tex">
P(X=x_i, Y=y_j)=p_{ij}, i=1,2,...,n; j=1,2,...,m
</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1.036108em;vertical-align:-0.286108em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.13889em;">P</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="mrel">=</span><span class="mord"><span class="mord mathit">x</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight">i</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathit" style="margin-right:0.22222em;">Y</span><span class="mrel">=</span><span class="mord"><span class="mord mathit" style="margin-right:0.03588em;">y</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:-0.03588em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mclose">)</span><span class="mrel">=</span><span class="mord"><span class="mord mathit">p</span><span class="msupsub"><span class="vlist"><span style="top:0.15em;margin-right:0.05em;margin-left:0em;"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span><span class="reset-textstyle scriptstyle cramped mtight"><span class="mord scriptstyle cramped mtight"><span class="mord mathit mtight">i</span><span class="mord mathit mtight" style="margin-right:0.05724em;">j</span></span></span></span><span class="baseline-fix"><span class="fontsize-ensurer reset-size5 size5"><span style="font-size:0em;">&#x200B;</span></span>&#x200B;</span></span></span></span><span class="mpunct">,</span><span class="mord mathit">i</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">n</span><span class="mpunct">;</span><span class="mord mathit" style="margin-right:0.05724em;">j</span><span class="mrel">=</span><span class="mord mathrm">1</span><span class="mpunct">,</span><span class="mord mathrm">2</span><span class="mpunct">,</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mord mathrm">.</span><span class="mpunct">,</span><span class="mord mathit">m</span></span></span></span></p>
<p>&#x90A3;&#x5982;&#x679C;&#x6211;&#x60F3;&#x77E5;&#x9053;&#x5728;&#x6211;&#x4E8B;&#x4EF6; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span> &#x53D1;&#x751F;&#x7684;&#x524D;&#x63D0;&#x4E0B;&#xFF0C;&#x4E8B;&#x4EF6; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.22222em;">Y</span></span></span></span> &#x53D1;&#x751F;&#x7684;&#x71B5;&#x662F;&#x591A;&#x5C11;&#x7684;&#x8BDD;&#xFF0C;&#x8FD9;&#x79CD;&#x71B5;&#x6211;&#x4EEC;&#x53EB;&#x5B83;<strong>&#x6761;&#x4EF6;&#x71B5;</strong>&#x3002;&#x6761;&#x4EF6;&#x71B5; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>H</mi><mo>(</mo><mi>Y</mi><mi mathvariant="normal">&#x2223;</mi><mi>X</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">H(Y|X)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.22222em;">Y</span><span class="mord mathrm">&#x2223;</span><span class="mord mathit" style="margin-right:0.07847em;">X</span><span class="mclose">)</span></span></span></span> &#x8868;&#x793A;&#x968F;&#x673A;&#x53D8;&#x91CF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span> &#x7684;&#x6761;&#x4EF6;&#x4E0B;&#x968F;&#x673A;&#x53D8;&#x91CF; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.22222em;">Y</span></span></span></span> &#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x3002;&#x6761;&#x4EF6;&#x71B5;&#x7684;&#x8BA1;&#x7B97;&#x516C;&#x5F0F;&#x662F;&#x8FD9;&#x6837;&#x7684;&#xFF1A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>H</mi><mo>(</mo><mi>Y</mi><mi mathvariant="normal">&#x2223;</mi><mi>X</mi><mo>)</mo><mo>=</mo><msubsup><mo>&#x2211;</mo><mrow><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></msubsup><msub><mi>p</mi><mi>i</mi></msub><mi>H</mi><mo>(</mo><mi>Y</mi><mi mathvariant="normal">&#x2223;</mi><mi>X</mi><mo>=</mo><msub><mi>x</mi><mi>i</mi></msub><mo>)</mo></mrow><annotation encoding="application/x-tex">H(Y|X)=\sum^n_{i=1}p_iH(Y|X=x_i)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1.0500099999999999em;vertical-align:-0.30001em;"></span><span class="base textstyle uncramped"><span class="mord mat
<p><strong>&#x5F53;&#x7136;&#x6761;&#x4EF6;&#x71B5;&#x7684;&#x4E00;&#x4E2A;&#x6027;&#x8D28;&#x4E5F;&#x71B5;&#x7684;&#x6027;&#x8D28;&#x4E00;&#x6837;&#xFF0C;&#x6211;&#x6982;&#x7387;&#x8D8A;&#x786E;&#x5B9A;&#xFF0C;&#x6761;&#x4EF6;&#x71B5;&#x5C31;&#x8D8A;&#x5C0F;&#xFF0C;&#x6982;&#x7387;&#x8D8A;&#x4E94;&#x4E94;&#x5F00;&#xFF0C;&#x6761;&#x4EF6;&#x71B5;&#x5C31;&#x8D8A;&#x5927;</strong>&#x3002;</p>
<p>OK&#xFF0C;&#x73B0;&#x5728;&#x5DF2;&#x7ECF;&#x77E5;&#x9053;&#x4E86;&#x4EC0;&#x4E48;&#x662F;&#x71B5;&#xFF0C;&#x4EC0;&#x4E48;&#x662F;&#x6761;&#x4EF6;&#x71B5;&#x3002;&#x63A5;&#x4E0B;&#x6765;&#x5C31;&#x53EF;&#x4EE5;&#x770B;&#x770B;&#x4EC0;&#x4E48;&#x662F;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x4E86;&#x3002;&#x6240;&#x8C13;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x5C31;&#x662F;&#x8868;&#x793A;&#x6211;&#x5DF2;&#x77E5;&#x6761;&#x4EF6; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>X</mi></mrow><annotation encoding="application/x-tex">X</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.07847em;">X</span></span></span></span> &#x540E;&#x80FD;&#x5F97;&#x5230;&#x4FE1;&#x606F; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>Y</mi></mrow><annotation encoding="application/x-tex">Y</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.22222em;">Y</span></span></span></span> &#x7684;&#x4E0D;&#x786E;&#x5B9A;&#x6027;&#x7684;&#x51CF;&#x5C11;&#x7A0B;&#x5EA6;&#x3002;&#x5C31;&#x597D;&#x6BD4;&#xFF0C;&#x6211;&#x5728;&#x73A9;&#x8BFB;&#x5FC3;&#x672F;&#x3002;&#x60A8;&#x5FC3;&#x91CC;&#x60F3;&#x4E00;&#x4EF6;&#x4E1C;&#x897F;&#xFF0C;&#x6211;&#x6765;&#x731C;&#x3002;&#x6211;&#x5DF2;&#x5F00;&#x59CB;&#x4EC0;&#x4E48;&#x90FD;&#x6CA1;&#x95EE;&#x4F60;&#xFF0C;&#x6211;&#x8981;&#x731C;&#x7684;&#x8BDD;&#xFF0C;&#x80AF;&#x5B9A;&#x662F;&#x778E;&#x731C;&#x3002;&#x8FD9;&#x4E2A;&#x65F6;&#x5019;&#x6211;&#x7684;&#x71B5;&#x5C31;&#x975E;&#x5E38;&#x9AD8;&#x5BF9;&#x4E0D;&#x5BF9;&#x3002;&#x7136;&#x540E;&#x6211;&#x63A5;&#x4E0B;&#x6765;&#x6211;&#x4F1A;&#x53BB;&#x8BD5;&#x7740;&#x95EE;&#x4F60;&#x662F;&#x975E;&#x9898;&#xFF0C;&#x5F53;&#x6211;&#x95EE;&#x4E86;&#x662F;&#x975E;&#x9898;&#x4E4B;&#x540E;&#xFF0C;&#x6211;&#x5C31;&#x80FD;&#x51CF;&#x5C0F;&#x731C;&#x6D4B;&#x4F60;&#x5FC3;&#x4E2D;&#x60F3;&#x5230;&#x7684;&#x4E1C;&#x897F;&#x7684;&#x8303;&#x56F4;&#xFF0C;&#x8FD9;&#x6837;&#x5176;&#x5B9E;&#x5C31;&#x662F;&#x51CF;&#x5C0F;&#x4E86;&#x6211;&#x7684;&#x71B5;&#x3002;&#x90A3;&#x4E48;&#x6211;&#x71B5;&#x7684;&#x51CF;&#x5C0F;&#x7A0B;&#x5EA6;&#x5C31;&#x662F;&#x6211;&#x7684;<strong>&#x4FE1;&#x606F;&#x589E;&#x76CA;</strong>&#x3002;</p>
<p>&#x6240;&#x4EE5;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x5982;&#x679C;&#x5957;&#x4E0A;&#x673A;&#x5668;&#x5B66;&#x4E60;&#x7684;&#x8BDD;&#x5C31;&#x662F;&#xFF0C;&#x5982;&#x679C;&#x628A;&#x7279;&#x5F81; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>A</mi></mrow><annotation encoding="application/x-tex">A</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit">A</span></span></span></span> &#x5BF9;&#x8BAD;&#x7EC3;&#x96C6; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span> &#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x8BB0;&#x4E3A; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mo>(</mo><mi>D</mi><mo separator="true">,</mo><mi>A</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(D, A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mord mathit">A</span><span class="mclose">)</span></span></span></span> &#x7684;&#x8BDD;&#xFF0C;&#x90A3;&#x4E48; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mo>(</mo><mi>D</mi><mo separator="true">,</mo><mi>A</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(D, A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mord mathit">A</span><span class="mclose">)</span></span></span></span> &#x7684;&#x8BA1;&#x7B97;&#x516C;&#x5F0F;&#x5C31;&#x662F;&#xFF1A;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>g</mi><mo>(</mo><mi>D</mi><mo separator="true">,</mo><mi>A</mi><mo>)</mo><mo>=</mo><mi>H</mi><mo>(</mo><mi>D</mi><mo>)</mo><mo>&#x2212;</mo><mi>H</mi><mo>(</mo><mi>D</mi><mi mathvariant="normal">&#x2223;</mi><mi>A</mi><mo>)</mo></mrow><annotation encoding="application/x-tex">g(D,A)=H(D)-H(D|A)</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.03588em;">g</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mpunct">,</span><span class="mord mathit">A</span><span class="mclose">)</span><span class="mrel">=</span><span class="mord mathit" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mclose">)</span><span class="mbin">&#x2212;</span><span class="mord mathit" style="margin-right:0.08125em;">H</span><span class="mopen">(</span><span class="mord mathit" style="margin-right:0.02778em;">D</span><span class="mord mathrm">&#x2223;</span><span class="mord mathit
<p>&#x5982;&#x679C;&#x770B;&#x5230;&#x8FD9;&#x4E00;&#x5806;&#x516C;&#x5F0F;&#x53EF;&#x80FD;&#x4F1A;&#x61F5;&#x903C;&#xFF0C;&#x90A3;&#x4E0D;&#x5982;&#x4E3E;&#x4E2A;&#x6817;&#x5B50;&#x6765;&#x770B;&#x770B;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x600E;&#x4E48;&#x7B97;&#x3002;&#x5047;&#x8BBE;&#x6211;&#x73B0;&#x5728;&#x6709;&#x8FD9;&#x4E00;&#x4E2A;&#x6570;&#x636E;&#x8868;&#xFF0C;&#x7B2C;&#x4E00;&#x5217;&#x662F;&#x6027;&#x522B;&#xFF0C;&#x7B2C;&#x4E8C;&#x5217;&#x662F;&#x6D3B;&#x8DC3;&#x5EA6;&#xFF0C; &#x7B2C;&#x4E09;&#x5217;&#x662F;&#x5BA2;&#x6237;&#x662F;&#x5426;&#x6D41;&#x5931;&#x7684; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>l</mi><mi>a</mi><mi>b</mi><mi>e</mi><mi>l</mi></mrow><annotation encoding="application/x-tex">label</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">a</span><span class="mord mathit">b</span><span class="mord mathit">e</span><span class="mord mathit" style="margin-right:0.01968em;">l</span></span></span></span>&#x3002;</p>
<p><img src="img/22.jpg" alt=""></p>
<p>&#x90A3;&#x5982;&#x679C;&#x6211;&#x8981;&#x7B97;&#x6027;&#x522B;&#x548C;&#x6D3B;&#x8DC3;&#x5EA6;&#x8FD9;&#x4E24;&#x4E2A;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x7684;&#x8BDD;&#xFF0C;&#x9996;&#x5148;&#x8981;&#x5148;&#x7B97;&#x603B;&#x7684;&#x71B5;&#x548C;&#x6761;&#x4EF6;&#x71B5;&#x3002;( <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn><mi mathvariant="normal">/</mi><mn>1</mn><mn>5</mn></mrow><annotation encoding="application/x-tex">5/15</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">5</span><span class="mord mathrm">/</span><span class="mord mathrm">1</span><span class="mord mathrm">5</span></span></span></span> &#x7684;&#x610F;&#x601D;&#x662F;&#x603B;&#x5171;&#x6709; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn><mn>5</mn></mrow><annotation encoding="application/x-tex">15</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span><span class="mord mathrm">5</span></span></span></span> &#x6761;&#x6837;&#x672C;&#x91CC;&#x9762; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>l</mi><mi>a</mi><mi>b</mi><mi>e</mi><mi>l</mi></mrow><annotation encoding="application/x-tex">label</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.69444em;"></span><span class="strut bottom" style="height:0.69444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.01968em;">l</span><span class="mord mathit">a</span><span class="mord mathit">b</span><span class="mord mathit">e</span><span class="mord mathit" style="margin-right:0.01968em;">l</span></span></span></span> &#x4E3A; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span></span></span></span> &#x7684;&#x6837;&#x672C;&#x6709; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">5</span></span></span></span> &#x6761;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>3</mn><mi mathvariant="normal">/</mi><mn>8</mn></mrow><annotation encoding="application/x-tex">3/8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.75em;"></span><span class="strut bottom" style="height:1em;vertical-align:-0.25em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">3</span><span class="mord mathrm">/</span><span class="mord mathrm">8</span></span></span></span> &#x7684;&#x610F;&#x601D;&#x662F;&#x6027;&#x522B;&#x4E3A;&#x7537;&#x7684;&#x6837;&#x672C;&#x6709; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>8</mn></mrow><annotation encoding="application/x-tex">8</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span cla
<p>&#x603B;&#x71B5;= (-5/15)<em>log(5/15)-(10/15)</em>log(10/15)=0.9182</p>
<p>&#x6027;&#x522B;&#x4E3A;&#x7537;&#x7684;&#x71B5;= -(3/8)<em>log(3/8)-(5/8)</em>log(5/8)=0.9543</p>
<p>&#x6027;&#x522B;&#x4E3A;&#x5973;&#x7684;&#x71B5;= -(2/7)<em>log(2/7)-(5/7)</em>log(5/7)=0.8631</p>
<p>&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4F4E;&#x7684;&#x71B5;= -(4/4)*log(4/4)-0=0</p>
<p>&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4E2D;&#x7684;&#x71B5;= -(1/5)<em>log(1/5)-(4/5)</em>log(4/5)=0.7219</p>
<p>&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x9AD8;&#x7684;&#x71B5;= -0-(6/6)*log(6/6)=0</p>
<p>&#x73B0;&#x5728;&#x6709;&#x4E86;&#x603B;&#x7684;&#x71B5;&#x548C;&#x6761;&#x4EF6;&#x71B5;&#x4E4B;&#x540E;&#x6211;&#x4EEC;&#x5C31;&#x80FD;&#x7B97;&#x51FA;&#x6027;&#x522B;&#x548C;&#x6D3B;&#x8DC3;&#x5EA6;&#x8FD9;&#x4E24;&#x4E2A;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x4E86;&#x3002;</p>
<p>&#x6027;&#x522B;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;=&#x603B;&#x7684;&#x71B5;-(8/15)<em>&#x6027;&#x522B;&#x4E3A;&#x7537;&#x7684;&#x71B5;-(7/15)</em>&#x6027;&#x522B;&#x4E3A;&#x5973;&#x7684;&#x71B5;=0.0064</p>
<p>&#x6D3B;&#x8DC3;&#x5EA6;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;=&#x603B;&#x7684;&#x71B5;-(6/15)<em>&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x9AD8;&#x7684;&#x71B5;-(5/15)</em>&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4E2D;&#x7684;&#x71B5;-(4/15)*&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4F4E;&#x7684;&#x71B5;=0.6776</p>
<p>&#x90A3;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x7B97;&#x51FA;&#x6765;&#x4E4B;&#x540E;&#x6709;&#x4EC0;&#x4E48;&#x610F;&#x4E49;&#x5462;&#xFF1F;&#x56DE;&#x5230;&#x8BFB;&#x5FC3;&#x672F;&#x7684;&#x95EE;&#x9898;&#xFF0C;&#x4E3A;&#x4E86;&#x6211;&#x80FD;&#x66F4;&#x52A0;&#x51C6;&#x786E;&#x7684;&#x731C;&#x51FA;&#x4F60;&#x5FC3;&#x4E2D;&#x6240;&#x60F3;&#xFF0C;&#x6211;&#x80AF;&#x5B9A;&#x662F;&#x95EE;&#x7684;&#x95EE;&#x9898;&#x8D8A;&#x597D;&#x5C31;&#x80FD;&#x731C;&#x5F97;&#x8D8A;&#x51C6;&#xFF01;&#x6362;&#x53E5;&#x8BDD;&#x6765;&#x8BF4;&#x6211;&#x80AF;&#x5B9A;&#x662F;&#x8981;&#x60F3;&#x51FA;&#x4E00;&#x4E2A;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6700;&#x5927;&#x7684;&#x95EE;&#x9898;&#x6765;&#x95EE;&#x4F60;&#xFF0C;&#x5BF9;&#x4E0D;&#x5BF9;&#xFF1F;&#x5176;&#x5B9E;<strong>ID3&#x7B97;&#x6CD5;</strong>&#x4E5F;&#x662F;&#x8FD9;&#x4E48;&#x60F3;&#x7684;&#x3002;<strong>ID3&#x7B97;&#x6CD5;</strong>&#x7684;&#x601D;&#x60F3;&#x662F;&#x4ECE;&#x8BAD;&#x7EC3;&#x96C6; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mi>D</mi></mrow><annotation encoding="application/x-tex">D</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.68333em;"></span><span class="strut bottom" style="height:0.68333em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathit" style="margin-right:0.02778em;">D</span></span></span></span> &#x4E2D;&#x8BA1;&#x7B97;&#x6BCF;&#x4E2A;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#xFF0C;&#x7136;&#x540E;&#x770B;&#x54EA;&#x4E2A;&#x6700;&#x5927;&#x5C31;&#x9009;&#x54EA;&#x4E2A;&#x4F5C;&#x4E3A;&#x5F53;&#x524D;&#x8282;&#x70B9;&#x3002;&#x7136;&#x540E;&#x7EE7;&#x7EED;&#x91CD;&#x590D;&#x521A;&#x521A;&#x7684;&#x6B65;&#x9AA4;&#x6765;&#x6784;&#x5EFA;&#x51B3;&#x7B56;&#x6811;&#x3002;</p>
<h3 id="&#x51B3;&#x7B56;&#x6811;&#x6784;&#x6D41;&#x7A0B;">&#x51B3;&#x7B56;&#x6811;&#x6784;&#x6D41;&#x7A0B;</h3>
<p><strong>ID3&#x7B97;&#x6CD5;</strong>&#x5176;&#x5B9E;&#x5C31;&#x662F;&#x4F9D;&#x636E;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6765;&#x6784;&#x5EFA;&#x6811;&#x7684;&#x3002;&#x5177;&#x4F53;&#x5957;&#x8DEF;&#x5C31;&#x662F;&#x4ECE;&#x6839;&#x8282;&#x70B9;&#x5F00;&#x59CB;&#xFF0C;&#x5BF9;&#x8282;&#x70B9;&#x8BA1;&#x7B97;&#x6240;&#x6709;&#x53EF;&#x80FD;&#x7684;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#xFF0C;&#x7136;&#x540E;&#x9009;&#x62E9;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6700;&#x5927;&#x7684;&#x7279;&#x5F81;&#x4F5C;&#x4E3A;&#x8282;&#x70B9;&#x7684;&#x7279;&#x5F81;&#xFF0C;&#x7531;&#x8BE5;&#x7279;&#x5F81;&#x7684;&#x4E0D;&#x540C;&#x53D6;&#x503C;&#x5EFA;&#x7ACB;&#x5B50;&#x8282;&#x70B9;&#xFF0C;&#x7136;&#x540E;&#x5BF9;&#x5B50;&#x8282;&#x70B9;&#x9012;&#x5F52;&#x6267;&#x884C;&#x4E0A;&#x9762;&#x7684;&#x5957;&#x8DEF;&#x76F4;&#x5230;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x5F88;&#x5C0F;&#x6216;&#x8005;&#x6CA1;&#x6709;&#x7279;&#x5F81;&#x53EF;&#x4EE5;&#x7EE7;&#x7EED;&#x9009;&#x62E9;&#x4E3A;&#x6B62;&#x3002;</p>
<p>&#x8FD9;&#x6837;&#x770B;&#x4E0A;&#x53BB;&#x53EF;&#x80FD;&#x4F1A;&#x61F5;&#xFF0C;&#x4E0D;&#x5982;&#x7528;&#x521A;&#x521A;&#x7684;&#x6570;&#x636E;&#x6765;&#x6784;&#x5EFA;&#x4E00;&#x9897;&#x51B3;&#x7B56;&#x6811;&#x3002;</p>
<p>&#x4E00;&#x5F00;&#x59CB;&#x6211;&#x4EEC;&#x5DF2;&#x7ECF;&#x7B97;&#x8FC7;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6700;&#x5927;&#x7684;&#x662F;&#x6D3B;&#x8DC3;&#x5EA6;&#xFF0C;&#x6240;&#x4EE5;&#x51B3;&#x7B56;&#x6811;&#x7684;&#x6839;&#x8282;&#x70B9;&#x662F;&#x6D3B;&#x8DC3;&#x5EA6; &#x3002;&#x6240;&#x4EE5;&#x8FD9;&#x4E2A;&#x65F6;&#x5019;&#x6811;&#x662F;&#x8FD9;&#x6837;&#x7684;&#xFF1A;</p>
<p><img src="img/23.jpg" alt=""></p>
<p>&#x7136;&#x540E;&#x53D1;&#x73B0;&#x8BAD;&#x7EC3;&#x96C6;&#x4E2D;&#x7684;&#x6570;&#x636E;&#x8868;&#x793A;&#x5F53;&#x6211;&#x6D3B;&#x8DC3;&#x5EA6;&#x4F4E;&#x7684;&#x65F6;&#x5019;&#x4E00;&#x5B9A;&#x4F1A;&#x6D41;&#x5931;&#xFF0C;&#x6D3B;&#x8DC3;&#x5EA6;&#x9AD8;&#x7684;&#x65F6;&#x5019;&#x4E00;&#x5B9A;&#x4E0D;&#x6D41;&#x5931;&#xFF0C;&#x6240;&#x4EE5;&#x53EF;&#x4EE5;&#x5148;&#x5728;&#x6839;&#x8282;&#x70B9;&#x4E0A;&#x63A5;&#x4E0A;&#x4E24;&#x4E2A;&#x53F6;&#x5B50;&#x8282;&#x70B9;&#x3002;</p>
<p><img src="img/24.jpg" alt=""></p>
<p>&#x4F46;&#x662F;&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4E2D;&#x7684;&#x65F6;&#x5019;&#x5C31;&#x4E0D;&#x4E00;&#x5B9A;&#x6D41;&#x5931;&#x4E86;&#xFF0C;&#x6240;&#x4EE5;&#x8FD9;&#x4E2A;&#x65F6;&#x5019;&#x5C31;&#x53EF;&#x4EE5;&#x628A;&#x6D3B;&#x8DC3;&#x5EA6;&#x4E3A;&#x4F4E;&#x548C;&#x4E3A;&#x9AD8;&#x7684;&#x6570;&#x636E;&#x5C4F;&#x853D;&#x6389;&#xFF0C;&#x5C4F;&#x853D;&#x6389;&#x4E4B;&#x540E; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">5</span></span></span></span> &#x6761;&#x6570;&#x636E;&#xFF0C;&#x63A5;&#x7740;&#x628A;&#x8FD9; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>5</mn></mrow><annotation encoding="application/x-tex">5</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">5</span></span></span></span> &#x6761;&#x6570;&#x636E;&#x5F53;&#x6210;&#x8BAD;&#x7EC3;&#x96C6;&#x6765;&#x7EE7;&#x7EED;&#x7B97;&#x54EA;&#x4E2A;&#x7279;&#x5F81;&#x7684;&#x4FE1;&#x606F;&#x589E;&#x76CA;&#x6700;&#x9AD8;&#xFF0C;&#x5F88;&#x660E;&#x663E;&#x7B97;&#x5B8C;&#x4E4B;&#x540E;&#x662F;&#x6027;&#x522B;&#x8FD9;&#x4E2A;&#x7279;&#x5F81;&#xFF0C;&#x6240;&#x4EE5;&#x8FD9;&#x65F6;&#x5019;&#x6811;&#x53D8;&#x6210;&#x4E86;&#x8FD9;&#x6837;&#xFF1A;</p>
<p><img src="img/25.jpg" alt=""></p>
<p>&#x8FD9;&#x65F6;&#x5019;&#x5462;&#xFF0C;&#x6570;&#x636E;&#x96C6;&#x91CC;&#x6CA1;&#x6709;&#x5176;&#x4ED6;&#x7279;&#x5F81;&#x53EF;&#x4EE5;&#x9009;&#x62E9;&#x4E86;&#xFF08;&#x603B;&#x5171;&#x5C31;&#x4E24;&#x4E2A;&#x7279;&#x5F81;&#xFF0C;&#x6D3B;&#x8DC3;&#x5EA6;&#x5DF2;&#x7ECF;&#x662F;&#x6839;&#x8282;&#x70B9;&#x4E86;&#xFF09;&#xFF0C;&#x6240;&#x4EE5;&#x5C31;&#x770B;&#x6211;&#x6027;&#x522B;&#x662F;&#x7537;&#x6216;&#x5973;&#x7684;&#x65F6;&#x5019;&#x90A3;&#x79CD;&#x60C5;&#x51B5;&#x6700;&#x6709;&#x53EF;&#x80FD;&#x51FA;&#x73B0;&#x4E86;&#x3002;&#x6B64;&#x65F6;&#x6027;&#x522B;&#x4E3A;&#x7537;&#x7684;&#x7528;&#x6237;&#x4E2D;&#x6709; <span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span></span></span></span> &#x4E2A;&#x662F;&#x6D41;&#x5931;&#xFF0C;<span class="katex"><span class="katex-mathml"><math><semantics><mrow><mn>1</mn></mrow><annotation encoding="application/x-tex">1</annotation></semantics></math></span><span class="katex-html" aria-hidden="true"><span class="strut" style="height:0.64444em;"></span><span class="strut bottom" style="height:0.64444em;vertical-align:0em;"></span><span class="base textstyle uncramped"><span class="mord mathrm">1</span></span></span></span> &#x4E2A;&#x662F;&#x4E0D;&#x6D41;&#x5931;&#xFF0C;&#x4E94;&#x4E94;&#x5F00;&#x3002;&#x6240;&#x4EE5;&#x53EF;&#x4EE5;&#x8003;&#x8651;&#x968F;&#x673A;&#x9009;&#x4E2A;&#x7ED3;&#x679C;&#x5F53;&#x8F93;&#x51FA;&#x4E86;&#x3002;&#x6027;&#x522B;&#x4E3A;&#x5973;&#x7684;&#x7528;&#x6237;&#x4E2D;&#x6709;&#x5168;&#x90E8;&#x90FD;&#x6D41;&#x5931;&#xFF0C;&#x6240;&#x4EE5;&#x6027;&#x522B;&#x4E3A;&#x5973;&#x65F6;&#x8F93;&#x51FA;&#x662F;&#x6D41;&#x5931;&#x3002;&#x6240;&#x4EE5;&#x5462;&#xFF0C;&#x6811;&#x5C31;&#x6210;&#x4E86;&#x8FD9;&#x6837;&#xFF1A;</p>
<p><img src="img/26.jpg" alt=""></p>
<p>&#x597D;&#x4E86;&#xFF0C;&#x51B3;&#x7B56;&#x6811;&#x6784;&#x9020;&#x597D;&#x4E86;&#x3002;&#x4ECE;&#x56FE;&#x53EF;&#x4EE5;&#x770B;&#x51FA;&#x51B3;&#x7B56;&#x6811;&#x6709;&#x4E00;&#x4E2A;&#x975E;&#x5E38;&#x597D;&#x7684;&#x5730;&#x65B9;&#x5C31;&#x662F;&#x6A21;&#x578B;&#x7684;&#x89E3;&#x91CA;&#x6027;&#x975E;&#x5E38;&#x5F3A;&#xFF01;&#xFF01;&#x5F88;&#x660E;&#x663E;&#xFF0C;&#x5982;&#x679C;&#x73B0;&#x5728;&#x6765;&#x4E86;&#x4E00;&#x6761;&#x6570;&#x636E;(&#x7537;, &#x9AD8;)&#x7684;&#x8BDD;&#xFF0C;&#x8F93;&#x51FA;&#x4F1A;&#x662F;&#x4E0D;&#x6D41;&#x5931;&#x3002;</p>
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