From e0e54c2d02b9bb891929c4847e58ed3b0fa91d59 Mon Sep 17 00:00:00 2001
From: shataowei <taowei.sha@ymm56.com>
Date: Wed, 20 Nov 2019 18:57:15 +0800
Subject: [PATCH] =?UTF-8?q?gbdt=E9=83=A8=E5=88=86?=
MIME-Version: 1.0
Content-Type: text/plain; charset=UTF-8
Content-Transfer-Encoding: 8bit

---
 .idea/workspace.xml                           | 68 ++++++++++++-------
 .../GBDT.md"                                  |  6 +-
 2 files changed, 48 insertions(+), 26 deletions(-)

diff --git a/.idea/workspace.xml b/.idea/workspace.xml
index 579f66b..3023173 100644
--- a/.idea/workspace.xml
+++ b/.idea/workspace.xml
@@ -2,9 +2,7 @@
 <project version="4">
   <component name="ChangeListManager">
     <list default="true" id="be5bf74e-ad1c-4197-8a1f-ac93566d8aa7" name="Default" comment="init">
-      <change type="NEW" beforePath="" afterPath="$PROJECT_DIR$/机器学习/集成学习/Xgboost.md" />
-      <change type="MODIFICATION" beforePath="$PROJECT_DIR$/.idea/workspace.xml" afterPath="$PROJECT_DIR$/.idea/workspace.xml" />
-      <change type="MODIFICATION" beforePath="$PROJECT_DIR$/README.md" afterPath="$PROJECT_DIR$/README.md" />
+      <change type="MODIFICATION" beforePath="$PROJECT_DIR$/机器学习/集成学习/GBDT.md" afterPath="$PROJECT_DIR$/机器学习/集成学习/GBDT.md" />
     </list>
     <ignored path="Reflection_Summary.iws" />
     <ignored path=".idea/workspace.xml" />
@@ -25,7 +23,7 @@
   </component>
   <component name="FileEditorManager">
     <leaf SIDE_TABS_SIZE_LIMIT_KEY="300">
-      <file leaf-file-name="README.md" pinned="false" current-in-tab="true">
+      <file leaf-file-name="README.md" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/README.md">
           <provider editor-type-id="split-provider[text-editor;markdown-preview-editor]">
             <state split_layout="SPLIT">
@@ -49,6 +47,30 @@
           </provider>
         </entry>
       </file>
+      <file leaf-file-name="GBDT.md" pinned="false" current-in-tab="true">
+        <entry file="file://$PROJECT_DIR$/机器学习/集成学习/GBDT.md">
+          <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
+            <state split_layout="SPLIT">
+              <first_editor relative-caret-position="720">
+                <caret line="62" column="10" selection-start-line="62" selection-start-column="10" selection-end-line="62" selection-end-column="10" />
+                <folding />
+              </first_editor>
+              <second_editor />
+            </state>
+          </provider>
+          <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
+            <state split_layout="SPLIT">
+              <first_editor relative-caret-position="0">
+                <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+                <folding />
+              </first_editor>
+              <second_editor>
+                <js_state />
+              </second_editor>
+            </state>
+          </provider>
+        </entry>
+      </file>
       <file leaf-file-name="Xgboost.md" pinned="false" current-in-tab="false">
         <entry file="file://$PROJECT_DIR$/机器学习/集成学习/Xgboost.md">
           <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
@@ -115,9 +137,9 @@
         <option value="$PROJECT_DIR$/机器学习/逻辑回归/lr.md" />
         <option value="$PROJECT_DIR$/机器学习/支持向量机/支持向量机.md" />
         <option value="$PROJECT_DIR$/数据预处理/特征提取/数据变换.md" />
-        <option value="$PROJECT_DIR$/机器学习/集成学习/GBDT.md" />
         <option value="$PROJECT_DIR$/机器学习/集成学习/Xgboost.md" />
         <option value="$PROJECT_DIR$/README.md" />
+        <option value="$PROJECT_DIR$/机器学习/集成学习/GBDT.md" />
       </list>
     </option>
   </component>
@@ -531,7 +553,7 @@
     <frame x="0" y="23" width="1440" height="823" extended-state="0" />
     <editor active="true" />
     <layout>
-      <window_info id="Project" active="false" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.23462088" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
+      <window_info id="Project" active="true" anchor="left" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="true" show_stripe_button="true" weight="0.23462088" sideWeight="0.5" order="0" side_tool="false" content_ui="combo" />
       <window_info id="TODO" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="6" side_tool="false" content_ui="tabs" />
       <window_info id="Event Log" active="false" anchor="bottom" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="7" side_tool="true" content_ui="tabs" />
       <window_info id="Database" active="false" anchor="right" auto_hide="false" internal_type="DOCKED" type="DOCKED" visible="false" show_stripe_button="true" weight="0.33" sideWeight="0.5" order="3" side_tool="false" content_ui="tabs" />
@@ -1387,11 +1409,11 @@
         </state>
       </provider>
     </entry>
-    <entry file="file://$PROJECT_DIR$/机器学习/集成学习/GBDT.md">
+    <entry file="file://$PROJECT_DIR$/机器学习/集成学习/Xgboost.md">
       <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="1095">
-            <caret line="73" column="0" selection-start-line="73" selection-start-column="0" selection-end-line="73" selection-end-column="0" />
+          <first_editor relative-caret-position="495">
+            <caret line="38" column="23" selection-start-line="38" selection-start-column="2" selection-end-line="38" selection-end-column="23" />
             <folding />
           </first_editor>
           <second_editor />
@@ -1409,20 +1431,20 @@
         </state>
       </provider>
     </entry>
-    <entry file="file://$PROJECT_DIR$/机器学习/集成学习/Xgboost.md">
-      <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
+    <entry file="file://$PROJECT_DIR$/README.md">
+      <provider editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="495">
-            <caret line="38" column="23" selection-start-line="38" selection-start-column="2" selection-end-line="38" selection-end-column="23" />
+          <first_editor relative-caret-position="0">
+            <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
             <folding />
           </first_editor>
           <second_editor />
         </state>
       </provider>
-      <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
+      <provider selected="true" editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="0">
-            <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <first_editor relative-caret-position="415">
+            <caret line="239" column="28" selection-start-line="239" selection-start-column="28" selection-end-line="239" selection-end-column="28" />
             <folding />
           </first_editor>
           <second_editor>
@@ -1431,20 +1453,20 @@
         </state>
       </provider>
     </entry>
-    <entry file="file://$PROJECT_DIR$/README.md">
-      <provider editor-type-id="split-provider[text-editor;markdown-preview-editor]">
+    <entry file="file://$PROJECT_DIR$/机器学习/集成学习/GBDT.md">
+      <provider selected="true" editor-type-id="split-provider[text-editor;markdown-preview-editor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="0">
-            <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
+          <first_editor relative-caret-position="720">
+            <caret line="62" column="10" selection-start-line="62" selection-start-column="10" selection-end-line="62" selection-end-column="10" />
             <folding />
           </first_editor>
           <second_editor />
         </state>
       </provider>
-      <provider selected="true" editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
+      <provider editor-type-id="split-provider[text-editor;MarkdownPreviewEditor]">
         <state split_layout="SPLIT">
-          <first_editor relative-caret-position="415">
-            <caret line="239" column="28" selection-start-line="239" selection-start-column="28" selection-end-line="239" selection-end-column="28" />
+          <first_editor relative-caret-position="0">
+            <caret line="0" column="0" selection-start-line="0" selection-start-column="0" selection-end-line="0" selection-end-column="0" />
             <folding />
           </first_editor>
           <second_editor>
diff --git "a/\346\234\272\345\231\250\345\255\246\344\271\240/\351\233\206\346\210\220\345\255\246\344\271\240/GBDT.md" "b/\346\234\272\345\231\250\345\255\246\344\271\240/\351\233\206\346\210\220\345\255\246\344\271\240/GBDT.md"
index a305700..7d89fde 100644
--- "a/\346\234\272\345\231\250\345\255\246\344\271\240/\351\233\206\346\210\220\345\255\246\344\271\240/GBDT.md"
+++ "b/\346\234\272\345\231\250\345\255\246\344\271\240/\351\233\206\346\210\220\345\255\246\344\271\240/GBDT.md"
@@ -45,7 +45,7 @@ Cart tree，但是都是回归树
 
 当loss函数为均方误差![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94ajgymkuj303w011jr6.jpg)，gbdt中的残差的负梯度的结果y-H(x)正好与boostingtree的拟合残差一致
 
-# 如何用残差的负梯度实现gbdt？
+# 如何用损失函数的负梯度实现gbdt？
 - 利用![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94afa5h1lj3060017mx0.jpg)可以计算得到x对应的损失函数的负梯度![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94ars964uj301h00ijr5.jpg),据此我们可以构造出第t棵回归树，其对应的叶子结点区域![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94atb0k7zj300p00i3y9.jpg)j为叶子结点位置
 - 构建回归树的过程中，需要考虑找到特征A中最合适的切分点，使得切分后的数据集D1和D2的均方误差最小![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94b0klia2j30ee017aa0.jpg)
 - 针对每一个叶子节点里的样本，我们求出使损失函数最小，也就是拟合叶子节点最好的输出值𝑐𝑡𝑗,![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94b5ffnyoj308g0173yd.jpg)
@@ -54,13 +54,13 @@ Cart tree，但是都是回归树
     - 这样就完整的构造出一棵树：![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94bfr5cn5j303d01kjr6.jpg)
 - 本轮最终得到的强学习器的表达式如下：![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94binx5prj307o01k0sl.jpg)
 
-# 拟合残差的负梯度为什么是可行的？
+# 拟合损失函数的负梯度为什么是可行的？
 - 泰勒展开的一阶形式：![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94h6rkexqj305x00ijr7.jpg)
 - m轮树模型可以写成：![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94h8zovulj305v00iglf.jpg)
     - 对![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94hak9e26j303n00idfm.jpg)进行泰勒展开：![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94hd5sz8vj309400kglg.jpg),其中m-1轮对残差梯度为![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94hey2xksj3052017a9w.jpg)
 - 我们拟合了残差的负梯度，![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94hi3epnaj302r00kmwx.jpg),所以![](https://tva1.sinaimg.cn/large/006y8mN6gy1g94hd5sz8vj309400kglg.jpg)内会让损失向下降对方向前进
 
-# 即便拟合负梯度是可行的，为什么不直接拟合残差？ 拟合负梯度好在哪里？
+# 即便拟合损失函数负梯度是可行的，为什么不直接拟合残差？ 拟合负梯度好在哪里？
 - 前者不用残差的负梯度而是使用残差，是全局最优值，后者使用的是 局部最优方向（负梯度）*步长（𝛽）
 - 依赖残差进行优化，损失函数一般固定为反映残差的均方差损失函数，因此 当均方差损失函数失效（该损失函数对异常值敏感）的时候，换了其他一般的损失函数，便很难得到优化的结果。同时，因为损失函数的问题，Boosting Tree也很难处理回归之外问题。 而后者使用梯度下降的方法，对于任意可以求导的损失函数它都可以处理