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提交 ab99dede 编写于 作者: D dangqingqing
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.gitignore
浏览文件 @ ab99dede
pandoc.template
\ No newline at end of file
pandoc.template
.DS_Store
\ No newline at end of file
.pre-commit-config.yaml
浏览文件 @ ab99dede
......@@ -10,7 +10,6 @@
- repo: https://github.com/pre-commit/pre-commit-hooks
sha: 7539d8bd1a00a3c1bfd34cdb606d3a6372e83469
hooks:
- id: check-added-large-files
- id: check-merge-conflict
- id: check-symlinks
- id: detect-private-key
......
.tmpl/convert-markdown-into-html.sh 0 → 100755
浏览文件 @ ab99dede
markdown_file=$1
# Notice: the single-quotes around EOF below make outputs
# verbatium. c.f. http://stackoverflow.com/a/9870274/724872
cat <<'EOF'
<html>
<head>
<script type="text/x-mathjax-config">
MathJax.Hub.Config({
extensions: ["tex2jax.js", "TeX/AMSsymbols.js", "TeX/AMSmath.js"],
jax: ["input/TeX", "output/HTML-CSS"],
tex2jax: {
inlineMath: [ ['$','$'], ["\\(","\\)"] ],
displayMath: [ ['$$','$$'], ["\\[","\\]"] ],
processEscapes: true
},
"HTML-CSS": { availableFonts: ["TeX"] }
});
</script>
<script src="https://cdnjs.cloudflare.com/ajax/libs/mathjax/2.7.0/MathJax.js" async></script>
<script type="text/javascript" src="../.tmpl/marked.js">
</script>
<link href="http://cdn.bootcss.com/highlight.js/9.9.0/styles/darcula.min.css" rel="stylesheet">
<script src="http://cdn.bootcss.com/highlight.js/9.9.0/highlight.min.js"></script>
<link href="http://cdn.bootcss.com/bootstrap/4.0.0-alpha.6/css/bootstrap.min.css" rel="stylesheet">
<link href="https://cdn.jsdelivr.net/perfect-scrollbar/0.6.14/css/perfect-scrollbar.min.css" rel="stylesheet">
<link href="../.tmpl/github-markdown.css" rel='stylesheet'>
</head>
<style type="text/css" >
.markdown-body {
box-sizing: border-box;
min-width: 200px;
max-width: 980px;
margin: 0 auto;
padding: 45px;
}
</style>
<body>
<div id="context" class="container markdown-body">
</div>
<!-- This block will be replaced by each markdown file content. Please do not change lines below.-->
<div id="markdown" style='display:none'>
EOF
cat $markdown_file
cat <<'EOF'
</div>
<!-- You can change the lines below now. -->
<script type="text/javascript">
marked.setOptions({
renderer: new marked.Renderer(),
gfm: true,
breaks: false,
smartypants: true,
highlight: function(code, lang) {
code = code.replace(/&amp;/g, "&")
code = code.replace(/&gt;/g, ">")
code = code.replace(/&lt;/g, "<")
code = code.replace(/&nbsp;/g, " ")
return hljs.highlightAuto(code, [lang]).value;
}
});
document.getElementById("context").innerHTML = marked(
document.getElementById("markdown").innerHTML)
</script>
</body>
EOF
.tmpl/github-markdown.css 0 → 100644
浏览文件 @ ab99dede
@font-face {
font-family: octicons-link;
src: url(data:font/woff;charset=utf-8;base64,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) format('woff');
}
.markdown-body {
-ms-text-size-adjust: 100%;
-webkit-text-size-adjust: 100%;
line-height: 1.5;
color: #333;
font-family: -apple-system, BlinkMacSystemFont, "Segoe UI", Roboto, Helvetica, Arial, sans-serif, "Apple Color Emoji", "Segoe UI Emoji", "Segoe UI Symbol";
font-size: 16px;
line-height: 1.5;
word-wrap: break-word;
}
.markdown-body .pl-c {
color: #969896;
}
.markdown-body .pl-c1,
.markdown-body .pl-s .pl-v {
color: #0086b3;
}
.markdown-body .pl-e,
.markdown-body .pl-en {
color: #795da3;
}
.markdown-body .pl-smi,
.markdown-body .pl-s .pl-s1 {
color: #333;
}
.markdown-body .pl-ent {
color: #63a35c;
}
.markdown-body .pl-k {
color: #a71d5d;
}
.markdown-body .pl-s,
.markdown-body .pl-pds,
.markdown-body .pl-s .pl-pse .pl-s1,
.markdown-body .pl-sr,
.markdown-body .pl-sr .pl-cce,
.markdown-body .pl-sr .pl-sre,
.markdown-body .pl-sr .pl-sra {
color: #183691;
}
.markdown-body .pl-v {
color: #ed6a43;
}
.markdown-body .pl-id {
color: #b52a1d;
}
.markdown-body .pl-ii {
color: #f8f8f8;
background-color: #b52a1d;
}
.markdown-body .pl-sr .pl-cce {
font-weight: bold;
color: #63a35c;
}
.markdown-body .pl-ml {
color: #693a17;
}
.markdown-body .pl-mh,
.markdown-body .pl-mh .pl-en,
.markdown-body .pl-ms {
font-weight: bold;
color: #1d3e81;
}
.markdown-body .pl-mq {
color: #008080;
}
.markdown-body .pl-mi {
font-style: italic;
color: #333;
}
.markdown-body .pl-mb {
font-weight: bold;
color: #333;
}
.markdown-body .pl-md {
color: #bd2c00;
background-color: #ffecec;
}
.markdown-body .pl-mi1 {
color: #55a532;
background-color: #eaffea;
}
.markdown-body .pl-mdr {
font-weight: bold;
color: #795da3;
}
.markdown-body .pl-mo {
color: #1d3e81;
}
.markdown-body .octicon {
display: inline-block;
vertical-align: text-top;
fill: currentColor;
}
.markdown-body a {
background-color: transparent;
-webkit-text-decoration-skip: objects;
}
.markdown-body a:active,
.markdown-body a:hover {
outline-width: 0;
}
.markdown-body strong {
font-weight: inherit;
}
.markdown-body strong {
font-weight: bolder;
}
.markdown-body h1 {
font-size: 2em;
margin: 0.67em 0;
}
.markdown-body img {
border-style: none;
}
.markdown-body svg:not(:root) {
overflow: hidden;
}
.markdown-body code,
.markdown-body kbd,
.markdown-body pre {
font-family: monospace, monospace;
font-size: 1em;
}
.markdown-body hr {
box-sizing: content-box;
height: 0;
overflow: visible;
}
.markdown-body input {
font: inherit;
margin: 0;
}
.markdown-body input {
overflow: visible;
}
.markdown-body [type="checkbox"] {
box-sizing: border-box;
padding: 0;
}
.markdown-body * {
box-sizing: border-box;
}
.markdown-body input {
font-family: inherit;
font-size: inherit;
line-height: inherit;
}
.markdown-body a {
color: #4078c0;
text-decoration: none;
}
.markdown-body a:hover,
.markdown-body a:active {
text-decoration: underline;
}
.markdown-body strong {
font-weight: 600;
}
.markdown-body hr {
height: 0;
margin: 15px 0;
overflow: hidden;
background: transparent;
border: 0;
border-bottom: 1px solid #ddd;
}
.markdown-body hr::before {
display: table;
content: "";
}
.markdown-body hr::after {
display: table;
clear: both;
content: "";
}
.markdown-body table {
border-spacing: 0;
border-collapse: collapse;
}
.markdown-body td,
.markdown-body th {
padding: 0;
}
.markdown-body h1,
.markdown-body h2,
.markdown-body h3,
.markdown-body h4,
.markdown-body h5,
.markdown-body h6 {
margin-top: 0;
margin-bottom: 0;
}
.markdown-body h1 {
font-size: 32px;
font-weight: 600;
}
.markdown-body h2 {
font-size: 24px;
font-weight: 600;
}
.markdown-body h3 {
font-size: 20px;
font-weight: 600;
}
.markdown-body h4 {
font-size: 16px;
font-weight: 600;
}
.markdown-body h5 {
font-size: 14px;
font-weight: 600;
}
.markdown-body h6 {
font-size: 12px;
font-weight: 600;
}
.markdown-body p {
margin-top: 0;
margin-bottom: 10px;
}
.markdown-body blockquote {
margin: 0;
}
.markdown-body ul,
.markdown-body ol {
padding-left: 0;
margin-top: 0;
margin-bottom: 0;
}
.markdown-body ol ol,
.markdown-body ul ol {
list-style-type: lower-roman;
}
.markdown-body ul ul ol,
.markdown-body ul ol ol,
.markdown-body ol ul ol,
.markdown-body ol ol ol {
list-style-type: lower-alpha;
}
.markdown-body dd {
margin-left: 0;
}
.markdown-body code {
font-family: Consolas, "Liberation Mono", Menlo, Courier, monospace;
font-size: 12px;
}
.markdown-body pre {
margin-top: 0;
margin-bottom: 0;
font: 12px Consolas, "Liberation Mono", Menlo, Courier, monospace;
}
.markdown-body .octicon {
vertical-align: text-bottom;
}
.markdown-body input {
-webkit-font-feature-settings: "liga" 0;
font-feature-settings: "liga" 0;
}
.markdown-body::before {
display: table;
content: "";
}
.markdown-body::after {
display: table;
clear: both;
content: "";
}
.markdown-body>*:first-child {
margin-top: 0 !important;
}
.markdown-body>*:last-child {
margin-bottom: 0 !important;
}
.markdown-body a:not([href]) {
color: inherit;
text-decoration: none;
}
.markdown-body .anchor {
float: left;
padding-right: 4px;
margin-left: -20px;
line-height: 1;
}
.markdown-body .anchor:focus {
outline: none;
}
.markdown-body p,
.markdown-body blockquote,
.markdown-body ul,
.markdown-body ol,
.markdown-body dl,
.markdown-body table,
.markdown-body pre {
margin-top: 0;
margin-bottom: 16px;
}
.markdown-body hr {
height: 0.25em;
padding: 0;
margin: 24px 0;
background-color: #e7e7e7;
border: 0;
}
.markdown-body blockquote {
padding: 0 1em;
color: #777;
border-left: 0.25em solid #ddd;
}
.markdown-body blockquote>:first-child {
margin-top: 0;
}
.markdown-body blockquote>:last-child {
margin-bottom: 0;
}
.markdown-body kbd {
display: inline-block;
padding: 3px 5px;
font-size: 11px;
line-height: 10px;
color: #555;
vertical-align: middle;
background-color: #fcfcfc;
border: solid 1px #ccc;
border-bottom-color: #bbb;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #bbb;
}
.markdown-body h1,
.markdown-body h2,
.markdown-body h3,
.markdown-body h4,
.markdown-body h5,
.markdown-body h6 {
margin-top: 24px;
margin-bottom: 16px;
font-weight: 600;
line-height: 1.25;
}
.markdown-body h1 .octicon-link,
.markdown-body h2 .octicon-link,
.markdown-body h3 .octicon-link,
.markdown-body h4 .octicon-link,
.markdown-body h5 .octicon-link,
.markdown-body h6 .octicon-link {
color: #000;
vertical-align: middle;
visibility: hidden;
}
.markdown-body h1:hover .anchor,
.markdown-body h2:hover .anchor,
.markdown-body h3:hover .anchor,
.markdown-body h4:hover .anchor,
.markdown-body h5:hover .anchor,
.markdown-body h6:hover .anchor {
text-decoration: none;
}
.markdown-body h1:hover .anchor .octicon-link,
.markdown-body h2:hover .anchor .octicon-link,
.markdown-body h3:hover .anchor .octicon-link,
.markdown-body h4:hover .anchor .octicon-link,
.markdown-body h5:hover .anchor .octicon-link,
.markdown-body h6:hover .anchor .octicon-link {
visibility: visible;
}
.markdown-body h1 {
padding-bottom: 0.3em;
font-size: 2em;
border-bottom: 1px solid #eee;
}
.markdown-body h2 {
padding-bottom: 0.3em;
font-size: 1.5em;
border-bottom: 1px solid #eee;
}
.markdown-body h3 {
font-size: 1.25em;
}
.markdown-body h4 {
font-size: 1em;
}
.markdown-body h5 {
font-size: 0.875em;
}
.markdown-body h6 {
font-size: 0.85em;
color: #777;
}
.markdown-body ul,
.markdown-body ol {
padding-left: 2em;
}
.markdown-body ul ul,
.markdown-body ul ol,
.markdown-body ol ol,
.markdown-body ol ul {
margin-top: 0;
margin-bottom: 0;
}
.markdown-body li>p {
margin-top: 16px;
}
.markdown-body li+li {
margin-top: 0.25em;
}
.markdown-body dl {
padding: 0;
}
.markdown-body dl dt {
padding: 0;
margin-top: 16px;
font-size: 1em;
font-style: italic;
font-weight: bold;
}
.markdown-body dl dd {
padding: 0 16px;
margin-bottom: 16px;
}
.markdown-body table {
display: block;
width: 100%;
overflow: auto;
}
.markdown-body table th {
font-weight: bold;
}
.markdown-body table th,
.markdown-body table td {
padding: 6px 13px;
border: 1px solid #ddd;
}
.markdown-body table tr {
background-color: #fff;
border-top: 1px solid #ccc;
}
.markdown-body table tr:nth-child(2n) {
background-color: #f8f8f8;
}
.markdown-body img {
max-width: 100%;
box-sizing: content-box;
background-color: #fff;
}
.markdown-body code {
padding: 0;
padding-top: 0.2em;
padding-bottom: 0.2em;
margin: 0;
font-size: 85%;
background-color: rgba(0,0,0,0.04);
border-radius: 3px;
}
.markdown-body code::before,
.markdown-body code::after {
letter-spacing: -0.2em;
content: "\00a0";
}
.markdown-body pre {
word-wrap: normal;
}
.markdown-body pre>code {
padding: 0;
margin: 0;
font-size: 100%;
word-break: normal;
white-space: pre;
background: transparent;
border: 0;
}
.markdown-body .highlight {
margin-bottom: 16px;
}
.markdown-body .highlight pre {
margin-bottom: 0;
word-break: normal;
}
.markdown-body .highlight pre,
.markdown-body pre {
padding: 16px;
overflow: auto;
font-size: 85%;
line-height: 1.45;
background-color: #f7f7f7;
border-radius: 3px;
}
.markdown-body pre code {
display: inline;
max-width: auto;
padding: 0;
margin: 0;
overflow: visible;
line-height: inherit;
word-wrap: normal;
background-color: transparent;
border: 0;
}
.markdown-body pre code::before,
.markdown-body pre code::after {
content: normal;
}
.markdown-body .pl-0 {
padding-left: 0 !important;
}
.markdown-body .pl-1 {
padding-left: 3px !important;
}
.markdown-body .pl-2 {
padding-left: 6px !important;
}
.markdown-body .pl-3 {
padding-left: 12px !important;
}
.markdown-body .pl-4 {
padding-left: 24px !important;
}
.markdown-body .pl-5 {
padding-left: 36px !important;
}
.markdown-body .pl-6 {
padding-left: 48px !important;
}
.markdown-body .full-commit .btn-outline:not(:disabled):hover {
color: #4078c0;
border: 1px solid #4078c0;
}
.markdown-body kbd {
display: inline-block;
padding: 3px 5px;
font: 11px Consolas, "Liberation Mono", Menlo, Courier, monospace;
line-height: 10px;
color: #555;
vertical-align: middle;
background-color: #fcfcfc;
border: solid 1px #ccc;
border-bottom-color: #bbb;
border-radius: 3px;
box-shadow: inset 0 -1px 0 #bbb;
}
.markdown-body :checked+.radio-label {
position: relative;
z-index: 1;
border-color: #4078c0;
}
.markdown-body .task-list-item {
list-style-type: none;
}
.markdown-body .task-list-item+.task-list-item {
margin-top: 3px;
}
.markdown-body .task-list-item input {
margin: 0 0.2em 0.25em -1.6em;
vertical-align: middle;
}
.markdown-body hr {
border-bottom-color: #eee;
}
.tmpl/marked.js 0 → 100644
浏览文件 @ ab99dede
此差异已折叠。
README.md
浏览文件 @ ab99dede
# 深度学习入门
1. 新手入门[[.html](fit_a_line/README.html)] [[.pdf](fit_a_line/README.pdf)] [[.src](fit_a_line/)]
1. 个性化推荐[[.html](recommender_system/README.html)] [[.pdf](recommender_system/README.pdf)] [[.src](recommender_system/)]
1. 识别数字[[.html](recognize_digits/README.html)] [[.pdf](recognize_digits/README.pdf)] [[.src](recognize_digits/)]
1. 图像分类[[.html](classify_images/README.html)] [[.pdf](classify_images/README.pdf)] [[.src](classify_images/)]
1. 词向量[[.html](word2vec/README.html)] [[.pdf](word2vec/)] [[.src](word2vec/README.pdf)]
1. 情感分析[[.html](understand_sentiment/README.html)] [[.pdf](understand_sentiment/README.pdf)] [[.src](understand_sentiment/)]
1. 理解单词的语义[[.html](label_semantic_roles/README.html)] [[.pdf](label_semantic_roles/README.pdf)] [[.src](label_semantic_roles/)]
1. 机器翻译[[.html](machine_translation/README.html)] [[.pdf](machine_translation/README.pdf)] [[.src](machine_translation/)]
1. 新手入门 [[fit_a_line](fit_a_line/)] [[html](http://book.paddlepaddle.org/fit_a_line)]
1. 识别数字 [[recognize_digits](recognize_digits/)] [[html](http://book.paddlepaddle.org/recognize_digits)]
1. 图像分类 [[image_classification](image_classification/)] [[html](http://book.paddlepaddle.org/image_classification)]
1. 词向量 [[word2vec](word2vec/)] [[html](http://book.paddlepaddle.org/word2vec)]
1. 情感分析 [[understand_sentiment](understand_sentiment/)] [[html](http://book.paddlepaddle.org/understand_sentiment)]
1. 语义角色标注 [[label_semantic_roles](label_semantic_roles/)] [[html](http://book.paddlepaddle.org/label_semantic_roles)]
1. 机器翻译 [[machine_translation](machine_translation/)] [[html](http://book.paddlepaddle.org/machine_translation)]
1. 个性化推荐 [[recommender_system](recommender_system/)] [[html](http://book.paddlepaddle.org/recommender_system)]
<br/>
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#!/bin/bash
for i in $(du -a | grep '\.\/.\+\/README.md' | cut -f 2); do
.tmpl/convert-markdown-into-html.sh $i > $(dirname $i)/index.html
done
for i in $(du -a | grep '\.\/.\+\/README.en.md' | cut -f 2); do
.tmpl/convert-markdown-into-html.sh $i > $(dirname $i)/index.en.html
done
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# Linear Regression
Let us begin the tutorial with a classical problem called Linear Regression \[[1](#References)\]. In this chapter, we will train a model from a realistic dataset to predict house prices. Some important concepts in Machine Learning will be covered through this example.
The source code for this tutorial is at [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/fit_a_line). If this is your first time using PaddlePaddle, please refer to the [Install Guide](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html).
## Problem
Suppose we have a dataset of $n$ houses. Each house $i$ has $d$ properties and the price $y_i$. A property $x_{i,d}$ describes one aspect of the house, for example, the number of rooms in the house, the number of schools or hospitals in the neighborhood, the nearby traffic condition, etc. Our task is to predict $y_i$ given a set of properties $\{x_{i,1}, ..., x_{i,d}\}$. We assume that the price is a linear combination of all the properties, i.e.,
$$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b, i=1,\ldots,n$$
where $\omega_{d}$ and $b$ are the model parameters we want to estimate. Once they are learned, given a set of properties of a house, we will be able to predict a price for that house. The model we have here is called Linear Regression, namely, we want to regress a value as a linear combination of several values. In practice this linear model for our problem is hardly true, because the real relationship between the house properties and the price is much more complicated. However, due to its simple formulation which makes the model training and analysis easy, Linear Regression has been applied to lots of real problems. It is always an important topic in many classical Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
## Results Demonstration
We first show the training result of our model. We use the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) to train a linear model and predict the house prices in Boston. The figure below shows the predictions the model makes for some house prices. The $X$ coordinate of each point represents the median value of the prices of a certain type of houses, while the $Y$ coordinate represents the predicted value by our linear model. When $X=Y$, the point lies exactly on the dotted line. In other words, the more precise the model predicts, the closer the point is to the dotted line.
<p align="center">
<img src = "image/predictions_en.png" width=400><br/>
Figure 1. Predicted Value V.S. Actual Value
</p>
## Model Overview
### Model Definition
In the UCI Housing Data Set, there are 13 house properties $x_{i,d}$ that are related to the median house price $y_i$. Thus our model is:
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
where $\hat{Y}$ is the predicted value used to differentiate from the actual value $Y$. The model parameters to be learned are: $\omega_1, \ldots, \omega_{13}, b$, where $\omega$ are called the weights and $b$ is called the bias.
Now we need an optimization goal, so that with the learned parameters, $\hat{Y}$ is close to $Y$ as much as possible. Here we introduce the concept of [Loss Function (Cost Function)](https://en.wikipedia.org/wiki/Loss_function). The Loss Function has such property: given any pair of the actual value $y_i$ and the predicted value $\hat{y_i}$, its output is always non-negative. This non-negative value reflects the model error.
For Linear Regression, the most common Loss Function is [Mean Square Error (MSE)](https://en.wikipedia.org/wiki/Mean_squared_error) which has the following form:
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
For a dataset of size $n$, MSE is the average value of the $n$ predicted errors.
### Training
After defining our model, we have several major steps for the training:
1. Initialize the parameters including the weights $\omega$ and the bias $b$. For example, we can set their mean values as 0s, and their standard deviations as 1s.
2. Feedforward to compute the network output and the Loss Function.
3. Backward to [backpropagate](https://en.wikipedia.org/wiki/Backpropagation) the errors. The errors will be propagated from the output layer back to the input layer, during which the model parameters will be updated with the corresponding errors.
4. Repeat steps 2~3, until the loss is below a predefined threshold or the maximum number of repeats is reached.
## Data Preparation
Follow the command below to prepare data:
```bash
cd data && python prepare_data.py
```
This line of code will download the dataset from the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) and perform some [preprocessing](#Preprocessing). The dataset is split into a training set and a test set.
The dataset contains 506 lines in total, each line describing the properties and the median price of a certain type of houses in Boston. The meaning of each line is below:
| Property Name | Explanation | Data Type |
| ------| ------ | ------ |
| CRIM | per capita crime rate by town | Continuous|
| ZN | proportion of residential land zoned for lots over 25,000 sq.ft. | Continuous |
| INDUS | proportion of non-retail business acres per town | Continuous |
| CHAS | Charles River dummy variable | Discrete, 1 if tract bounds river; 0 otherwise|
| NOX | nitric oxides concentration (parts per 10 million) | Continuous |
| RM | average number of rooms per dwelling | Continuous |
| AGE | proportion of owner-occupied units built prior to 1940 | Continuous |
| DIS | weighted distances to five Boston employment centres | Continuous |
| RAD | index of accessibility to radial highways | Continuous |
| TAX | full-value property-tax rate per $10,000 | Continuous |
| PTRATIO | pupil-teacher ratio by town | Continuous |
| B | 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town | Continuous |
| LSTAT | % lower status of the population | Continuous |
| MEDV | Median value of owner-occupied homes in $1000's | Continuous |
The last entry is the median house price.
### Preprocessing
#### Continuous and Discrete Data
We define a feature vector of length 13 for each house, where each entry of the feature vector corresponds to a property of that house. Our first observation is that among the 13 dimensions, there are 12 continuous dimensions and 1 discrete dimension. Note that although a discrete value is also written as digits such as 0, 1, or 2, it has a quite different meaning from a continuous value. The reason is that the difference between two discrete values has no practical meaning. For example, if we use 0, 1, and 2 to represent `red`, `green`, and `blue` respectively, although the numerical difference between `red` and `green` is smaller than that between `red` and `blue`, we cannot say that the extent to which `blue` is different from `red` is greater than the extent to which `green` is different from `red`. Therefore, when handling a discrete feature that has $d$ possible values, we will usually convert it to $d$ new features where each feature can only take 0 or 1, indicating whether the original $d$th value is present or not. Or we can map the discrete feature to a continuous multi-dimensional vector through an embedding table. For our problem here, because CHAS itself is a binary discrete value, we do not need to do any preprocessing.
#### Feature Normalization
Another observation we have is that there is a huge difference among the value ranges of the 13 features (Figure 2). For example, feature B has a value range of [0.32, 396.90] while feature NOX has a range of [0.3850, 0.8170]. For an effective optimization, here we need data normalization. The goal of data normalization is to scale each feature into roughly the same value range, for example [-0.5, 0.5]. In this example, we adopt a standard way of normalization: substracting the mean value from the feature and divide the result by the original value range.
There are at least three reasons for [Feature Normalization](https://en.wikipedia.org/wiki/Feature_scaling) (Feature Scaling):
- A value range that is too large or too small might cause floating number overflow or underflow during computation.
- Different value ranges might result in different importances of different features to the model (at least in the beginning of the training process), which however is an unreasonable assumption. Such assumption makes the optimization more difficult and increases the training time a lot.
- Many Machine Learning techniques or models (e.g., L1/L2 regularization and Vector Space Model) are based on the assumption that all the features have roughly zero means and their value ranges are similar.
<p align="center">
<img src = "image/ranges_en.png" width=550><br/>
Figure 2. The value ranges of the features
</p>
#### Prepare Training and Test Sets
We split the dataset into two subsets, one for estimating the model parameters, namely, model training, and the other for model testing. The model error on the former is called the **training error**, and the error on the latter is called the **test error**. Our goal of training a model is to find the statistical dependency between the outputs and the inputs, so that we can predict new outputs given new inputs. As a result, the test error reflects the performance of the model better than the training error does. We consider two things when deciding the ratio of the training set to the test set: 1) More training data will decrease the variance of the parameter estimation, yielding more reliable models; 2) More test data will decrease the variance of the test error, yielding more reliable test errors. One standard split ratio is $8:2$. You can try different split ratios to observe how the two variances change.
Executing the following command to split the dataset and write the training and test set into the `train.list` and `test.list` files, so that later PaddlePaddle can read from them.
```python
python prepare_data.py -r 0.8 #8:2 is the default split ratio
```
When training complex models, we usually have one more split: the validation set. Complex models usually have [Hyperparameters](https://en.wikipedia.org/wiki/Hyperparameter_optimization) that need to be set before the training process begins. These hyperparameters are not part of the model parameters and cannot be trained using the same Loss Function (e.g., the number of layers in the network). Thus we will try several sets of hyperparameters to get several models, and compare these trained models on the validation set to pick the best one, and finally it on the test set. Because our model is relatively simple in this problem, we ignore this validation process for now.
### Provide Data to PaddlePaddle
After the data is prepared, we use a Python Data Provider to provide data for PaddlePaddle. A Data Provider is a Python function which will be called by PaddlePaddle during training. In this example, the Data Provider only needs to read the data and return it to the training process of PaddlePaddle line by line.
```python
from paddle.trainer.PyDataProvider2 import *
import numpy as np
#define data type and dimensionality
@provider(input_types=[dense_vector(13), dense_vector(1)])
def process(settings, input_file):
data = np.load(input_file.strip())
for row in data:
yield row[:-1].tolist(), row[-1:].tolist()
```
## Model Configuration
### Data Definition
We first call the function `define_py_data_sources2` to let PaddlePaddle read training and test data from the `dataprovider.py` in the above. PaddlePaddle can accept configuration info from the command line, for example, here we pass a variable named `is_predict` to control the model to have different structures during training and test.
```python
from paddle.trainer_config_helpers import *
is_predict = get_config_arg('is_predict', bool, False)
define_py_data_sources2(
train_list='data/train.list',
test_list='data/test.list',
module='dataprovider',
obj='process')
```
### Algorithm Settings
Next we need to set the details of the optimization algorithm. Due to the simplicity of the Linear Regression model, we only need to set the `batch_size` which defines how many samples are used every time for updating the parameters.
```python
settings(batch_size=2)
```
### Network
Finally, we use `fc_layer` and `LinearActivation` to represent the Linear Regression model.
```python
#input data of 13 dimensional house information
x = data_layer(name='x', size=13)
y_predict = fc_layer(
input=x,
param_attr=ParamAttr(name='w'),
size=1,
act=LinearActivation(),
bias_attr=ParamAttr(name='b'))
if not is_predict: #when training, we use MSE (i.e., regression_cost) as the Loss Function
y = data_layer(name='y', size=1)
cost = regression_cost(input=y_predict, label=y)
outputs(cost) #output MSE to view the loss change
else: #during test, output the prediction value
outputs(y_predict)
```
## Training Model
We can run the PaddlePaddle command line trainer in the root directory of the code. Here we name the configuration file as `trainer_config.py`. We train 30 passes and save the result in the directory `output`:
```bash
./train.sh
```
## Use Model
Now we can use the trained model to do prediction.
```bash
python predict.py
```
Here by default we use the model in `output/pass-00029` for prediction, and compare the actual house price with the predicted one. The result is shown in `predictions.png`.
If you want to use another model or test on other data, you can pass in a new model path or data path:
```bash
python predict.py -m output/pass-00020 -t data/housing.test.npy
```
## Summary
In this chapter, we have introduced the Linear Regression model using the UCI Housing Data Set as an example. We have shown how to train and test this model with PaddlePaddle. Many more complex models and techniques are derived from this simple linear model, thus it is important for us to understand how it works.
## References
1. https://en.wikipedia.org/wiki/Linear_regression
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
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# 线性回归
让我们从经典的线性回归（Linear Regression \[[1](#参考文献)\]）模型开始这份教程。在这一章里，你将使用真实的数据集建立起一个房价预测模型，并且了解到机器学习中的若干重要概念。
本教程源代码目录在[book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/fit_a_line)， 初次使用请参考PaddlePaddle[安装教程](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html)。
## 背景介绍
给定一个大小为$n$的数据集 ${\{y_{i}, x_{i1}, ..., x_{id}\}}_{i=1}^{n}$，其中$x_{i1}, \ldots, x_{id}$是第$i$个样本$d$个属性上的取值，$y_i$是该样本待预测的目标。线性回归模型假设目标$y_i$可以被属性间的线性组合描述，即
......@@ -182,3 +184,6 @@ python predict.py -m output/pass-00020 -t data/housing.test.npy
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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# Linear Regression
Let us begin the tutorial with a classical problem called Linear Regression \[[1](#References)\]. In this chapter, we will train a model from a realistic dataset to predict house prices. Some important concepts in Machine Learning will be covered through this example.
The source code for this tutorial is at [book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/fit_a_line). If this is your first time using PaddlePaddle, please refer to the [Install Guide](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html).
## Problem
Suppose we have a dataset of $n$ houses. Each house $i$ has $d$ properties and the price $y_i$. A property $x_{i,d}$ describes one aspect of the house, for example, the number of rooms in the house, the number of schools or hospitals in the neighborhood, the nearby traffic condition, etc. Our task is to predict $y_i$ given a set of properties $\{x_{i,1}, ..., x_{i,d}\}$. We assume that the price is a linear combination of all the properties, i.e.,
$$y_i = \omega_1x_{i,1} + \omega_2x_{i,2} + \ldots + \omega_dx_{i,d} + b, i=1,\ldots,n$$
where $\omega_{d}$ and $b$ are the model parameters we want to estimate. Once they are learned, given a set of properties of a house, we will be able to predict a price for that house. The model we have here is called Linear Regression, namely, we want to regress a value as a linear combination of several values. In practice this linear model for our problem is hardly true, because the real relationship between the house properties and the price is much more complicated. However, due to its simple formulation which makes the model training and analysis easy, Linear Regression has been applied to lots of real problems. It is always an important topic in many classical Statistical Learning and Machine Learning textbooks \[[2,3,4](#References)\].
## Results Demonstration
We first show the training result of our model. We use the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) to train a linear model and predict the house prices in Boston. The figure below shows the predictions the model makes for some house prices. The $X$ coordinate of each point represents the median value of the prices of a certain type of houses, while the $Y$ coordinate represents the predicted value by our linear model. When $X=Y$, the point lies exactly on the dotted line. In other words, the more precise the model predicts, the closer the point is to the dotted line.
<p align="center">
<img src = "image/predictions_en.png" width=400><br/>
Figure 1. Predicted Value V.S. Actual Value
</p>
## Model Overview
### Model Definition
In the UCI Housing Data Set, there are 13 house properties $x_{i,d}$ that are related to the median house price $y_i$. Thus our model is:
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
where $\hat{Y}$ is the predicted value used to differentiate from the actual value $Y$. The model parameters to be learned are: $\omega_1, \ldots, \omega_{13}, b$, where $\omega$ are called the weights and $b$ is called the bias.
Now we need an optimization goal, so that with the learned parameters, $\hat{Y}$ is close to $Y$ as much as possible. Here we introduce the concept of [Loss Function (Cost Function)](https://en.wikipedia.org/wiki/Loss_function). The Loss Function has such property: given any pair of the actual value $y_i$ and the predicted value $\hat{y_i}$, its output is always non-negative. This non-negative value reflects the model error.
For Linear Regression, the most common Loss Function is [Mean Square Error (MSE)](https://en.wikipedia.org/wiki/Mean_squared_error) which has the following form:
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
For a dataset of size $n$, MSE is the average value of the $n$ predicted errors.
### Training
After defining our model, we have several major steps for the training:
1. Initialize the parameters including the weights $\omega$ and the bias $b$. For example, we can set their mean values as 0s, and their standard deviations as 1s.
2. Feedforward to compute the network output and the Loss Function.
3. Backward to [backpropagate](https://en.wikipedia.org/wiki/Backpropagation) the errors. The errors will be propagated from the output layer back to the input layer, during which the model parameters will be updated with the corresponding errors.
4. Repeat steps 2~3, until the loss is below a predefined threshold or the maximum number of repeats is reached.
## Data Preparation
Follow the command below to prepare data:
```bash
cd data && python prepare_data.py
```
This line of code will download the dataset from the [UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing) and perform some [preprocessing](#Preprocessing). The dataset is split into a training set and a test set.
The dataset contains 506 lines in total, each line describing the properties and the median price of a certain type of houses in Boston. The meaning of each line is below:
| Property Name | Explanation | Data Type |
| ------| ------ | ------ |
| CRIM | per capita crime rate by town | Continuous|
| ZN | proportion of residential land zoned for lots over 25,000 sq.ft. | Continuous |
| INDUS | proportion of non-retail business acres per town | Continuous |
| CHAS | Charles River dummy variable | Discrete, 1 if tract bounds river; 0 otherwise|
| NOX | nitric oxides concentration (parts per 10 million) | Continuous |
| RM | average number of rooms per dwelling | Continuous |
| AGE | proportion of owner-occupied units built prior to 1940 | Continuous |
| DIS | weighted distances to five Boston employment centres | Continuous |
| RAD | index of accessibility to radial highways | Continuous |
| TAX | full-value property-tax rate per $10,000 | Continuous |
| PTRATIO | pupil-teacher ratio by town | Continuous |
| B | 1000(Bk - 0.63)^2 where Bk is the proportion of blacks by town | Continuous |
| LSTAT | % lower status of the population | Continuous |
| MEDV | Median value of owner-occupied homes in $1000's | Continuous |
The last entry is the median house price.
### Preprocessing
#### Continuous and Discrete Data
We define a feature vector of length 13 for each house, where each entry of the feature vector corresponds to a property of that house. Our first observation is that among the 13 dimensions, there are 12 continuous dimensions and 1 discrete dimension. Note that although a discrete value is also written as digits such as 0, 1, or 2, it has a quite different meaning from a continuous value. The reason is that the difference between two discrete values has no practical meaning. For example, if we use 0, 1, and 2 to represent `red`, `green`, and `blue` respectively, although the numerical difference between `red` and `green` is smaller than that between `red` and `blue`, we cannot say that the extent to which `blue` is different from `red` is greater than the extent to which `green` is different from `red`. Therefore, when handling a discrete feature that has $d$ possible values, we will usually convert it to $d$ new features where each feature can only take 0 or 1, indicating whether the original $d$th value is present or not. Or we can map the discrete feature to a continuous multi-dimensional vector through an embedding table. For our problem here, because CHAS itself is a binary discrete value, we do not need to do any preprocessing.
#### Feature Normalization
Another observation we have is that there is a huge difference among the value ranges of the 13 features (Figure 2). For example, feature B has a value range of [0.32, 396.90] while feature NOX has a range of [0.3850, 0.8170]. For an effective optimization, here we need data normalization. The goal of data normalization is to scale each feature into roughly the same value range, for example [-0.5, 0.5]. In this example, we adopt a standard way of normalization: substracting the mean value from the feature and divide the result by the original value range.
There are at least three reasons for [Feature Normalization](https://en.wikipedia.org/wiki/Feature_scaling) (Feature Scaling):
- A value range that is too large or too small might cause floating number overflow or underflow during computation.
- Different value ranges might result in different importances of different features to the model (at least in the beginning of the training process), which however is an unreasonable assumption. Such assumption makes the optimization more difficult and increases the training time a lot.
- Many Machine Learning techniques or models (e.g., L1/L2 regularization and Vector Space Model) are based on the assumption that all the features have roughly zero means and their value ranges are similar.
<p align="center">
<img src = "image/ranges_en.png" width=550><br/>
Figure 2. The value ranges of the features
</p>
#### Prepare Training and Test Sets
We split the dataset into two subsets, one for estimating the model parameters, namely, model training, and the other for model testing. The model error on the former is called the **training error**, and the error on the latter is called the **test error**. Our goal of training a model is to find the statistical dependency between the outputs and the inputs, so that we can predict new outputs given new inputs. As a result, the test error reflects the performance of the model better than the training error does. We consider two things when deciding the ratio of the training set to the test set: 1) More training data will decrease the variance of the parameter estimation, yielding more reliable models; 2) More test data will decrease the variance of the test error, yielding more reliable test errors. One standard split ratio is $8:2$. You can try different split ratios to observe how the two variances change.
Executing the following command to split the dataset and write the training and test set into the `train.list` and `test.list` files, so that later PaddlePaddle can read from them.
```python
python prepare_data.py -r 0.8 #8:2 is the default split ratio
```
When training complex models, we usually have one more split: the validation set. Complex models usually have [Hyperparameters](https://en.wikipedia.org/wiki/Hyperparameter_optimization) that need to be set before the training process begins. These hyperparameters are not part of the model parameters and cannot be trained using the same Loss Function (e.g., the number of layers in the network). Thus we will try several sets of hyperparameters to get several models, and compare these trained models on the validation set to pick the best one, and finally it on the test set. Because our model is relatively simple in this problem, we ignore this validation process for now.
### Provide Data to PaddlePaddle
After the data is prepared, we use a Python Data Provider to provide data for PaddlePaddle. A Data Provider is a Python function which will be called by PaddlePaddle during training. In this example, the Data Provider only needs to read the data and return it to the training process of PaddlePaddle line by line.
```python
from paddle.trainer.PyDataProvider2 import *
import numpy as np
#define data type and dimensionality
@provider(input_types=[dense_vector(13), dense_vector(1)])
def process(settings, input_file):
data = np.load(input_file.strip())
for row in data:
yield row[:-1].tolist(), row[-1:].tolist()
```
## Model Configuration
### Data Definition
We first call the function `define_py_data_sources2` to let PaddlePaddle read training and test data from the `dataprovider.py` in the above. PaddlePaddle can accept configuration info from the command line, for example, here we pass a variable named `is_predict` to control the model to have different structures during training and test.
```python
from paddle.trainer_config_helpers import *
is_predict = get_config_arg('is_predict', bool, False)
define_py_data_sources2(
train_list='data/train.list',
test_list='data/test.list',
module='dataprovider',
obj='process')
```
### Algorithm Settings
Next we need to set the details of the optimization algorithm. Due to the simplicity of the Linear Regression model, we only need to set the `batch_size` which defines how many samples are used every time for updating the parameters.
```python
settings(batch_size=2)
```
### Network
Finally, we use `fc_layer` and `LinearActivation` to represent the Linear Regression model.
```python
#input data of 13 dimensional house information
x = data_layer(name='x', size=13)
y_predict = fc_layer(
input=x,
param_attr=ParamAttr(name='w'),
size=1,
act=LinearActivation(),
bias_attr=ParamAttr(name='b'))
if not is_predict: #when training, we use MSE (i.e., regression_cost) as the Loss Function
y = data_layer(name='y', size=1)
cost = regression_cost(input=y_predict, label=y)
outputs(cost) #output MSE to view the loss change
else: #during test, output the prediction value
outputs(y_predict)
```
## Training Model
We can run the PaddlePaddle command line trainer in the root directory of the code. Here we name the configuration file as `trainer_config.py`. We train 30 passes and save the result in the directory `output`:
```bash
./train.sh
```
## Use Model
Now we can use the trained model to do prediction.
```bash
python predict.py
```
Here by default we use the model in `output/pass-00029` for prediction, and compare the actual house price with the predicted one. The result is shown in `predictions.png`.
If you want to use another model or test on other data, you can pass in a new model path or data path:
```bash
python predict.py -m output/pass-00020 -t data/housing.test.npy
```
## Summary
In this chapter, we have introduced the Linear Regression model using the UCI Housing Data Set as an example. We have shown how to train and test this model with PaddlePaddle. Many more complex models and techniques are derived from this simple linear model, thus it is important for us to understand how it works.
## References
1. https://en.wikipedia.org/wiki/Linear_regression
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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# 线性回归
让我们从经典的线性回归（Linear Regression \[[1](#参考文献)\]）模型开始这份教程。在这一章里，你将使用真实的数据集建立起一个房价预测模型，并且了解到机器学习中的若干重要概念。
本教程源代码目录在[book/fit_a_line](https://github.com/PaddlePaddle/book/tree/develop/fit_a_line)， 初次使用请参考PaddlePaddle[安装教程](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html)。
## 背景介绍
给定一个大小为$n$的数据集 ${\{y_{i}, x_{i1}, ..., x_{id}\}}_{i=1}^{n}$，其中$x_{i1}, \ldots, x_{id}$是第$i$个样本$d$个属性上的取值，$y_i$是该样本待预测的目标。线性回归模型假设目标$y_i$可以被属性间的线性组合描述，即
$$y_i = \omega_1x_{i1} + \omega_2x_{i2} + \ldots + \omega_dx_{id} + b, i=1,\ldots,n$$
例如，在我们将要建模的房价预测问题里，$x_{ij}$是描述房子$i$的各种属性（比如房间的个数、周围学校和医院的个数、交通状况等），而 $y_i$是房屋的价格。
初看起来，这个假设实在过于简单了，变量间的真实关系很难是线性的。但由于线性回归模型有形式简单和易于建模分析的优点，它在实际问题中得到了大量的应用。很多经典的统计学习、机器学习书籍\[[2,3,4](#参考文献)\]也选择对线性模型独立成章重点讲解。
## 效果展示
我们使用从[UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing)获得的波士顿房价数据集进行模型的训练和预测。下面的散点图展示了使用模型对部分房屋价格进行的预测。其中，每个点的横坐标表示同一类房屋真实价格的中位数，纵坐标表示线性回归模型根据特征预测的结果，当二者值完全相等的时候就会落在虚线上。所以模型预测得越准确，则点离虚线越近。
<p align="center">
<img src = "image/predictions.png" width=400><br/>
图1. 预测值 V.S. 真实值
</p>
## 模型概览
### 模型定义
在波士顿房价数据集中，和房屋相关的值共有14个：前13个用来描述房屋相关的各种信息，即模型中的 $x_i$；最后一个值为我们要预测的该类房屋价格的中位数，即模型中的 $y_i$。因此，我们的模型就可以表示成：
$$\hat{Y} = \omega_1X_{1} + \omega_2X_{2} + \ldots + \omega_{13}X_{13} + b$$
$\hat{Y}$ 表示模型的预测结果，用来和真实值$Y$区分。模型要学习的参数即：$\omega_1, \ldots, \omega_{13}, b$。
建立模型后，我们需要给模型一个优化目标，使得学到的参数能够让预测值$\hat{Y}$尽可能地接近真实值$Y$。这里我们引入损失函数（[Loss Function](https://en.wikipedia.org/wiki/Loss_function)，或Cost Function）这个概念。 输入任意一个数据样本的目标值$y_{i}$和模型给出的预测值$\hat{y_{i}}$，损失函数输出一个非负的实值。这个实质通常用来反映模型误差的大小。
对于线性回归模型来讲，最常见的损失函数就是均方误差（Mean Squared Error， [MSE](https://en.wikipedia.org/wiki/Mean_squared_error)）了，它的形式是：
$$MSE=\frac{1}{n}\sum_{i=1}^{n}{(\hat{Y_i}-Y_i)}^2$$
即对于一个大小为$n$的测试集，$MSE$是$n$个数据预测结果误差平方的均值。
### 训练过程
定义好模型结构之后，我们要通过以下几个步骤进行模型训练
1. 初始化参数，其中包括权重$\omega_i$和偏置$b$，对其进行初始化（如0均值，1方差）。
2. 网络正向传播计算网络输出和损失函数。
3. 根据损失函数进行反向误差传播 （[backpropagation](https://en.wikipedia.org/wiki/Backpropagation)），将网络误差从输出层依次向前传递, 并更新网络中的参数。
4. 重复2~3步骤，直至网络训练误差达到规定的程度或训练轮次达到设定值。
## 数据准备
执行以下命令来准备数据:
```bash
cd data && python prepare_data.py
```
这段代码将从[UCI Housing Data Set](https://archive.ics.uci.edu/ml/datasets/Housing)下载数据并进行[预处理](#数据预处理)，最后数据将被分为训练集和测试集。
这份数据集共506行，每行包含了波士顿郊区的一类房屋的相关信息及该类房屋价格的中位数。其各维属性的意义如下：
| 属性名 | 解释 | 类型 |
| ------| ------ | ------ |
| CRIM | 该镇的人均犯罪率 | 连续值 |
| ZN | 占地面积超过25,000平方呎的住宅用地比例 | 连续值 |
| INDUS | 非零售商业用地比例 | 连续值 |
| CHAS | 是否邻近 Charles River | 离散值，1=邻近；0=不邻近 |
| NOX | 一氧化氮浓度 | 连续值 |
| RM | 每栋房屋的平均客房数 | 连续值 |
| AGE | 1940年之前建成的自用单位比例 | 连续值 |
| DIS | 到波士顿5个就业中心的加权距离 | 连续值 |
| RAD | 到径向公路的可达性指数 | 连续值 |
| TAX | 全值财产税率 | 连续值 |
| PTRATIO | 学生与教师的比例 | 连续值 |
| B | 1000(BK - 0.63)^2，其中BK为黑人占比 | 连续值 |
| LSTAT | 低收入人群占比 | 连续值 |
| MEDV | 同类房屋价格的中位数 | 连续值 |
### 数据预处理
#### 连续值与离散值
观察一下数据，我们的第一个发现是：所有的13维属性中，有12维的连续值和1维的离散值（CHAS）。离散值虽然也常使用类似0、1、2这样的数字表示，但是其含义与连续值是不同的，因为这里的差值没有实际意义。例如，我们用0、1、2来分别表示红色、绿色和蓝色的话，我们并不能因此说“蓝色和红色”比“绿色和红色”的距离更远。所以通常对一个有$d$个可能取值的离散属性，我们会将它们转为$d$个取值为0或1的二值属性或者将每个可能取值映射为一个多维向量。不过就这里而言，因为CHAS本身就是一个二值属性，就省去了这个麻烦。
#### 属性的归一化
另外一个稍加观察即可发现的事实是，各维属性的取值范围差别很大（如图2所示）。例如，属性B的取值范围是[0.32, 396.90]，而属性NOX的取值范围是[0.3850, 0.8170]。这里就要用到一个常见的操作-归一化（normalization）了。归一化的目标是把各位属性的取值范围放缩到差不多的区间，例如[-0.5,0.5]。这里我们使用一种很常见的操作方法：减掉均值，然后除以原取值范围。
做归一化（或 [Feature scaling](https://en.wikipedia.org/wiki/Feature_scaling)）至少有以下3个理由：
- 过大或过小的数值范围会导致计算时的浮点上溢或下溢。
- 不同的数值范围会导致不同属性对模型的重要性不同（至少在训练的初始阶段如此），而这个隐含的假设常常是不合理的。这会对优化的过程造成困难，使训练时间大大的加长。
- 很多的机器学习技巧/模型（例如L1，L2正则项，向量空间模型-Vector Space Model）都基于这样的假设：所有的属性取值都差不多是以0为均值且取值范围相近的。
<p align="center">
<img src = "image/ranges.png" width=550><br/>
图2. 各维属性的取值范围
</p>
#### 整理训练集与测试集
我们将数据集分割为两份：一份用于调整模型的参数，即进行模型的训练，模型在这份数据集上的误差被称为**训练误差**；另外一份被用来测试，模型在这份数据集上的误差被称为**测试误差**。我们训练模型的目的是为了通过从训练数据中找到规律来预测未知的新数据，所以测试误差是更能反映模型表现的指标。分割数据的比例要考虑到两个因素：更多的训练数据会降低参数估计的方差，从而得到更可信的模型；而更多的测试数据会降低测试误差的方差，从而得到更可信的测试误差。一种常见的分割比例为$8:2$，感兴趣的读者朋友们也可以尝试不同的设置来观察这两种误差的变化。
执行如下命令可以分割数据集，并将训练集和测试集的地址分别写入train.list 和 test.list两个文件中，供PaddlePaddle读取。
```python
python prepare_data.py -r 0.8 #默认使用8:2的比例进行分割
```
在更复杂的模型训练过程中，我们往往还会多使用一种数据集：验证集。因为复杂的模型中常常还有一些超参数（[Hyperparameter](https://en.wikipedia.org/wiki/Hyperparameter_optimization)）需要调节，所以我们会尝试多种超参数的组合来分别训练多个模型，然后对比它们在验证集上的表现选择相对最好的一组超参数，最后才使用这组参数下训练的模型在测试集上评估测试误差。由于本章训练的模型比较简单，我们暂且忽略掉这个过程。
### 提供数据给PaddlePaddle
准备好数据之后，我们使用一个Python data provider来为PaddlePaddle的训练过程提供数据。一个 data provider 就是一个Python函数，它会被PaddlePaddle的训练过程调用。在这个例子里，只需要读取已经保存好的数据，然后一行一行地返回给PaddlePaddle的训练进程即可。
```python
from paddle.trainer.PyDataProvider2 import *
import numpy as np
#定义数据的类型和维度
@provider(input_types=[dense_vector(13), dense_vector(1)])
def process(settings, input_file):
data = np.load(input_file.strip())
for row in data:
yield row[:-1].tolist(), row[-1:].tolist()
```
## 模型配置说明
### 数据定义
首先，通过 `define_py_data_sources2` 来配置PaddlePaddle从上面的`dataprovider.py`里读入训练数据和测试数据。 PaddlePaddle接受从命令行读入的配置信息，例如这里我们传入一个名为`is_predict`的变量来控制模型在训练和测试时的不同结构。
```python
from paddle.trainer_config_helpers import *
is_predict = get_config_arg('is_predict', bool, False)
define_py_data_sources2(
train_list='data/train.list',
test_list='data/test.list',
module='dataprovider',
obj='process')
```
### 算法配置
接着，指定模型优化算法的细节。由于线性回归模型比较简单，我们只要设置基本的`batch_size`即可，它指定每次更新参数的时候使用多少条数据计算梯度信息。
```python
settings(batch_size=2)
```
### 网络结构
最后，使用`fc_layer`和`LinearActivation`来表示线性回归的模型本身。
```python
#输入数据，13维的房屋信息
x = data_layer(name='x', size=13)
y_predict = fc_layer(
input=x,
param_attr=ParamAttr(name='w'),
size=1,
act=LinearActivation(),
bias_attr=ParamAttr(name='b'))
if not is_predict: #训练时，我们使用MSE，即regression_cost作为损失函数
y = data_layer(name='y', size=1)
cost = regression_cost(input=y_predict, label=y)
outputs(cost) #训练时输出MSE来监控损失的变化
else: #测试时，输出预测值
outputs(y_predict)
```
## 训练模型
在对应代码的根目录下执行PaddlePaddle的命令行训练程序。这里指定模型配置文件为`trainer_config.py`，训练30轮，结果保存在`output`路径下。
```bash
./train.sh
```
## 应用模型
现在来看下如何使用已经训练好的模型进行预测。
```bash
python predict.py
```
这里默认使用`output/pass-00029`中保存的模型进行预测，并将数据中的房价与预测结果进行对比，结果保存在 `predictions.png`中。
如果你想使用别的模型或者其它的数据进行预测，只要传入新的路径即可：
```bash
python predict.py -m output/pass-00020 -t data/housing.test.npy
```
## 总结
在这章里，我们借助波士顿房价这一数据集，介绍了线性回归模型的基本概念，以及如何使用PaddlePaddle实现训练和测试的过程。很多的模型和技巧都是从简单的线性回归模型演化而来，因此弄清楚线性模型的原理和局限非常重要。
## 参考文献
1. https://en.wikipedia.org/wiki/Linear_regression
2. Friedman J, Hastie T, Tibshirani R. The elements of statistical learning[M]. Springer, Berlin: Springer series in statistics, 2001.
3. Murphy K P. Machine learning: a probabilistic perspective[M]. MIT press, 2012.
4. Bishop C M. Pattern recognition[J]. Machine Learning, 2006, 128.
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
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image_classification/README.md
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图像分类
=======
本教程源代码目录在[book/image_classification](https://github.com/PaddlePaddle/book/tree/develop/image_classification)， 初次使用请参考PaddlePaddle[安装教程](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html)。
## 背景介绍
图像相比文字能够提供更加生动、容易理解及更具艺术感的信息，是人们转递与交换信息的重要来源。在本教程中，我们专注于图像识别领域的一个重要问题，即图像分类。
......@@ -136,9 +138,9 @@ ResNet(Residual Network) \[[15](#参考文献)\] 是2015年ImageNet图像分类
### 数据介绍与下载
通用图像分类公开的标准数据集常用的有[CIFAR](<https://www.cs.toronto.edu/~kriz/cifar.html)、[ImageNet](http://image-net.org/)、[COCO](http://mscoco.org/)等，常用的细粒度图像分类数据集包括[CUB-200-2011](http://www.vision.caltech.edu/visipedia/CUB-200-2011.html)、[Stanford Dog](http://vision.stanford.edu/aditya86/ImageNetDogs/)、[Oxford-flowers](http://www.robots.ox.ac.uk/~vgg/data/flowers/)等。其中ImageNet数据集规模相对较大，如[模型概览](#模型概览)一章所讲，大量研究成果基于ImageNet。ImageNet数据从2010年来稍有变化，常用的是ImageNet-2012数据集，该数据集包含1000个类别：训练集包含1,281,167张图片，每个类别数据732至1300张不等，验证集包含50,000张图片，平均每个类别50张图片。
通用图像分类公开的标准数据集常用的有[CIFAR](https://www.cs.toronto.edu/~kriz/cifar.html)、[ImageNet](http://image-net.org/)、[COCO](http://mscoco.org/)等，常用的细粒度图像分类数据集包括[CUB-200-2011](http://www.vision.caltech.edu/visipedia/CUB-200-2011.html)、[Stanford Dog](http://vision.stanford.edu/aditya86/ImageNetDogs/)、[Oxford-flowers](http://www.robots.ox.ac.uk/~vgg/data/flowers/)等。其中ImageNet数据集规模相对较大，如[模型概览](#模型概览)一章所讲，大量研究成果基于ImageNet。ImageNet数据从2010年来稍有变化，常用的是ImageNet-2012数据集，该数据集包含1000个类别：训练集包含1,281,167张图片，每个类别数据732至1300张不等，验证集包含50,000张图片，平均每个类别50张图片。
由于ImageNet数据集较大，下载和训练较慢，为了方便大家学习，我们使用[CIFAR10](<https://www.cs.toronto.edu/~kriz/cifar.html>)数据集。CIFAR10数据集包含60,000张32x32的彩色图片，10个类别，每个类包含6,000张。其中50,000张图片作为训练集，10000张作为测试集。图11从每个类别中随机抽取了10张图片，展示了所有的类别。
由于ImageNet数据集较大，下载和训练较慢，为了方便大家学习，我们使用[CIFAR10](https://www.cs.toronto.edu/~kriz/cifar.html)数据集。CIFAR10数据集包含60,000张32x32的彩色图片，10个类别，每个类包含6,000张。其中50,000张图片作为训练集，10000张作为测试集。图11从每个类别中随机抽取了10张图片，展示了所有的类别。
<p align="center">
<img src="image/cifar.png" width="350"><br/>
......@@ -175,7 +177,7 @@ def initializer(settings, mean_path, is_train, **kwargs):
}
@provider(init_hook=initializer, cache=CacheType.CACHE_PASS_IN_MEM)
@provider(init_hook=initializer, pool_size=50000)
def process(settings, file_list):
with open(file_list, 'r') as fdata:
for fname in fdata:
......@@ -186,7 +188,9 @@ def process(settings, file_list):
labels = batch['labels']
for im, lab in zip(images, labels):
if settings.is_train and np.random.randint(2):
im = im.reshape(3, 32, 32)
im = im[:,:,::-1]
im = im.flatten()
im = im - settings.mean
yield {
'image': im.astype('float32'),
......@@ -245,7 +249,6 @@ $$ lr = lr_{0} * a^ {\lfloor \frac{n}{ b}\rfloor} $$
网络输入定义为 `data_layer` (数据层)，在图像分类中即为图像像素信息。CIFRAR10是RGB 3通道32x32大小的彩色图，因此输入数据大小为3072(3x32x32)，类别大小为10，即10分类。
```python
datadim = 3 * 32 * 32
classdim = 10
data = data_layer(name='image', size=datadim)
......@@ -297,7 +300,7 @@ $$ lr = lr_{0} * a^ {\lfloor \frac{n}{ b}\rfloor} $$
3. 定义分类器
通过上面VGG网络提取高层特征，然后经过全连接层映射到类别维度大小的向量，再通过Softmax归一化得到每个类别的概率，也可称作分类器。
```python
out = fc_layer(input=net, size=class_num, act=SoftmaxActivation())
```
......@@ -539,3 +542,6 @@ python classify.py --job=extract --model=output/pass-00299 --data=image/dog.png
[21] https://www.cs.toronto.edu/~kriz/cifar.html
[22] http://cs231n.github.io/classification/
<br/>
<a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/"><img alt="知识共享许可协议" style="border-width:0" src="https://i.creativecommons.org/l/by-nc-sa/4.0/88x31.png" /></a><br /><span xmlns:dct="http://purl.org/dc/terms/" href="http://purl.org/dc/dcmitype/Text" property="dct:title" rel="dct:type">本教程</span> 由 <a xmlns:cc="http://creativecommons.org/ns#" href="http://book.paddlepaddle.org" property="cc:attributionName" rel="cc:attributionURL">PaddlePaddle</a> 创作，采用 <a rel="license" href="http://creativecommons.org/licenses/by-nc-sa/4.0/">知识共享 署名-非商业性使用-相同方式共享 4.0 国际 许可协议</a>进行许可。
image_classification/dataprovider.py
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......@@ -27,7 +27,7 @@ def initializer(settings, mean_path, is_train, **kwargs):
}
@provider(init_hook=initializer, cache=CacheType.CACHE_PASS_IN_MEM)
@provider(init_hook=initializer, pool_size=50000)
def process(settings, file_list):
with open(file_list, 'r') as fdata:
for fname in fdata:
......@@ -38,6 +38,8 @@ def process(settings, file_list):
labels = batch['labels']
for im, lab in zip(images, labels):
if settings.is_train and np.random.randint(2):
im = im.reshape(3, 32, 32)
im = im[:, :, ::-1]
im = im.flatten()
im = im - settings.mean
yield {'image': im.astype('float32'), 'label': int(lab)}
image_classification/image/resnet.png
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image_classification/train.sh
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......@@ -14,15 +14,15 @@
# limitations under the License.
set -e
#config=models/resnet.py
config=models/vgg.py
#cfg=models/resnet.py
cfg=models/vgg.py
output=output
log=train.log
paddle train \
--config=$config \
--use_gpu=1 \
--trainer_count=4 \
--config=$cfg \
--use_gpu=true \
--trainer_count=1 \
--log_period=100 \
--num_passes=300 \
--save_dir=$output \
......
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<body>
<a href="https://github.com/paddlepaddle/book">Please access github home page</a>
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label_semantic_roles/README.md
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# 语义角色标注
本教程源代码目录在[book/label_semantic_roles](https://github.com/PaddlePaddle/book/tree/develop/label_semantic_roles)， 初次使用请参考PaddlePaddle[安装教程](http://www.paddlepaddle.org/doc_cn/build_and_install/index.html)。
## 背景介绍
自然语言分析技术大致分为三个层面：词法分析、句法分析和语义分析。语义角色标注是实现浅层语义分析的一种方式。在一个句子中，谓词是对主语的陈述或说明，指出“做什么”、“是什么”或“怎么样，代表了一个事件的核心，跟谓词搭配的名词称为论元。语义角色是指论元在动词所指事件中担任的角色。主要有：施事者（Agent）、受事者（Patient）、客体（Theme）、经验者（Experiencer）、受益者（Beneficiary）、工具（Instrument）、处所（Location）、目标（Goal）和来源（Source）等。
......@@ -19,7 +21,7 @@ $$\mbox{[小明]}_{\mbox{Agent}}\mbox{[昨天]}_{\mbox{Time}}\mbox{[晚上]}_\mb
5. 对第4步的结果，通过多分类得到论元的语义角色标签。可以看到，句法分析是基础，并且后续步骤常常会构造的一些人工特征，这些特征往往也来自句法分析。
<div align="center">
<img src="image/dependency_parsing.png" width = "80%" height = "80%" align=center /><br>
<img src="image/dependency_parsing.png" width = "80%" align=center /><br>
图1. 依存句法分析句法树示例
</div>
......@@ -28,7 +30,7 @@ $$\mbox{[小明]}_{\mbox{Agent}}\mbox{[昨天]}_{\mbox{Time}}\mbox{[晚上]}_\mb
我们继续以上面的这句话为例，图1展示了BIO表示方法。
<div align="center">
<img src="image/bio_example.png" width = "90%" height = "90%" align=center /><br>
<img src="image/bio_example.png" width = "90%" align=center /><br>
图2. BIO标注方法示例
</div>
......@@ -51,7 +53,7 @@ $$\mbox{[小明]}_{\mbox{Agent}}\mbox{[昨天]}_{\mbox{Time}}\mbox{[晚上]}_\mb
图3是最终得到的栈式循环神经网络结构示意图。
<p align="center">
<img src="./image/stacked_lstm.png" width = "40%" height = "40%" align=center><br>
<img src="./image/stacked_lstm.png" width = "40%" align=center><br>
图3. 基于LSTM的栈式循环神经网络结构示意图
</p>
......@@ -62,7 +64,7 @@ $$\mbox{[小明]}_{\mbox{Agent}}\mbox{[昨天]}_{\mbox{Time}}\mbox{[晚上]}_\mb
为了克服这一缺陷，我们可以设计一种双向循环网络单元，它的思想简单且直接：对上一节的栈式循环神经网络进行一个小小的修改，堆叠多个LSTM单元，让每一层LSTM单元分别以：正向、反向、正向 …… 的顺序学习上一层的输出序列。于是，从第2层开始，$t$时刻我们的LSTM单元便总是可以看到历史和未来的信息。图4是基于LSTM的双向循环神经网络结构示意图。
<p align="center">
<img src="./image/bidirectional_stacked_lstm.png" width = "60%" height = "60%" align=center><br>
<img src="./image/bidirectional_stacked_lstm.png" width = "60%" align=center><br>
图4. 基于LSTM的双向循环神经网络结构示意图
</p>
......@@ -77,7 +79,7 @@ CRF是一种概率化结构模型，可以看作是一个概率无向图模型
序列标注任务只需要考虑输入和输出都是一个线性序列，并且由于我们只是将输入序列作为条件，不做任何条件独立假设，因此输入序列的元素之间并不存在图结构。综上，在序列标注任务中使用的是如图5所示的定义在链式图上的CRF，称之为线性链条件随机场（Linear Chain Conditional Random Field）。
<p align="center">
<img src="./image/linear_chain_crf.png" width = "35%" height = "35%" align=center><br>
<img src="./image/linear_chain_crf.png" width = "35%" align=center><br>
图5. 序列标注任务中使用的线性链条件随机场
</p>
......@@ -121,7 +123,7 @@ $$L(\lambda, D) = - \text{log}\left(\prod_{m=1}^{N}p(Y_m|X_m, W)\right) + C \fra
4. CRF以第3步中LSTM学习到的特征为输入，以标记序列为监督信号，完成序列标注；
<div align="center">
<img src="image/db_lstm_network.png" width = "60%" height = "60%" align=center /><br>
<img src="image/db_lstm_network.png" width = "60%" align=center /><br>
图6. SRL任务上的深层双向LSTM模型
</div>
......@@ -472,3 +474,6 @@ The interest-only securities were priced at 35 1\/2 to yield 10.72 % . B-A0 I-A
8. Palmer M, Gildea D, Kingsbury P. [The proposition bank: An annotated corpus of semantic roles](http://www.mitpressjournals.org/doi/pdfplus/10.1162/0891201053630264)[J]. Computational linguistics, 2005, 31(1): 71-106.
9. Carreras X, Màrquez L. [Introduction to the CoNLL-2005 shared task: Semantic role labeling](http://www.cs.upc.edu/~srlconll/st05/papers/intro.pdf)[C]//Proceedings of the Ninth Conference on Computational Natural Language Learning. Association for Computational Linguistics, 2005: 152-164.
10. Zhou J, Xu W. [End-to-end learning of semantic role labeling using recurrent neural networks](http://www.aclweb.org/anthology/P/P15/P15-1109.pdf)[C]//Proceedings of the Annual Meeting of the Association for Computational Linguistics. 2015.
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}
def get_batch_size(yeild_data):
return len(yeild_data[0])
def get_batch_size(yield_data):
return len(yield_data[0])
@provider(
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