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    <li>经典的线性回归任务</li>
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  <div class="section" id="id1">
<h1>经典的线性回归任务<a class="headerlink" href="#id1" title="永久链接至标题">¶</a></h1>
<p>PaddlePaddle是源于百度的一个深度学习平台。这份简短的介绍将向你展示如何利用PaddlePaddle来解决一个经典的线性回归问题。</p>
<div class="section" id="id2">
<h2>任务简介<a class="headerlink" href="#id2" title="永久链接至标题">¶</a></h2>
<p>我们展示如何用PaddlePaddle解决 <a class="reference external" href="https://www.baidu.com/s?wd=单变量线性回归">单变量的线性回归</a> 问题。线性回归的输入是一批点 <cite>(x, y)</cite> ，其中 <cite>y = wx + b + ε</cite>， 而 ε 是一个符合高斯分布的随机变量。线性回归的输出是从这批点估计出来的参数 <cite>w</cite> 和 <cite>b</cite> 。</p>
<p>一个例子是房产估值。我们假设房产的价格（y）是其大小（x）的一个线性函数，那么我们可以通过收集市场上房子的大小和价格，用来估计线性函数的参数w 和 b。</p>
</div>
<div class="section" id="id4">
<h2>准备数据<a class="headerlink" href="#id4" title="永久链接至标题">¶</a></h2>
<p>假设变量 <cite>x</cite> 和 <cite>y</cite> 的真实关系为： <cite>y = 2x + 0.3 + ε</cite>，这里展示如何使用观测数据来拟合这一线性关系。首先，Python代码将随机产生2000个观测点，作为线性回归的输入。下面脚本符合PaddlePaddle期待的读取数据的Python程序的模式。</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="c1"># dataprovider.py</span>
<span class="kn">from</span> <span class="nn">paddle.trainer.PyDataProvider2</span> <span class="kn">import</span> <span class="o">*</span>
<span class="kn">import</span> <span class="nn">random</span>

<span class="c1"># 定义输入数据的类型: 2个浮点数</span>
<span class="nd">@provider</span><span class="p">(</span><span class="n">input_types</span><span class="o">=</span><span class="p">[</span><span class="n">dense_vector</span><span class="p">(</span><span class="mi">1</span><span class="p">),</span> <span class="n">dense_vector</span><span class="p">(</span><span class="mi">1</span><span class="p">)],</span><span class="n">use_seq</span><span class="o">=</span><span class="bp">False</span><span class="p">)</span>
<span class="k">def</span> <span class="nf">process</span><span class="p">(</span><span class="n">settings</span><span class="p">,</span> <span class="n">input_file</span><span class="p">):</span>
    <span class="k">for</span> <span class="n">i</span> <span class="ow">in</span> <span class="nb">xrange</span><span class="p">(</span><span class="mi">2000</span><span class="p">):</span>
        <span class="n">x</span> <span class="o">=</span> <span class="n">random</span><span class="o">.</span><span class="n">random</span><span class="p">()</span>
        <span class="k">yield</span> <span class="p">[</span><span class="n">x</span><span class="p">],</span> <span class="p">[</span><span class="mi">2</span><span class="o">*</span><span class="n">x</span><span class="o">+</span><span class="mf">0.3</span><span class="p">]</span>
</pre></div>
</div>
</div>
<div class="section" id="id5">
<h2>训练模型<a class="headerlink" href="#id5" title="永久链接至标题">¶</a></h2>
<p>为了还原 <cite>y = 2x + 0.3</cite>，我们先从一条随机的直线 <cite>y&#8217; = wx + b</cite> 开始，然后利用观测数据调整 <cite>w</cite> 和 <cite>b</cite> 使得 <cite>y&#8217;</cite> 和 <cite>y</cite> 的差距不断减小，最终趋于接近。这个过程就是模型的训练过程，而 <cite>w</cite> 和 <cite>b</cite> 就是模型的参数，即我们的训练目标。</p>
<p>在PaddlePaddle里，该模型的网络配置如下。</p>
<div class="highlight-python"><div class="highlight"><pre><span></span># trainer_config.py
from paddle.trainer_config_helpers import *

# 1. 定义数据来源，调用上面的process函数获得观测数据
data_file = &#39;empty.list&#39;
with open(data_file, &#39;w&#39;) as f: f.writelines(&#39; &#39;)
define_py_data_sources2(train_list=data_file, test_list=None,
                        module=&#39;dataprovider&#39;, obj=&#39;process&#39;,args={})

# 2. 学习算法。控制如何改变模型参数 w 和 b
settings(batch_size=12, learning_rate=1e-3, learning_method=MomentumOptimizer())

# 3. 神经网络配置
x = data_layer(name=&#39;x&#39;, size=1)
y = data_layer(name=&#39;y&#39;, size=1)
# 线性计算网络层: ȳ = wx + b
ȳ = fc_layer(input=x, param_attr=ParamAttr(name=&#39;w&#39;), size=1, act=LinearActivation(), bias_attr=ParamAttr(name=&#39;b&#39;))
# 计算误差函数，即  ȳ 和真实 y 之间的距离
cost = square_error_cost(input= ȳ, label=y)
outputs(cost)
</pre></div>
</div>
<p>这段简短的配置展示了PaddlePaddle的基本用法：</p>
<ul>
<li><p class="first">第一部分定义了数据输入。一般情况下，PaddlePaddle先从一个文件列表里获得数据文件地址，然后交给用户自定义的函数（例如上面的 <cite>process`函数）进行读入和预处理从而得到真实输入。本文中由于输入数据是随机生成的不需要读输入文件，所以放一个空列表（`empty.list</cite>）即可。</p>
</li>
<li><p class="first">第二部分主要是选择学习算法，它定义了模型参数改变的规则。PaddlePaddle提供了很多优秀的学习算法，这里使用一个基于momentum的随机梯度下降(SGD)算法，该算法每批量(batch)读取12个采样数据进行随机梯度计算来更新更新。</p>
</li>
<li><p class="first">最后一部分是神经网络的配置。由于PaddlePaddle已经实现了丰富的网络层，所以很多时候你需要做的只是定义正确的网络层并把它们连接起来。这里使用了三种网络单元：</p>
<blockquote>
<div><ul class="simple">
<li><strong>数据层</strong>：数据层 <cite>data_layer</cite> 是神经网络的入口，它读入数据并将它们传输到接下来的网络层。这里数据层有两个，分别对应于变量 <cite>x</cite> 和 <cite>y</cite>。</li>
<li><strong>全连接层</strong>：全连接层 <cite>fc_layer</cite> 是基础的计算单元，这里利用它建模变量之间的线性关系。计算单元是神经网络的核心，PaddlePaddle支持大量的计算单元和任意深度的网络连接，从而可以拟合任意的函数来学习复杂的数据关系。</li>
<li><strong>回归误差代价层</strong>：回归误差代价层 <cite>square_error_cost</cite> 是众多误差代价函数层的一种，它们在训练过程作为网络的出口，用来计算模型的误差，是模型参数优化的目标函数。</li>
</ul>
</div></blockquote>
</li>
</ul>
<p>定义了网络结构并保存为 <cite>trainer_config.py</cite> 之后，运行以下训练命令：</p>
<div class="highlight-bash"><div class="highlight"><pre><span></span>paddle train --config<span class="o">=</span>trainer_config.py --save_dir<span class="o">=</span>./output --num_passes<span class="o">=</span><span class="m">30</span>
</pre></div>
</div>
<p>PaddlePaddle将在观测数据集上迭代训练30轮，并将每轮的模型结果存放在 <cite>./output</cite> 路径下。从输出日志可以看到，随着轮数增加误差代价函数的输出在不断的减小，这意味着模型在训练数据上不断的改进，直到逼近真实解：` y = 2x + 0.3 `</p>
</div>
<div class="section" id="id6">
<h2>模型检验<a class="headerlink" href="#id6" title="永久链接至标题">¶</a></h2>
<p>训练完成后，我们希望能够检验模型的好坏。一种常用的做法是用学习的模型对另外一组测试数据进行预测，评价预测的效果。在这个例子中，由于已经知道了真实答案，我们可以直接观察模型的参数是否符合预期来进行检验。</p>
<p>PaddlePaddle将每个模型参数作为一个numpy数组单独存为一个文件，所以可以利用如下方法读取模型的参数。</p>
<div class="highlight-python"><div class="highlight"><pre><span></span><span class="kn">import</span> <span class="nn">numpy</span> <span class="kn">as</span> <span class="nn">np</span>
<span class="kn">import</span> <span class="nn">os</span>

<span class="k">def</span> <span class="nf">load</span><span class="p">(</span><span class="n">file_name</span><span class="p">):</span>
    <span class="k">with</span> <span class="nb">open</span><span class="p">(</span><span class="n">file_name</span><span class="p">,</span> <span class="s1">&#39;rb&#39;</span><span class="p">)</span> <span class="k">as</span> <span class="n">f</span><span class="p">:</span>
        <span class="n">f</span><span class="o">.</span><span class="n">read</span><span class="p">(</span><span class="mi">16</span><span class="p">)</span> <span class="c1"># skip header for float type.</span>
        <span class="k">return</span> <span class="n">np</span><span class="o">.</span><span class="n">fromfile</span><span class="p">(</span><span class="n">f</span><span class="p">,</span> <span class="n">dtype</span><span class="o">=</span><span class="n">np</span><span class="o">.</span><span class="n">float32</span><span class="p">)</span>

<span class="k">print</span> <span class="s1">&#39;w=</span><span class="si">%.6f</span><span class="s1">, b=</span><span class="si">%.6f</span><span class="s1">&#39;</span> <span class="o">%</span> <span class="p">(</span><span class="n">load</span><span class="p">(</span><span class="s1">&#39;output/pass-00029/w&#39;</span><span class="p">),</span> <span class="n">load</span><span class="p">(</span><span class="s1">&#39;output/pass-00029/b&#39;</span><span class="p">))</span>
<span class="c1"># w=1.999743, b=0.300137</span>
</pre></div>
</div>
<a class="reference internal image-reference" href="../../_images/parameters.png"><img alt="../../_images/parameters.png" class="align-center" src="../../_images/parameters.png" style="width: 512.0px; height: 344.8px;" /></a>
<p>从图中可以看到，虽然 <cite>w</cite> 和 <cite>b</cite> 都使用随机值初始化，但在起初的几轮训练中它们都在快速逼近真实值，并且后续仍在不断改进，使得最终得到的模型几乎与真实模型一致。</p>
<p>这样，我们用PaddlePaddle解决了单变量线性回归问题， 包括数据输入、模型训练和最后的结果验证。</p>
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