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            <h1 id="seo-header">菜鸟博主对神经网络的简单理解（一）</h1>
            
            
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                <p>博主最近在看临床预测模型，里面涉及到一些神经网络的相关知识，这里记录一下博主的简单理解。</p>
<h2 id="基本概念"><a href="#基本概念" class="headerlink" title="基本概念"></a>基本概念</h2><ul>
<li><code>X</code>：一个nx维的输入张量，可以是nx&#x3D;0的标量，nx&#x3D;1的向量，nx&#x3D;2的矩阵，或更高维的张量</li>
<li><code>Y</code>：一个ny维的输出张量，可以是nx&#x3D;0的标量，nx&#x3D;1的向量，nx&#x3D;2的矩阵，或更高维的张量</li>
<li><code>f</code>：一个特定结构的<a target="_blank" rel="noopener" href="https://zhuanlan.zhihu.com/p/159305118">神经网络</a>，如简单的BP神经网络、复杂的深度神经网络<strong>DNN</strong>等，用于将X映射到Y</li>
<li><code>W</code>：一个nw维的张量，用来代表f中的所有权重，nw与f、X、Y有关，具体多少不用管</li>
<li><code>L</code>：损失函数，可以是交叉熵、残差平方等，用来计算f(X)与实际Y的差距</li>
</ul>
<p>一个简单的例子：假设<code>f</code>是DNN，<code>X</code>是一个256*256图片的像素矩阵，<code>Y</code>是一个3维分类向量，那么<code>f</code>就可以用于将一张特定的256*256图片<code>X0</code>映射到一个特定的<code>Y0(P(🐱), P(🐕), P(🐖))</code>，那么我们输出<code>(🐱,🐕,🐖)[which.max(Y0)]</code>，就可以对图片<code>X0</code>进行<code>(🐱,🐕,🐖)</code>的分类。</p>
<h2 id="对训练的理解"><a href="#对训练的理解" class="headerlink" title="对训练的理解"></a>对训练的理解</h2><p>假设我们有一个训练好的权重<code>W</code>，那么我们就可以得到任意<code>X</code>下对实际<code>Y</code>的良好估计<code>f(X,W)</code>,有<code>L(f(X,W),Y)</code>相对较小。我们训练的目的，就是根据已有的数据集<code>D&#123;(X,Y)&#125;</code>，通过适当的拟合来找到这样一个权重<code>W</code>，它可以实现前面假设中的效果。</p>
<p>那么如何进行适当的拟合呢？一个简单的思路是梯度下降法。根据定义，我们知道<code>L</code>是<code>f(X)</code>和<code>Y</code>的函数，那么变换视角，<code>L</code>就是关于<code>W</code>的函数。假设学习率为<code>η</code>，初始权重为<code>W0</code>，对于<code>D</code>中的任意<code>(X0,Y0)</code>，我们可以求<code>ΔW0=-η∇L(W0`(X0,Y0),f`)</code>。根据梯度的特性，我们可以知道对于更新后的权重<code>W1=W0+ΔW0</code>，有<code>L(W1`(X0,Y0),f`)&lt;L(W0`(X0,Y0),f`)</code>。在适当的参数下，通过不断循环上述过程，就能得到最终的<code>W</code>。</p>
<p>那么<code>∇L(W`f`)</code>如何求呢？作为医学生，我们不必了解具体的数学原理来编程，只要构建好我们想要的网络结构<code>f</code>，<a target="_blank" rel="noopener" href="https://pytorch.org/">PyTorch</a>的<a target="_blank" rel="noopener" href="https://www.codercto.com/a/81317.html#:~:text=PyTorch%E8%87%AA%E5%8A%A8%E6%B1%82%E5%AF%BC%EF%BC%88Autograd%EF%BC%89%E5%8E%9F%E7%90%86%E8%A7%A3%E6%9E%90%20%E6%88%91%E4%BB%AC%E7%9F%A5%E9%81%93%EF%BC%8C%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E6%9C%80%E6%A0%B8%E5%BF%83%E7%9A%84%E5%85%B6%E4%B8%AD%E4%B8%80%E4%B8%AA%E6%AD%A5%E9%AA%A4%EF%BC%8C%E5%B0%B1%E6%98%AF%E6%B1%82%E5%AF%BC%EF%BC%9A%E6%A0%B9%E6%8D%AE%E5%87%BD%E6%95%B0%EF%BC%88linear%20%2B%20activation%20function%EF%BC%89%E6%B1%82weights%E7%9B%B8%E5%AF%B9%E4%BA%8Eloss%E7%9A%84%E5%AF%BC%E6%95%B0%EF%BC%88%E8%BF%98%E6%98%AFloss%E7%9B%B8%E5%AF%B9%E4%BA%8Eweights%E7%9A%84%E5%AF%BC%E6%95%B0%EF%BC%9F,%EF%BC%89%E3%80%82%20%E7%84%B6%E5%90%8E%E6%A0%B9%E6%8D%AE%E5%BE%97%E5%87%BA%E7%9A%84%E5%AF%BC%E6%95%B0%EF%BC%8C%E7%9B%B8%E5%BA%94%E7%9A%84%E4%BF%AE%E6%94%B9weights%EF%BC%8C%E8%AE%A9loss%E6%9C%80%E5%B0%8F%E5%8C%96%E3%80%82%20%E5%90%84%E5%A4%A7%E6%B7%B1%E5%BA%A6%E5%AD%A6%E4%B9%A0%E6%A1%86%E6%9E%B6Tensorflow%EF%BC%8CKeras%EF%BC%8CPyTorch%E9%83%BD%E8%87%AA%E5%B8%A6%E6%9C%89%E8%87%AA%E5%8A%A8%E6%B1%82%E5%AF%BC%E5%8A%9F%E8%83%BD%EF%BC%8C%E4%B8%8D%E9%9C%80%E8%A6%81%E6%88%91%E4%BB%AC%E6%89%8B%E5%8A%A8%E7%AE%97%E3%80%82%20%E5%9C%A8%E5%88%9D%E6%AD%A5%E5%AD%A6%E4%B9%A0PyTorch%E7%9A%84%E6%97%B6%E5%80%99%EF%BC%8C%E7%9C%8B%E5%88%B0PyTorch%E7%9A%84%E8%87%AA%E5%8A%A8%E6%B1%82%E5%AF%BC%E8%BF%87%E7%A8%8B%E6%97%B6%EF%BC%8C%E6%84%9F%E8%A7%89%E9%9D%9E%E5%B8%B8%E7%9A%84%E5%88%AB%E6%89%AD%E5%92%8C%E4%B8%8D%E7%9B%B4%E8%A7%82%E3%80%82%20%E6%88%91%E4%B8%8B%E9%9D%A2%E4%B8%BE%E4%B8%AA%E4%BE%8B%E5%AD%90%EF%BC%8C%E5%A4%A7%E5%AE%B6%E8%87%AA%E5%B7%B1%E6%84%9F%E5%8F%97%E4%B8%80%E4%B8%8B%E3%80%82">自动求导</a>功能就可以自动帮我们计算出<code>∇L(W`f`)</code>啦。</p>

                
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