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# 斯坦福大学2014机器学习教程中文笔记目录

* [第一周](week1.md)
* [第一周](html/week1.html)

一、 引言(Introduction)

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3.6 逆、转置

* [第二周](week2.md)
* [第二周](html/week2.html)

四、多变量线性回归(Linear Regression with Multiple Variables)

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5.7 工作和提交的编程练习

* [第三周](week3.md)
* [第三周](html/week3.html)

六、逻辑回归(Logistic Regression)

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7.4 正则化的逻辑回归模型

* [第四周](week4.md)
* [第四周](html/week4.html)

第八、神经网络:表述(Neural Networks: Representation)

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8.7 多类分类

* [第五周](week5.md)
* [第五周](html/week5.html)

九、神经网络的学习(Neural Networks: Learning)

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9.8 自主驾驶

* [第六周](week6.md)
* [第六周](html/week6.html)

十、应用机器学习的建议(Advice for Applying Machine Learning)

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11.5 机器学习的数据

[第7周](week7.md)
[第7周](html/week7.html)

十二、支持向量机(Support Vector Machines)

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12.6 使用支持向量机

* [第八周](week8.md)
* [第八周](html/week8.html)

十三、聚类(Clustering)

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14.7 主成分分析法的应用建议

* [第九周](week9.md)
* [第九周](html/week9.html)

十五、异常检测(Anomaly Detection)

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16.6 推行工作上的细节:均值归一化

* [第十周](week10.md)
* [第十周](html/week10.html)

十七、大规模机器学习(Large Scale Machine Learning)

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首先应该做的事是去检查一个这么大规模的训练集是否真的必要,也许我们只用1000个训练集也能获得较好的效果,我们可以绘制学习曲线来帮助判断。

![](images/bdf069136b4b661dd14158496d1d1419.png)
![](../images/bdf069136b4b661dd14158496d1d1419.png)

### 17.2 随机梯度下降法

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随机梯度下降算法在每一次计算之后便更新参数 ${{\theta }}$ ,而不需要首先将所有的训练集求和,在梯度下降算法还没有完成一次迭代时,随机梯度下降算法便已经走出了很远。但是这样的算法存在的问题是,不是每一步都是朝着”正确”的方向迈出的。因此算法虽然会逐渐走向全局最小值的位置,但是可能无法站到那个最小值的那一点,而是在最小值点附近徘徊。

![](images/9710a69ba509a9dcbca351fccc6e7aae.jpg)
![](../images/9710a69ba509a9dcbca351fccc6e7aae.jpg)

### 17.3 小批量梯度下降

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在随机梯度下降中,我们在每一次更新 ${{\theta }}$ 之前都计算一次代价,然后每$x$次迭代后,求出这$x$次对训练实例计算代价的平均值,然后绘制这些平均值与$x$次迭代的次数之间的函数图表。

![](images/76fb1df50bdf951f4b880fa66489e367.png)
![](../images/76fb1df50bdf951f4b880fa66489e367.png)

当我们绘制这样的图表时,可能会得到一个颠簸不平但是不会明显减少的函数图像(如上面左下图中蓝线所示)。我们可以增加$α$来使得函数更加平缓,也许便能看出下降的趋势了(如上面左下图中红线所示);或者可能函数图表仍然是颠簸不平且不下降的(如洋红色线所示),那么我们的模型本身可能存在一些错误。

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随着我们不断地靠近全局最小值,通过减小学习率,我们迫使算法收敛而非在最小值附近徘徊。
但是通常我们不需要这样做便能有非常好的效果了,对$α$进行调整所耗费的计算通常不值得

![](images/f703f371dbb80d22fd5e4aec48aa9fd4.jpg)
![](../images/f703f371dbb80d22fd5e4aec48aa9fd4.jpg)

总结下,这段视频中,我们介绍了一种方法,近似地监测出随机梯度下降算法在最优化代价函数中的表现,这种方法不需要定时地扫描整个训练集,来算出整个样本集的代价函数,而是只需要每次对最后1000个,或者多少个样本,求一下平均值。应用这种方法,你既可以保证随机梯度下降法正在正常运转和收敛,也可以用它来调整学习速率$α$的大小。

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例如,我们有400个训练实例,我们可以将批量梯度下降的求和任务分配给4台计算机进行处理:

![](images/919eabe903ef585ec7d08f2895551a1f.jpg)
![](../images/919eabe903ef585ec7d08f2895551a1f.jpg)

很多高级的线性代数函数库已经能够利用多核CPU的多个核心来并行地处理矩阵运算,这也是算法的向量化实现如此重要的缘故(比调用循环快)。

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图像文字识别应用所作的事是,从一张给定的图片中识别文字。这比从一份扫描文档中识别文字要复杂的多。

![](images/095e4712376c26ff7ffa260125760140.jpg)
![](../images/095e4712376c26ff7ffa260125760140.jpg)

为了完成这样的工作,需要采取如下步骤:

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3. 字符分类(Character classification)——确定每一个字符是什么
可以用任务流程图来表达这个问题,每一项任务可以由一个单独的小队来负责解决:

![](images/610fffb413d8d577882d6345c166a9fb.png)
![](../images/610fffb413d8d577882d6345c166a9fb.png)

### 18.2 滑动窗口

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一旦完成后,我们按比例放大剪裁的区域,再以新的尺寸对图片进行剪裁,将新剪裁的切片按比例缩小至模型所采纳的尺寸,交给模型进行判断,如此循环。

![](images/1e00d03719e20eeaf1f414f99d7f4109.jpg)
![](../images/1e00d03719e20eeaf1f414f99d7f4109.jpg)

滑动窗口技术也被用于文字识别,首先训练模型能够区分字符与非字符,然后,运用滑动窗口技术识别字符,一旦完成了字符的识别,我们将识别得出的区域进行一些扩展,然后将重叠的区域进行合并。接着我们以宽高比作为过滤条件,过滤掉高度比宽度更大的区域(认为单词的长度通常比高度要大)。下图中绿色的区域是经过这些步骤后被认为是文字的区域,而红色的区域是被忽略的。

![](images/bc48a4b0c7257591643eb50f2bf46db6.jpg)
![](../images/bc48a4b0c7257591643eb50f2bf46db6.jpg)

以上便是文字侦测阶段。
下一步是训练一个模型来完成将文字分割成一个个字符的任务,需要的训练集由单个字符的图片和两个相连字符之间的图片来训练模型。

![](images/0a930f2083bbeb85837f018b74fd0a02.jpg)
![](../images/0a930f2083bbeb85837f018b74fd0a02.jpg)

![](images/0bde4f379c8a46c2074336ecce1a955f.jpg)
![](../images/0bde4f379c8a46c2074336ecce1a955f.jpg)

模型训练完后,我们仍然是使用滑动窗口技术来进行字符识别。

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回到我们的文字识别应用中,我们的流程图如下:

![](images/55d41ee748680a62e755d6aa5b95b53c.png)
![](../images/55d41ee748680a62e755d6aa5b95b53c.png)

流程图中每一部分的输出都是下一部分的输入,上限分析中,我们选取一部分,手工提供100%正确的输出结果,然后看应用的整体效果提升了多少。假使我们的例子中总体效果为72%的正确率。

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最后我们手工选择数据,让字符分类输出的结果100%正确,系统的总体效果又提升了10%,这意味着我们可能也会应该投入更多的时间和精力来提高应用的总体表现。

![](images/f1ecee10884098f98032648da08f8937.jpg)
![](../images/f1ecee10884098f98032648da08f8937.jpg)

十九、总结(Conclusion)
----------------------
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