April 2019
Intermediate to advanced
172 pages
4h 39m
Chinese
Content preview from 精通特征工程
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线性建模与线性代数基础
｜
155
“零空间”这个名称听起来像是一种存在性危机的悲伤结局。如果零空间中除了全零向量
之外还有其他向量，那么方程
Aw
=
y
就有无穷多解。有很多解可供选择本身不是一件坏
事，有时候我们可以选择任意一个解。但如果有很多可能的答案，就会有多个特征集合可
以用于分类任务。这时就很难弄清楚哪个特征才是真正重要的。
解决零空间过大这个问题的一种方法是添加额外的限制条件，从而对模型进行
调整
：
Aw
=
y
其中
w
满足
w
T
w
=
c
。
这种正则化方式限制了权重向量具有特定的范数
c
。这种正则化的强度是通过一个正则化
参数来控制的，和前面实验中的做法一样，这个参数必须调优。
一般来说，
特征选择
方法需要选取出最有用的特征来降低计算负担，减轻模型的模糊性，
并使得学习出的模型更与众不同。这也是
2.6
节中的重点。
另一个问题是数据矩阵的谱的“不均匀性”。在训练线性分类器时，我们关心的不仅是线
性系统是否有通用解，还有我们是否能容易地找到这个解。通常，训练过程使用的求解器
要计算损失函数的梯度，然后沿着梯度以较小的步长求解。当某些奇异值非常大而其余
奇异值非常接近于
0
时，要想找到真实答案，求解器需要非常小心地绕过较长的奇异向量
（对应于大奇异值的奇异向量），花费大量时间在较短的奇异向量附近进行探索。这种谱的
“不均匀性”可以由矩阵的条件数来表示，也就是最大奇异值和最小奇异值的绝对值之间
的比值。
总结一下，为了找出一个与众不同的好线性模型，也为了比较容易地找到它，我们需要以
下条件。
(1)
标签向量能比较好地通过特征 ...
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I wanted to learn C and C++, but it didn't click for me until I picked up an O'Reilly book. When I went on the O’Reilly platform, I was astonished to find all the books there, plus live events and sandboxes so you could play around with the technology.Addison B.
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I'm always learning. So when I got on to O'Reilly, I was like a kid in a candy store. There are playlists. There are answers. There's on-demand training. It's worth its weight in gold, in terms of what it allows me to do.