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Requirement

In this assignment, you will compare the characteristics and performance of different classifiers, namely logistic regression, k-nearest neighbours and naive Bayes. You will experiment with these extensions and extend the provided code. Note that you should understand the code first instead of using it as a black box.
Python versions of the code have been provided. You are free to work with whichever you wish.

Analysis

作为Machine Learning的三大基础算法

1. Logistic regression，也就是logistic回归，常用于数据挖掘，疾病自动诊断，经济预测等领域
2. K-nearest neighbours，也就是K邻近算法，常用于数据挖掘，以及分类，对未知事物的识别等领域
3. Naive Bayes，也就是朴素贝叶斯，常用于分类器，文本分类识别

本题给出了以上三大算法的基本实现，但是需要根据测试框架的调度逻辑，实现未完成的测试函数。
本题偏重工程性质，在不断的调试中，会加深对算法的理解。

Tips

下面是check_grad函数的实现

def check_grad(func, X, epsilon, *args):
  if len(X.shape) != 2 or X.shape[1] != 1:
    raise ValueError("X must be a vector")

  y, dy, = func(X, *args)[:2]         # get the partial derivatives dy
  dh = np.zeros((len(X), 1))

  for j in xrange(len(X)):
    dx = np.zeros((len(X), 1))
    dx[j] += epsilon
    y2 = func(X+dx, *args)[0]
    dx = -dx
    y1 = func(X+dx, *args)[0]
    dh[j] = (y2 - y1)/(2*epsilon)

  print np.hstack((dy, dh))          # print the two vectors
  d = LA.norm(dh-dy)/LA.norm(dh+dy)  # return norm of diff divided by norm of sum

  return d
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