牛顿法python代码_python 牛顿法实现逻辑回归（Logistic Regression）

本文采用的训练方法是牛顿法（Newton Method）。

代码

import numpy as np

class LogisticRegression(object):

"""

Logistic Regression Classifier training by Newton Method

"""

def __init__(self, error: float = 0.7, max_epoch: int = 100):

"""

:param error: float, if the distance between new weight and

old weight is less than error, the process

of traing will break.

:param max_epoch: if training epoch >= max_epoch the process

of traing will break.

"""

self.error = error

self.max_epoch = max_epoch

self.weight = None

self.sign = np.vectorize(lambda x: 1 if x >= 0.5 else 0)

def p_func(self, X_):

"""Get P(y=1 | x)

:param X_: shape = (n_samples + 1, n_features)

:return: shape = (n_samples)

"""

tmp = np.exp(self.weight @ X_.T)

return tmp / (1 + tmp)

def diff(self, X_, y, p):

"""Get derivative

:param X_: shape = (n_samples, n_features + 1)

:param y: shape = (n_samples)

:param p: shape = (n_samples) P(y=1 | x)

:return: shape = (n_features + 1) first derivative

"""

return -(y - p) @ X_

def hess_mat(self, X_, p):

"""Get Hessian Matrix

:param p: shape = (n_samples) P(y=1 | x)

:return: shape = (n_features + 1, n_features + 1) second derivative

"""

hess = np.zeros((X_.shape[1], X_.shape[1]))

for i in range(X_.shape[0]):

hess += self.X_XT[i] * p[i] * (1 - p[i])

return hess

def newton_method(self, X_, y):

"""Newton Method to calculate weight

:param X_: shape = (n_samples + 1, n_features)

:param y: shape = (n_samples)

:return: None

"""

self.weight = np.ones(X_.shape[1])

self.X_XT = []

for i in range(X_.shape[0]):

t = X_[i, :].reshape((-1, 1))

self.X_XT.append(t @ t.T)

for _ in range(self.max_epoch):

p = self.p_func(X_)

diff = self.diff(X_, y, p)

hess = self.hess_mat(X_, p)

new_weight = self.weight - (np.linalg.inv(hess) @ diff.reshape((-1, 1))).flatten()

if np.linalg.norm(new_weight - self.weight) <= self.error:

break

self.weight = new_weight

def fit(self, X, y):

"""

:param X_: shape = (n_samples, n_features)

:param y: shape = (n_samples)

:return: self

"""

X_ = np.c_[np.ones(X.shape[0]), X]

self.newton_method(X_, y)

return self

def predict(self, X) -> np.array:

"""

:param X: shape = (n_samples, n_features]

:return: shape = (n_samples]

"""

X_ = np.c_[np.ones(X.shape[0]), X]

return self.sign(self.p_func(X_))

测试代码

import matplotlib.pyplot as plt

import sklearn.datasets

def plot_decision_boundary(pred_func, X, y, title=None):

"""分类器画图函数，可画出样本点和决策边界

:param pred_func: predict函数

:param X: 训练集X

:param y: 训练集Y

:return: None

"""

# Set min and max values and give it some padding

x_min, x_max = X[:, 0].min() - .5, X[:, 0].max() + .5

y_min, y_max = X[:, 1].min() - .5, X[:, 1].max() + .5

h = 0.01

# Generate a grid of points with distance h between them

xx, yy = np.meshgrid(np.arange(x_min, x_max, h), np.arange(y_min, y_max, h))

# Predict the function value for the whole gid

Z = pred_func(np.c_[xx.ravel(), yy.ravel()])

Z = Z.reshape(xx.shape)

# Plot the contour and training examples

plt.contourf(xx, yy, Z, cmap=plt.cm.Spectral)

plt.scatter(X[:, 0], X[:, 1], s=40, c=y, cmap=plt.cm.Spectral)

if title:

plt.title(title)

plt.show()

效果

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