线性回归算法的简单实现

最近在看慕课网BOBO老师的机器学习入门课程，之前有看过很多的相关课程，讲数据原理推导及sklearn使用较多，顺便推荐一波，看过的课程中，个人觉得邹博老师讲的就蛮好(也看过吴恩达的斯坦福的课程，数学推导看的时候多看几遍也看的懂，过一会儿就忘了，哎)，文章的话可以参照https://www.cnblogs.com/pinard/category/894692.html这位的博客，觉得写得清楚明了，有不明白的提问一般都会讲清楚。

BOBO老师的课程里有讲算法的简单实现，也跟着手动敲了一下，算法里还是有python语法知识的(敲了一遍也还是懵逼)，不过还是有助于理解算法的，如果是初学了也可以看下。

一元线性回归简单实现，求解方式是最小二乘法计算求解

import numpy as np


class SimpleLinearRegression1:
    def __init__(self):

        self.a_ = None
        self.b_ = None


def fit(self, x_train, y_train):
    """根据训练数据集训练模型"""
    assert x_train.ndim == 1
    # 传入的数据是一维的
    assert len(x_train) == len(y_train)
    # 传入的x和y长度保持一致

    x_mean = np.mean(x_train)
    y_mean = np.mean(y_train)

    num = 0.0
    d = 0.0
    for x, y in zip(x_train, y_train):
        num += (x - x_mean) * (y - y_mean)
        d += (x - x_mean) ** 2

    self.a_ = num / d
    self.b_ = y_mean - self.a_ * x_mean

    return self


def predict(self, x_predict):
    """给定待预测数据集x_predict，返回表示x_predict的结果向量"""
    assert x_predict.ndim == 1

    assert self.a_ is not None and self.b_ is not None

    return np.array([self._predict(x) for x in x_predict])


def _predict(self, x_single):
    """给定单个待预测数据x_single，返回x_single的预测结果值"""
    return self.a_ * x_single + self.b_


def __repr__(self):
    return "SimpleLinearRegression1()"

多元线性回归的实现，求解方式是矩阵求解的方式

import numpy as np


class LinearRegression:
    def __init__(self):
        """初始化Linear Regression模型"""
        self.coef_ = None
        self.interception_ = None
        self._theta = None

    def fit_normal(self,X_train,y_train):
        """根据训练数据集X_train,y_train训练Linear Regression模型"""
        assert X_train.shape[0] == y_train.shape[0],\
            "the size of X_train must be equrt to the size of y_train"

        X_b = np.hstack([np.ones(len(X_train, 1), X_train)])
        self._theta = np.linalg.inv(X_b.T.dot(X_b)).dot(X_b.T).dot(y_train);

        self.interception_ = self._theta[0]
        self.coef_ = self._theta[1:]

        return self

    def predict(self, X_predict):
        """给定待预测数据集X_predict,返回表示X_predict的结果向量"""
        assert self.intercept_ is not None and self.coef_ is not None, \
            """must fit before predict!"""
        assert X_predict.shape[1] == len(self.coef_), \
            """the feature number of X_predict must be equal to X_train"""

        X_b = np.hstack([np.ones((len(X_predict), 1)),X_predict])
        return X_b.dot(self._theta)

    def score(self, X_test, y_test):
        """根据测试数据集X_test 和 y_test确定当前模型的准确度"""

        y_predict = self.predict(X_test)
        return r2_score(y_test, y_predict)

    def __repar__(self):
        return "LinearRegression()"