Question

出于培训目的，我在python中实现了线性回归。问题是成本在增加而不是减少。对于数据，我使用翼型自噪声数据集。可以找到数据here

我按如下所示导入数据：

import pandas as pd

def features():

    features = pd.read_csv("data/airfoil_self_noise/airfoil_self_noise.dat.txt", sep="\t", header=None)

    X = features.iloc[:, 0:5]
    Y = features.iloc[:, 5]

    return X.values, Y.values.reshape(Y.shape[0], 1)

我的线性回归代码如下：

import numpy as np
import random

class linearRegression():

    def __init__(self, learning_rate=0.01, max_iter=20):
        """
        Initialize the hyperparameters of the linear regression.

        :param learning_rate: the learning rate
        :param max_iter: the max numer of iteration to perform
        """

        self.lr = learning_rate
        self.max_iter = max_iter
        self.m = None
        self.weights = None
        self.bias = None

    def fit(self, X, Y):
        """
        Run gradient descent algorithm

        :param X: the inputs
        :param Y: the outputs
        :return:
        """

        self.m = X.shape[0]
        self.weights = np.random.normal(0, 0.1, (X.shape[1], 1))
        self.bias = random.normalvariate(0, 0.1)

        for iter in range(0, self.max_iter):

            A = self.__forward(X)
            dw, db = self.__backward(A, X, Y)

            J = (1/(2 * self.m)) * np.sum(np.power((A - Y), 2))

            print("at iteration %s cost is %s" % (iter, J))

            self.weights = self.weights - self.lr * dw
            self.bias = self.bias - self.lr * db

    def predict(self, X):
        """
        Make prediction on the inputs

        :param X: the inputs
        :return:
        """

        Y_pred = self.__forward(X)

        return Y_pred

    def __forward(self, X):
        """
        Compute the linear function on the inputs

        :param X: the inputs
        :return:
            A: the activation
        """

        A = np.dot(X, self.weights) + self.bias

        return A

    def __backward(self, A, X, Y):
        """

        :param A: the activation
        :param X: the inputs
        :param Y: the outputs
        :return:
            dw: the gradient for the weights
            db: the gradient for the bias
        """

        dw = (1 / self.m) * np.dot(X.T, (A - Y))
        db = (1 / self.m) * np.sum(A - Y)

        return dw, db

然后，我按如下所示实例化linearRegression类：

X, Y = features()
model = linearRegression()
X_train, X_test, y_train, y_test = train_test_split(X, Y, test_size=0.33, random_state=42)
model.fit(X_train, y_train)

我试图找出成本增加的原因，但到目前为止，我仍然无法找出原因。如果有人可以向我指出正确的方向，将不胜感激。

Answer 1

通常，如果您选择较高的学习率，则可能会遇到类似的问题。我试图检查您的代码，我的观察结果是：

您的成本函数J似乎还不错。
但是在倒退功能中，您似乎从猜测中减去了实际结果。这样做可能会导致负权重，并且由于您要从权重和梯度中减去学习率和比率的乘积，因此最终会得到成本函数结果增加

Answer 2

您的学习率很多太高。当我以未经修改的方式运行您的代码时，除了学习率是1e-7而不是0.01之外，我都能可靠地降低成本。

Answer 3

通常，成本增加时学习率就会过高。

线性回归的成本增加

3 个答案: