# LR 算法总结–斯坦福大学机器学习公开课学习笔记

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The model and parameters themselves specify how to make predictions for a given input, but do not tell us how to find a better parameter, so the objective function is needed. The general objective function contains the following two items

sigmod函数形式如下

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In this way, we get the model and parameters, and in the next step, we determine the objective function, the loss function of logical regression is the cross-entropy function, and the optimization algorithm used to obtain the parameters is maximum likelihood.

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You can write more succinctly.

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According to the maximum likelihood algorithm, the model should make the probability of obtaining samples as large as possible. assuming that the samples are independent of each other, the probability of obtaining samples using the model can be expressed as follows.

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This is the loss function of logical regression.

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The objective function can be solved by the method of random gradient descent.

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You can simply simplify the formula for finding the gradient as follows

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In this way, the samples can be constantly updated until the parameters that meet the requirements are found.

3: Principles of Data Mining, David Hand et al,2001. Chapter 1.5 Components of Data Mining Algorithms, 将数据挖掘算法解构为四个组件：1）模型结构（函数形式，如线性模型），2）评分函数（评估模型拟合数据的质量，如似然函数，误差平方和，误分类率），3）优化和搜索方法（评分函数的优化和模型参数的求解），4）数据管理策略（优化和搜索时对数据的高效访问）。

Original: https://www.cnblogs.com/bnuvincent/p/11221344.html
Author: Alexander
Title: LR 算法总结–斯坦福大学机器学习公开课学习笔记

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