Detailed explanation of logistic regression model in Python

Detailed explanation of logistic regression model in Python

Logistic regression is a machine learning algorithm widely used in classification problems. It can associate input data with corresponding labels to classify new data. Prediction. In Python, logistic regression is a commonly used classification algorithm. This article will introduce in detail the principle and use of the logistic regression model.

The principle of logistic regression

Logistic regression is a classic binary classification algorithm, which is usually used to predict which category a data belongs to. The output result is a probability value, which represents the probability that the sample belongs to a certain class, usually a real number between 0 and 1. The essence of logistic regression is a linear classifier, which predicts the input data and parameters through a linear function, and performs probability mapping through a sigmoid function to output the classification result.

The hypothesis function of the logistic regression model is defined as follows:

$$h_{ heta}(x)= rac{1}{1 e^{- heta^Tx}}$$

Among them, $ heta$ is the model parameter vector, and $x$ is the input data vector. If $h_{ heta}(x)geq0.5$, the sample is predicted to be a positive class, otherwise the sample is predicted to be a negative class.

The loss function of the logistic regression model is a logarithmic loss function, which indicates how well the model fits the training data. It is defined as follows:

$$J( heta)=- rac{1}{ m}sum_{i=1}^{m}{[y^{(i)}log{h_{ heta}(x^{(i)})} (1-y^{(i)})log( 1-h_{ heta}(x^{(i)}))]}$$

Among them, $y^{(i)}$ is the true label of sample $i$, $x^{ (i)}$ is the feature vector of sample $i$, and $m$ is the total number of samples.

The training process of the logistic regression model is the process of solving the model parameters $ heta $ by minimizing the loss function. Commonly used optimization algorithms include gradient descent method, Newton method, etc.

Implementation of logistic regression model in Python

In Python, we can use the Scikit-Learn library to build a logistic regression model. Scikit-Learn is a commonly used machine learning library in Python. It provides a wealth of algorithms and tools to facilitate user operations such as feature preprocessing, model selection, evaluation, and optimization.

First, we need to import relevant libraries and data sets, for example:

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split
from sklearn.linear_model import LogisticRegression
from sklearn import metrics
from sklearn.datasets import load_iris
 
iris = load_iris()
X = iris.data
y = iris.target

Next, we divide the data set into a training set and a test set:

X_train, X_test, y_train, y_test = train_test_split(X, y, test_size=0.3, random_state=0)

Then , we can use the logistic regression model for training and prediction:

lr = LogisticRegression()
lr.fit(X_train, y_train)
y_pred = lr.predict(X_test)

Finally, we can evaluate the model performance through indicators such as confusion matrix and accuracy:

cnf_matrix = metrics.confusion_matrix(y_test, y_pred)
print(cnf_matrix)
print("Accuracy:",metrics.accuracy_score(y_test, y_pred))

Summary

Logistic regression is a commonly used classification algorithm that can effectively predict binary classification problems. In Python, we can use the Scikit-Learn library to build and train logistic regression models. But it should be noted that in practical applications, we need to preprocess and select features to improve the performance and robustness of the model.

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