Logistic Regression

Creator

Creator

Created

Created

2023 Mar 16 1:58

Editor

Editor

Edited

Edited

2025 Feb 4 14:8

Refs

Refs

Sigmoid Function

Gaussian Discriminant Analysis

Data Classification

Log odds로 확률을
Linear Regression 처럼 선형적으로 변환

선형회귀와 달리 비선형도 잘 다루지만 수식적으로 선형적으로 다룰수 있어서

Sigmoid 함수를 사용하여 0과 1 사이의 값을 출력, log-likelihood를 최대화

notion image

to make convex cost function

notion image

Logistic Regression Notion

Multi-Class Logistic Regression

h_\theta(x) = g(\theta^Tx) = \frac{1}{1 + e^{-\theta^Tx}}

This leads to

p(u|x;\theta)

described by

Bernoulli Distribution

p(y|x;\theta) = (h_\theta(x))^y(1 - h_\theta(x))^{1 - y}

the

Likelihood function is

l(\theta) = logL(\theta) = \Sigma_{i=1}^ny^{(i)}logh(x^{(i)}) + (1 - y^{(i)})log(1 - h(x^{(i)}))

But 로지스틱 회귀의 y값은

you can use

Newton–Raphson method or

Stochastic Gradient Descent and prior one achieves faster convergence or

IRLS is much faster

difference between

Linear Regression is that usage of sigmoid function or logistic function

Logistic Multinomial Regression

Multinomial logistic regression

In statistics, multinomial logistic regression is a classification method that generalizes logistic regression to multiclass problems, i.e. with more than two possible discrete outcomes.[1] That is, it is a model that is used to predict the probabilities of the different possible outcomes of a categorically distributed dependent variable, given a set of independent variables (which may be real-valued, binary-valued, categorical-valued, etc.).

Multinomial logistic regression

https://en.wikipedia.org/wiki/Multinomial_logistic_regression

Recommendations

///////