Transcription of Logistic Regression - Stanford University
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Logistic Regression - Stanford University
1 Will MonroeCS 109 Lecture Notes #22 August 14, 2017 Logistic RegressionBased on a chapter by Chris PiechLogistic regressionis a classification algorithm1that works by trying to learn a function thatapproximatesP(Y|X). It makes the central assumption thatP(Y|X)can be approximated as asigmoid function applied to a linear combination of input features. It is particularly important tolearn because Logistic Regression is the basic building block of artificial neural , for a single training data point (x,y), Logistic Regression assumes:P(Y=1|X=x)= (z)wherez= 0+m i=1 ixiThis assumption is often written in the equivalent forms:P(Y=1|X=x)= ( Tx)where we always setx0to be 1P(Y=0|X=x)=1 ( Tx)by total law of probabilityUsing these equations for probability ofY|Xwe can create an algorithm that selects values oftheta that maximize that probability for all data.
Logistic regression is a classification algorithm1 that works by trying to learn a function that approximates P(YjX). ... estimation(MLE).Assuchwearegoingtohavetwosteps:(1)writethelog-likelihoodfunction ... In this section we provide the mathematical derivations for the gradient of log-likelihood. The
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