Logistic regression aims to train the parameters from the training set D ={(x(i),y(i)), i1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x)=g(0¹ x)1(here g(z) is the logistic or sigmod function g(z)can predict the probability of a1+ e-znew instance x being labeled as 1. Please derive the following stochastic gradient ascentupdate rule for a logistic regression problem.0j = 0j + a(y(¹) — hz(x)))x;ave.=

Given that, D=x⇀i,y⇀i;i=1,2,3,...,my∈0,1hθ⇀x⇀=gθ⇀Tx⇀g(z) is the logistic function of…

Answered: Logistic regression aims to train the…

Database System Concepts

7th Edition

ISBN:9780078022159

Author:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Publisher:Abraham Silberschatz Professor, Henry F. Korth, S. Sudarshan

Chapter1: Introduction

Section: Chapter Questions

Problem 1PE

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Logistic regression aims to train the parameters from the training set D =
{(x(i),y(i)), i
1,2,...,m, y ¤ {0,1}} so that the hypothesis function h(x)
=
g(0¹ x)
1
(here g(z) is the logistic or sigmod function g(z)
can predict the probability of a
1+ e-z
new instance x being labeled as 1. Please derive the following stochastic gradient ascent
update rule for a logistic regression problem.
0j = 0j + a(y(¹) — hz(x)))x;
ave.
=

Expert Solution

Step 1

Given that,

$D = \{(\overset{⇀ (i)}{x}, \overset{⇀ (i)}{y})\}; i = 1, 2, 3, . . ., m y \in \{0, 1\} h \overset{⇀}{θ} (\overset{⇀}{x}) = g (\overset{⇀ T}{θ} \overset{⇀}{x}) g (z) i s t h e l o g i s t i c f u n c t i o n o f g (z) = \frac{1}{1 + e^{- z}} θ j = θ j + α (y^{(i)} - h \overset{⇀}{\overset{⇀}{θ} (\overset{⇀ (i)}{x})}) x_{j}^{(i)}$

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