1. Logistic regression with ±1 labels. Logistic regression (with ±1 labels) maximizes the likelihood L(βο,β) = Π P(X;) Π (1 - p(X;)), = i:Y₁=1 i:Y₁=-1 1 e³o+BTI = 1+e-(Bo+BT) 1+eBo+3x p(x) = Show that this is equivalent to minimizing the cost function n l(Bo, B) = log(1 + exp(-Yi (Bo + BTX₂))). i=1 Hint: Maximizing the likelihood is equivalent to minimizing the negative log-likelihood.
1. Logistic regression with ±1 labels. Logistic regression (with ±1 labels) maximizes the likelihood L(βο,β) = Π P(X;) Π (1 - p(X;)), = i:Y₁=1 i:Y₁=-1 1 e³o+BTI = 1+e-(Bo+BT) 1+eBo+3x p(x) = Show that this is equivalent to minimizing the cost function n l(Bo, B) = log(1 + exp(-Yi (Bo + BTX₂))). i=1 Hint: Maximizing the likelihood is equivalent to minimizing the negative log-likelihood.
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Transcribed Image Text:1. Logistic regression with ±1 labels. Logistic regression (with ±1 labels) maximizes the
likelihood
L(Bo, B)= II P(Xi) II (1-p(Xi)),
i:Y₂=1
i:Yį=-1
1
eBo+3x
=
1+e-(Bo+BTx) 1+eo+T
p(x) =
Show that this is equivalent to minimizing the cost function
n
l(Bo, B) = log(1 + exp(-Y; (Bo + BTX;))).
i=1
Hint: Maximizing the likelihood is equivalent to minimizing the negative log-likelihood.
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