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10. Let o : R →R be the logistic function defined by e" o(u) = 1+ eu Assume that 0

10. Let o : R →R be the logistic function defined by e" o(u) = 1+ eu Assume that 0

College Algebra
College Algebra
1st Edition
ISBN:9781938168383
Author:Jay Abramson
Publisher:Jay Abramson
Chapter6: Exponential And Logarithmic Functions
Section6.8: Fitting Exponential Models To Data
Problem 56SE: Recall that the general form of a logistic equation for a population is given by P(t)=c1+aebt , such...
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10. Let o : R→ R be the logistic function defined by eu o(u) 1+eu Assume that 0 < p < 1 is a probability. If u E R, then o(u) is between 0 and 1 so o(u) can be thought of as a probability. We can compare p with o(u) by computing the binary cross-entropy h(u) = -p log(o(u)) – (1 – p) log(1 – - σ(u), Compute the derivative h'(u). (This calculation is a key step when training a logistic regression model for binary classification using gradient descent.)
Transcribed Image Text:10. Let o : R→ R be the logistic function defined by eu o(u) 1+eu Assume that 0 < p < 1 is a probability. If u E R, then o(u) is between 0 and 1 so o(u) can be thought of as a probability. We can compare p with o(u) by computing the binary cross-entropy h(u) = -p log(o(u)) – (1 – p) log(1 – - σ(u), Compute the derivative h'(u). (This calculation is a key step when training a logistic regression model for binary classification using gradient descent.)
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