For the following problem, select all answers that are correct. Under certain conditions, minimizing mean-squared error for linear regression is equivalent to maximizing the log-likelihood of a probabilistic model. As a reminder, the mean-squared error is defined as E1 (Un – aw)². The probabilistic model assumes that Lmse (w) = w aw + En, where En is a "noise variable" that describes the 2N Yn prediction error. What conditions are necessary for the equivalence? A) The noise parameter €, should follow a normal distribution. B) The parameter N follows an Einstein distribution C) The conditional probability p (yn |æn, w) should follow a Poisson distribution. D) The conditional probability p(yn |æn , w) should follow a Gaussian distribution.
For the following problem, select all answers that are correct. Under certain conditions, minimizing mean-squared error for linear regression is equivalent to maximizing the log-likelihood of a probabilistic model. As a reminder, the mean-squared error is defined as E1 (Un – aw)². The probabilistic model assumes that Lmse (w) = w aw + En, where En is a "noise variable" that describes the 2N Yn prediction error. What conditions are necessary for the equivalence? A) The noise parameter €, should follow a normal distribution. B) The parameter N follows an Einstein distribution C) The conditional probability p (yn |æn, w) should follow a Poisson distribution. D) The conditional probability p(yn |æn , w) should follow a Gaussian distribution.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:For the following problem, select all answers that are correct.
Under certain conditions, minimizing mean-squared error for linear regression
is equivalent to maximizing the log-likelihood of a probabilistic model. As a
reminder, the mean-squared error is defined as
Lmse (w) = E, (Yn – x,w)². The probabilistic model assumes that
aw + En, where En is a "noise variable" that describes the
2N Ln
Yn
prediction error. What conditions are necessary for the equivalence?
A) The noise parameter €, should follow a normal distribution.
B) The parameter N follows an Einstein distribution
C) The conditional probability p (yn |æn, w) should follow a Poisson
distribution.
D) The conditional probability p(yn |æn, w) should follow a Gaussian
distribution.
D
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