Assume a joint distribution px, y of two random vectors x 2 Rn and y 2 Rn
Question:
Assume a joint distribution p¹x, yº of two random vectors x 2 Rn and y 2 Rn is a linear Gaussian model defined as follows:
p¹xº = N
????
x
, ????1
, where 2 Rn is the mean vector; 2 Rnn is the precision matrix; and p¹y j xº = N
????
y Ax +
b, L????1
, where A 2 Rnn, b 2 Rn, and L 2 Rnn is the precision matrix. Derive the mean vector and covariance matrix of the marginal distribution p¹yº in which the variable x has been integrated out.
Hints:
with M = ????
A???? BD????1C ????1.
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Related Book For
Machine Learning Fundamentals A Concise Introduction
ISBN: 9781108940023
1st Edition
Authors: Hui Jiang
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