Report assignment (3)
Bayesian sparse regression
1. Prepare an arbitrary polynomial model Ex: y = x3 – x2
and generate a dataset of size N involving Gaussian noise Normal(0,1).
Ex: (x1,y1), …, (xN,yN)
where yi = xi3 + xi2 + epsiloni , epsiloni ~Normal(0,1) 2. Calculate Bayesian posterior probability of the parameters of
linear model. And, plot a relaMonship between N and the variance of the posterior. Here, let the prior be, P( betai | alphai ) =
Normal( 0, alphai ), where alphai = 1 is a constant for each i.
3. Implement the Bayesian sparse regression with ARD and apply to the generated dataset. Namely, let the prior alphai be a variable for each i and maximize the evidence with respect to alphai.
EsMmate the Bayesian posterior of the parameters of linear model under the esMmated alphai.
