Algorithm 1.

Pseudocode for the HVB algorithm.

Initialize the hyperprior parameters a0 and b0, and set the initial parameter value to 0 (i.e. β = 0).

while convergence criteria not met do

Evaluate the data-dependent variational parameters ξ = {ξt} for each data points xt (t = 1, …, T).

Update the parameter variational posterior mean μT and variance ΣT.

Update the noise precision hyperparameter [A].

Update the hyperprior parameters aT and bj,T (j = 0, …, d).

Compute the variational lower bound of marginal log-likelihood L̃ (Eq. 22).

end while

end