Algorithm 1.

MCMC inference of parametric dictionary learning variables

Require: Data xn, hyperparameters ℋn
1:	for n = 1, …, N do
2:	for m = 1, …, M do
3:	Sample atom indices ${\mathbf{z}}_{\mathbf{n}\mathbf{1}}^{(m)},\dots {\mathbf{z}}_{\mathbf{n}\mathbf{L}}^{(m)}$ or ${\mathbf{z}}_{\mathbf{n}}^{(m)}$
4:	Find ${ℐ}_{D_n}^{(m)}=\{k_1^{\prime },\dots ,k_L^{\prime }\}$ s.t. $z_{n{l}_{k_l^{\prime }}}^{(m)}=1$
5:	Sample atom coefficients $s_{n1}^{(m)},\dots ,s_{nL}^{(m)}$
6:	Sample noise vector ${\mathit{\epsilon }}_{\mathbf{n}}^{(m)}$
7:	Sample dictionary parameters ${\mathit{\theta }}_{\mathbf{n}\mathbf{k}}^{(m)},k\notin {ℐ}_{D_n}^{(m)}$
8:	Sample dictionary priors ${\mathbf{g}}_{\mathbf{n}\mathbf{1}}^{(m)},\dots ,{\mathbf{g}}_{\mathbf{n}\mathbf{K}}^{(m)},{\mathbf{G}}_{\mathbf{n}}^{(m)}$
9:	Sample atom selection probability priors ${\mathit{\pi }}_{\mathbf{n}}^{(m)}$
10:	Sample noise variance ${\gamma }_{{\epsilon }_n}^{(m)}$
11:	Sample ${\tilde{\mathit{\theta }}}_{\mathbf{n}}^{(m)}$ for generating ${\mathit{\theta }}_{\mathbf{n}\mathbf{k}}^{(m)},k\in {ℐ}_{D_n}^{(m)}$
12:	Compute ${\mathbf{D}}_{\mathbf{n}}^{(m)}=\left[\varphi \right({\mathit{\theta }}_{\mathbf{n}\mathbf{1}}^{(m)})\dots \varphi ({\mathit{\theta }}_{\mathbf{n}\mathbf{K}}^{(m)}\left)\right]$
13:	end for
14:	end for