Algorithm 1.

Stochastic search for MAP estimation of DPM-GGM parameters

	Input: Initial parameter configurations ${(L,{\xi }_{1:n},G_{1:L}^{*})}_{[1]},\dots ,{(L,{\xi }_{1:n},G_{1:L}^{*})}_{[I]}$.
	Input: # chains N, # follow-up moves C, max # of iterations without score increment before stopping S.
	Input: Max # consecutive mode-break moves R, # top modes disregarded in move-break moves D.
	Input: Split and merge move parameters Q, f, t.
	Input: Mixing ratios: local shotgun graph moves to local ξ-moves g, local ξ-moves to split moves h.
1
2	for i ← 1 to N do
3		% Select the initial configuration for the i-th search chain
4		if i ≤ I then
5			$(L,{\xi }_{1:n},G_{1:L}^{*})\leftarrow {(L,{\xi }_{1:n},G_{1:L}^{*})}_{[i]}$
6		else
7			d ~ Multinomial(1, exp(last_best_score[1:I]))
8			$(L,{\xi }_{1:n},G_{1:L}^{*})\leftarrow {(L,{\xi }_{1:n},G_{1:L}^{*})}_{[d]}$
9
10		% Start the i-th run of stochastic search
11		k ← 0, c ← 0, last_best_score[i] ← −∞
12		while c < S do
13			% Local moves
14			while c < C do
15				if g * k is an integer then
16					Perform local update moves on ξ1, …, ξn
17					Perform the merge move with tuning parameters (f, t)
18					if g * h * k is an integer then
19						Perform the split move with tuning parameters (f, t)
20				else
21					Perform local shotgun update moves on $G_1^{*},\dots ,G_L^{*}$
22
23				if score > last_best_score then c ← 0
24				else c ← c + 1
25
26			% Move break moves
27			r ← 1, B ← 1
28			while c ≥ C and r ≤ R do
29				Perform a mode break move with tuning parameters (B, D)
30				for j ← 1 to C do
31					Perform local shotgun update moves on $G_1^{*},\dots ,G_L^{*}$
32
33				if score > last_best_score then c ← 0
34				else c ← c + C, r ← r + 1, B ← B + 1
35
36			% Global graph jump move
37			if r > R then
38				l ~ uniform{1, …, L}
39				Perform a global jump move on $G_l^{*}$
40				c ← 0
41
42			k ← k + 1
43			if score > last_best_score[i] then last_best_score[i] = score, ${(L,{\xi }_{1:n},G_{1:L}^{*})}_{[i]}^{*}\leftarrow (L,{\xi }_{1:n},G_{1:L}^{*})$
44
45	return ${(L,{\xi }_{1:n},G_{1:L}^{*})}_{[1:N]}^{*}$