SlowGuess/NeurIPS_2023_OCR huggingface dataset:
PARAMETER a	5	7	9	11	13	15
ALGORITHM 1	0.40 (0.15)	0.62 (0.04)	0.93 (0.02)	1 (0)	1 (0)	1 (0)
EM-GMM	0.45 (0.04)	0.46 (0.03)	0.46 (0.04)	0.46 (0.04)	0.46 (0.04)	0.45 (0.07)
SC	0 (0)	0.07 (0.05)	0.83 (0.15)	0.85 (0.33)	0.93 (0.24)	0.82 (0.37)
IR_LS	0 (0)	0.20 (0.13)	0.93 (0.14)	1 (0)	0.98 (0.12)	1 (0)
attSBM	0 (0)	0.07 (0.05)	0.82 (0.15)	0.86 (0.33)	0.42 (0.48)	0.59 (0.49)
Table 3: Average ARI of the different algorithms over 60 trials with standard deviation in brackets obtained for Figure (4b).
PARAMETER r	0	1	2	3	4	5
ALGORITHM 1	0.47 (0.29)	0.82 (0.03)	0.97 (0.02)	1 (0)	1 (0)	1 (0)
EM-GMM	0 (0)	0.46 (0.04)	0.9 (0.02)	1 (0)	1 (0)	1 (0)
SC	0.36 (0.28)	0.38 (0.27)	0.35 (0.26)	0.40 (0.26)	0.37 (0.28)	0.35 (0.26)
IR_LS	0.42 (0.29)	0.65 (0.31)	0.91 (0.21)	0.97 (0.15)	0.97 (0.14)	0.98 (0.12)
attSBM	0.36 (0.28)	0.38 (0.27)	0.38 (0.30)	0.59 (0.43)	0.57 (0.46)	0.50 (0.43)
We also provide in Figure 4 comparison of Algorithm 1 with  $IR\_sLs$  and  $attSBM$  on weighted networks with attributes exponentially distributed. We observe that contrary to Algorithm 1,  $IR\_sLs$  and  $attSBM$  do not perform well in that setting (which is expected as they are designed for binary network and Gaussian attributes).
(a) Varying  $\lambda_w^{-1}$ , with  $\lambda_{a} = 1 / 2$ .
(b) Varying  $\lambda_{a}^{-1}$ , with  $\lambda_w = 1/2$ .
Figure 4: Performance on weighted networks ( $n = 600$ ,  $K = 2$ ) with edge-weight distributions  $f_{\mathrm{in}} = (1 - p)\delta_0 + p\operatorname{Exp}(\lambda_w)$ ,  $f_{\mathrm{out}} = (1 - p)\delta_0 + p\operatorname{Exp}(1)$  with  $p = 5n^{-1}\log n$ , and exponentially distributed attributes  $h_1 \sim \operatorname{Exp}(1)$  and  $h_2 = \operatorname{Exp}(\lambda_a)$ . Results are averaged over 20 runs.
C.1 Robustness to the choice of  $d_{\psi^*}$  and  $d_{\phi^*}$
We show in Figure 5 that using a divergence (distribution) for edge weights (Figure 5a and node attributes (Figure 5b different from the distribution used to generate the data does not impact the performance of Algorithm 1. We note that a similar observation was done in previous papers using Bregman divergence for clustering [6, 23].
(a) Various  $d_{\psi^*}$ . Poisson is the correct model.
(b) Various  $d_{\phi^*}$ . Poisson is the correct model.
Figure 5: Performance of Algorithm 1 when  $d_{\psi^*}$  or  $d_{\phi^*}$  do not correspond to the model that generated the data. The different curves show the Adjusted Rand Index (ARI) [21] averaged over 20 realisations with the standard deviations as error bars.
(a)  $n = 400$ ,  $K = 4$ ,  $f_{\mathrm{in}} = (1 - p)\delta_0(x) + p\mathrm{Poi}(\mu_{in})$  and  $f_{\mathrm{out}} = (1 - q)\delta_0(x) + q\mathrm{Poi}(5)$ , with  $p = 0.04$  and  $q = 0.01$ . Attributes are 2d-Gaussians with unit variances and mean equally spaced the circle of radius  $r = 2$ .
(b)  $n = 400$ ,  $K = 2$ ,  $f_{\mathrm{in}} = (1 - p)\delta_0(x) + p\mathrm{Nor}(2,1)$  and  $f_{\mathrm{out}} = (1 - q)\delta_0(x) + q\mathrm{Nor}(0,1)$ , with  $p = 0.04$  and  $q = 0.01$ . Attributes are Poisson with means  $\nu_{1}$  (for nodes in cluster 1) and 3 (for nodes in cluster 2).