θ(new)
n,c = EFn,c(D; θ)/

EFn,c(D; θ).

(4)

(cid:88)

c∈in(n)

This paper uses a hybrid EM algorithm, which uses mini-batch EM updates to initiate the training
process, and switch to full-batch EM updates afterwards. Speciﬁcally, in mini-batch EM, θ(new) are
computed using mini-batches of samples, and the parameters are updated towards the taget with a
step size η: θ(k+1)← (1 − η)θ(k) + ηθ(new); when using full-batch EM, we iteratively compute the
updated parameters θ(new) using the whole dataset. Fig. 3 demonstrates that this hybrid approach
offers faster convergence speed compared to using full-batch or mini-batch EM only.

4.2 Regularizing Deterministic PCs
Tractable Regularization of Probabilistic Circuits