Scaling Up Probabilistic Circuits by Latent Variable Distillation
This work addresses a bottleneck in scaling tractable probabilistic models for real-world applications, offering a novel method to improve performance, though it is incremental in leveraging existing deep models for supervision.
The paper tackles the challenge of scaling Probabilistic Circuits (PCs) to large datasets by proposing latent variable distillation, which uses deep generative models to supervise PC training, resulting in substantial performance boosts on image and language benchmarks, achieving competitive results against deep generative models.
Probabilistic Circuits (PCs) are a unified framework for tractable probabilistic models that support efficient computation of various probabilistic queries (e.g., marginal probabilities). One key challenge is to scale PCs to model large and high-dimensional real-world datasets: we observe that as the number of parameters in PCs increases, their performance immediately plateaus. This phenomenon suggests that the existing optimizers fail to exploit the full expressive power of large PCs. We propose to overcome such bottleneck by latent variable distillation: we leverage the less tractable but more expressive deep generative models to provide extra supervision over the latent variables of PCs. Specifically, we extract information from Transformer-based generative models to assign values to latent variables of PCs, providing guidance to PC optimizers. Experiments on both image and language modeling benchmarks (e.g., ImageNet and WikiText-2) show that latent variable distillation substantially boosts the performance of large PCs compared to their counterparts without latent variable distillation. In particular, on the image modeling benchmarks, PCs achieve competitive performance against some of the widely-used deep generative models, including variational autoencoders and flow-based models, opening up new avenues for tractable generative modeling. Our code can be found at https://github.com/UCLA-StarAI/LVD.