Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuits
arXiv:2004.06231
Abstract
Probabilistic circuits (PCs) are a promising avenue for probabilistic modeling, as they permit a wide range of exact and efficient inference routines. Recent ``deep-learning-style'' implementations of PCs strive for a better scalability, but are still difficult to train on real-world data, due to their sparsely connected computational graphs. In this paper, we propose Einsum Networks (EiNets), a novel implementation design for PCs, improving prior art in several regards. At their core, EiNets combine a large number of arithmetic operations in a single monolithic einsum-operation, leading to speedups and memory savings of up to two orders of magnitude, in comparison to previous implementations. As an algorithmic contribution, we show that the implementation of Expectation-Maximization (EM) can be simplified for PCs, by leveraging automatic differentiation. Furthermore, we demonstrate that EiNets scale well to datasets which were previously out of reach, such as SVHN and CelebA, and that they can be used as faithful generative image models.
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Cited by in corpus (6)
- On the Complexity of SHAP-Score-Based Explanations: Tractability via Knowledge Compilation and Non-Approximability Results
- Strudel: Learning Structured-Decomposable Probabilistic Circuits
- Continuous Mixtures of Tractable Probabilistic Models
- Anomaly Detection using Generative Models and Sum-Product Networks in Mammography Scans
- The Tractability of SHAP-Score-Based Explanations over Deterministic and Decomposable Boolean Circuits
- Scalable Probabilistic Routes