mlsanityData to 7 Oct 2026

Probabilistic Generating Circuits

arXiv 2102.09768 ↗First posted 19 Feb 2021cs.AI cs.LGcited by 24

Not on the map. Why?

Abstract (arXiv)

Generating functions, which are widely used in combinatorics and probability theory, encode function values into the coefficients of a polynomial. In this paper, we explore their use as a tractable probabilistic model, and propose probabilistic generating circuits (PGCs) for their efficient representation. PGCs are strictly more expressive efficient than many existing tractable probabilistic models, including determinantal point processes (DPPs), probabilistic circuits (PCs) such as sum-product networks, and tractable graphical models. We contend that PGCs are not just a theoretical framework that unifies vastly different existing models, but also show great potential in modeling realistic data. We exhibit a simple class of PGCs that are not trivially subsumed by simple combinations of PCs and DPPs, and obtain competitive performance on a suite of density estimation benchmarks. We also highlight PGCs' connection to the theory of strongly Rayleigh distributions.

Key facts. Cited by 24 papers in the map (data through 7 Oct 2026). Builds on 17 of its 48 references that are in the map. First posted on arXiv 19 Feb 2021.

Builds on

17 of 48 references.

References · 17

  1. 2014Adam: A Method for Stochastic Optimizationcited by 36,960
  2. 2020Einsum Networks: Fast and Scalable Learning of Tractable Probabilistic Circuitscited by 102
  3. 2013A Differential Approach to Inference in Bayesian Networkscited by 93
  4. 2020Strudel: Learning Structured-Decomposable Probabilistic Circuitscited by 24
  5. 2014Learning the Parameters of Determinantal Point Process Kernelscited by 21
  6. 2014Expectation-Maximization for Learning Determinantal Point Processescited by 19
  7. 2014On the Expressive Efficiency of Sum Product Networkscited by 16
  8. 2019Learning Nonsymmetric Determinantal Point Processescited by 15
  9. 2019Smoothing Structured Decomposable Circuitscited by 14
  10. 2015Fixed-point algorithms for learning determinantal point processescited by 13
  11. 2014Large-Margin Determinantal Point Processescited by 8
  12. 2016Fast Mixing Markov Chains for Strongly Rayleigh Measures, DPPs, and Constrained Samplingcited by 8
5 more
  1. 2020On the Relationship Between Probabilistic Circuits and Determinantal Point Processescited by 8
  2. 2014AND/OR Multi-Valued Decision Diagrams (AOMDDs) for Graphical Modelscited by 6
  3. 2019Flexible Modeling of Diversity with Strongly Log-Concave Distributionscited by 6
  4. 2016Kronecker Determinantal Point Processescited by 5
  5. 2015The Libra Toolkit for Probabilistic Modelscited by 2

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2021: 2; 2022: 4; 2023: 5; 2024: 5; 2025: 6; 2026: 2.

24 papers.

Sort:

  1. 2023Tractable Control for Autoregressive Language Generationcited by 65
  2. 2022Adversarial random forests for density estimation and generative modelingcited by 44
  3. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
  4. 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
  5. 2021HyperSPNs: Compact and Expressive Probabilistic Circuitscited by 14
  6. 2022Lifted Inference with Linear Order Axiomcited by 13
  7. 2024Polynomial Semantics of Tractable Probabilistic Circuitscited by 12
  8. 2023Characteristic Circuitscited by 8
  9. 2024Restructuring Tractable Probabilistic Circuitscited by 7
  10. 2025How to Square Tensor Networks and Circuits Without Squaring Themcited by 5
  11. 2023Exact Bayesian Inference on Discrete Models via Probability Generating Functions: A Probabilistic Programming Approachcited by 4
  12. 2024Probabilistic Generating Circuits -- Demystifiedcited by 4
12 more
  1. 2025Rethinking Probabilistic Circuit Parameter Learningcited by 4
  2. 2022Hardness of Maximum Likelihood Learning of DPPscited by 3
  3. 2023Mixtures of All Treescited by 3
  4. 2024On the Expressive Power of Tree-Structured Probabilistic Circuitscited by 3
  5. 2025On the Hardness of Approximating Distributions with Tractable Probabilistic Modelscited by 2
  6. 2025The Limits of Tractable Marginalizationcited by 2
  7. 2021Sum-Product-Attention Networks: Leveraging Self-Attention in Probabilistic Circuitscited by 1
  8. 2024Probabilistic Circuits for Cumulative Distribution Functionscited by 1
  9. 2026Every Feedforward Neural Network Definable in an o-Minimal Structure Has Finite Sample Complexitycited by 1
  10. 2025Tractable Probabilistic Models for Investment Planningcited by 0
  11. 2025Learning Tractable Distributions Of Language Model Continuationscited by 0
  12. 2026Variance Computation for Weighted Model Counting with Knowledge Compilation Approachcited by 0