mlsanityData to 7 Oct 2026

Characteristic Circuits

arXiv 2312.07790 ↗First posted 12 Dec 2023cs.LG stat.MLcited by 8

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Abstract (arXiv)

In many real-world scenarios, it is crucial to be able to reliably and efficiently reason under uncertainty while capturing complex relationships in data. Probabilistic circuits (PCs), a prominent family of tractable probabilistic models, offer a remedy to this challenge by composing simple, tractable distributions into a high-dimensional probability distribution. However, learning PCs on heterogeneous data is challenging and densities of some parametric distributions are not available in closed form, limiting their potential use. We introduce characteristic circuits (CCs), a family of tractable probabilistic models providing a unified formalization of distributions over heterogeneous data in the spectral domain. The one-to-one relationship between characteristic functions and probability measures enables us to learn high-dimensional distributions on heterogeneous data domains and facilitates efficient probabilistic inference even when no closed-form density function is available. We show that the structure and parameters of CCs can be learned efficiently from the data and find that CCs outperform state-of-the-art density estimators for heterogeneous data domains on common benchmark data sets.

Key facts. Cited by 8 papers in the map (data through 7 Oct 2026). Builds on 18 of its 49 references that are in the map. First posted on arXiv 12 Dec 2023.

Builds on

18 of 49 references.

References · 18

  1. 2022Semantic Probabilistic Layers for Neuro-Symbolic Learningcited by 103
  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. 2015Fast Two-Sample Testing with Analytic Representations of Probability Measurescited by 53
  5. 2019A Characteristic Function Approach to Deep Implicit Generative Modelingcited by 25
  6. 2013The Randomized Dependence Coefficientcited by 24
  7. 2019Bayesian Learning of Sum-Product Networkscited by 24
  8. 2020Strudel: Learning Structured-Decomposable Probabilistic Circuitscited by 24
  9. 2021Probabilistic Generating Circuitscited by 24
  10. 2021Interventional Sum-Product Networks: Causal Inference with Tractable Probabilistic Modelscited by 22
  11. 2020Probabilistic Circuits for Variational Inference in Discrete Graphical Modelscited by 20
  12. 2022Continuous Mixtures of Tractable Probabilistic Modelscited by 19
6 more
  1. 2019Deep Structured Mixtures of Gaussian Processescited by 16
  2. 2022Tractable Uncertainty for Structure Learningcited by 15
  3. 2018Automatic Bayesian Density Analysiscited by 10
  4. 2016The Sum-Product Theorem: A Foundation for Learning Tractable Modelscited by 8
  5. 2021Leveraging Probabilistic Circuits for Nonparametric Multi-Output Regressioncited by 8
  6. 2022Certifying Fairness of Probabilistic Circuitscited by 3

Built on by

Cited by year (2026 to 7 Oct)

Citing papers per year: 2024: 4; 2025: 3; 2026: 1.

8 papers.

  1. 2024What is the Relationship between Tensor Factorizations and Circuits (and How Can We Exploit it)?cited by 22
  2. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  3. 2024Building Expressive and Tractable Probabilistic Generative Models: A Reviewcited by 12
  4. 2025How to Square Tensor Networks and Circuits Without Squaring Themcited by 5
  5. 2024chiSPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domainscited by 3
  6. 2025The Limits of Tractable Marginalizationcited by 2
  7. 2025Approximate Bayesian Inference via Bitstring Representationscited by 1
  8. 2026Variance Computation for Weighted Model Counting with Knowledge Compilation Approachcited by 0