mlsanityData to 14 Oct 2026

PSD Representations for Effective Probability Models

arXiv 2106.16116 ↗First posted 30 Jun 2021cs.LG math.ST stat.MLcited by 23

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Abstract (arXiv)

Finding a good way to model probability densities is key to probabilistic inference. An ideal model should be able to concisely approximate any probability while being also compatible with two main operations: multiplications of two models (product rule) and marginalization with respect to a subset of the random variables (sum rule). In this work, we show that a recently proposed class of positive semi-definite (PSD) models for non-negative functions is particularly suited to this end. In particular, we characterize both approximation and generalization capabilities of PSD models, showing that they enjoy strong theoretical guarantees. Moreover, we show that we can perform efficiently both sum and product rule in closed form via matrix operations, enjoying the same versatility of mixture models. Our results open the way to applications of PSD models to density estimation, decision theory and inference.

Key facts. Cited by 23 papers in the map (data through 14 Oct 2026). Builds on 10 of its 44 references that are in the map. First posted on arXiv 30 Jun 2021.

Builds on

10 of 44 references.

References · 10

  1. 2013Auto-Encoding Variational Bayescited by 4,053
  2. 2016Kernel Mean Embedding of Distributions: A Review and Beyondcited by 364
  3. 2016Generalization Properties of Learning with Random Featurescited by 164
  4. 2013Density Estimation in Infinite Dimensional Exponential Familiescited by 42
  5. 2018Massively scalable Sinkhorn distances via the Nystr"om methodcited by 41
  6. 2020Non-parametric Models for Non-negative Functionscited by 41
  7. 2020A General Framework for Consistent Structured Prediction with Implicit Loss Embeddingscited by 35
  8. 2020Finding Global Minima via Kernel Approximationscited by 23
  9. 2020Interpolation and Learning with Scale Dependent Kernelscited by 7
  10. 2020A Statistical Perspective on Coreset Density Estimationcited by 6

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Cited by year (2026 to 14 Oct)

Citing papers per year: 2021: 2; 2022: 2; 2023: 7; 2024: 4; 2025: 4; 2026: 4.

23 papers.

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  1. 2023Subtractive Mixture Models via Squaring: Representation and Learningcited by 39
  2. 2024Sum of Squares Circuitscited by 21
  3. 2024On the Relationship Between Monotone and Squared Probabilistic Circuitscited by 14
  4. 2023Squared Neural Families: A New Class of Tractable Density Modelscited by 12
  5. 2021Sampling from Arbitrary Functions via PSD Modelscited by 8
  6. 2024Exact, Fast and Expressive Poisson Point Processes via Squared Neural Familiescited by 6
  7. 2021Learning PSD-valued functions using kernel sums-of-squarescited by 5
  8. 2025How to Square Tensor Networks and Circuits Without Squaring Themcited by 5
  9. 2023Non-Parametric Learning of Stochastic Differential Equations with Non-asymptotic Fast Rates of Convergencecited by 4
  10. 2022Non-Convex Optimization with Certificates and Fast Rates Through Kernel Sums of Squarescited by 2
  11. 2023Efficient Sampling of Stochastic Differential Equations with Positive Semi-Definite Modelscited by 1
  12. 2025Squared families: Searching beyond regular probability modelscited by 1
11 more
  1. 2025Scalable and adaptive prediction bands with kernel sum-of-squarescited by 1
  2. 2026How to Approximate Inference with Subtractive Mixture Modelscited by 1
  3. 2022Measuring dissimilarity with diffeomorphism invariancecited by 0
  4. 2023GloptiNets: Scalable Non-Convex Optimization with Certificatescited by 0
  5. 2023Kernelised Normalising Flowscited by 0
  6. 20232-Cats: 2D Copula Approximating Transformscited by 0
  7. 2024Closed-form Filtering for Non-linear Systemscited by 0
  8. 2025Scalable Expectation Estimation with Subtractive Mixture Modelscited by 0
  9. 2026Learning Markov Processes as Sum-of-Square Forms for Analytical Belief Propagationcited by 0
  10. 2026Distributionally Faithful Imputation via Positive Semi-Definite Kernel Density Estimationcited by 0
  11. 2026Density-Matrix Reinforcement Learningcited by 0