SPFlow: An Easy and Extensible Library for Deep Probabilistic Learning using Sum-Product Networks
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Abstract (arXiv)
We introduce SPFlow, an open-source Python library providing a simple interface to inference, learning and manipulation routines for deep and tractable probabilistic models called Sum-Product Networks (SPNs). The library allows one to quickly create SPNs both from data and through a domain specific language (DSL). It efficiently implements several probabilistic inference routines like computing marginals, conditionals and (approximate) most probable explanations (MPEs) along with sampling as well as utilities for serializing, plotting and structure statistics on an SPN. Moreover, many of the algorithms proposed in the literature to learn the structure and parameters of SPNs are readily available in SPFlow. Furthermore, SPFlow is extremely extensible and customizable, allowing users to promptly distill new inference and learning routines by injecting custom code into a lightweight functional-oriented API framework. This is achieved in SPFlow by keeping an internal Python representation of the graph structure that also enables practical compilation of an SPN into a TensorFlow graph, C, CUDA or FPGA custom code, significantly speeding-up computations.
Key facts. Cited by 26 papers in the map (data through 7 Oct 2026). First posted on arXiv 11 Jan 2019.
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Citing papers per year: 2021: 5; 2022: 9; 2023: 4; 2024: 2; 2025: 4; 2026: 2.
26 papers.
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- 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
- 2023Tractable Control for Autoregressive Language Generationcited by 65
- 2022Training and Inference on Any-Order Autoregressive Models the Right Waycited by 64
- 2021Tractable Regularization of Probabilistic Circuitscited by 39
- 2022Scaling Up Probabilistic Circuits by Latent Variable Distillationcited by 35
- 2024Scaling Tractable Probabilistic Circuits: A Systems Perspectivecited by 23
- 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuitscited by 19
- 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
- 2023Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisitioncited by 17
- 2025A Survey on Active Feature Acquisition Strategiescited by 16
- 2022Tractable Boolean and Arithmetic Circuitscited by 9
- 2021A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queriescited by 7
14 more
- 2023Probabilistic Circuits That Know What They Don't Knowcited by 7
- 2024Generating Likely Counterfactuals Using Sum-Product Networkscited by 6
- 2025Rethinking Probabilistic Circuit Parameter Learningcited by 4
- 2021Exchangeability-Aware Sum-Product Networkscited by 2
- 2022Certified Data Removal in Sum-Product Networkscited by 2
- 2022DeeProb-kit: a Python Library for Deep Probabilistic Modellingcited by 2
- 2021Explaining Deep Tractable Probabilistic Models: The sum-product network casecited by 1
- 2022Variational Flow Graphical Modelcited by 1
- 2021Fast Private Parameter Learning and Inference for Sum-Product Networkscited by 0
- 2022Outlier Explanation via Sum-Product Networkscited by 0
- 2025Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulationcited by 0
- 2025Tractable Probabilistic Models for Investment Planningcited by 0
- 2026The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Modelscited by 0
- 2026Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributionscited by 0
- 2026Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributions5 Aug 2026
- 2026The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models13 May 2026
- 2025Tractable Probabilistic Models for Investment Planning17 Nov 2025
- 2025Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation25 Jul 2025
- 2025Rethinking Probabilistic Circuit Parameter Learning26 May 2025
- 2025A Survey on Active Feature Acquisition Strategies16 Feb 2025
- 2024Scaling Tractable Probabilistic Circuits: A Systems Perspective2 Jun 2024
- 2024Generating Likely Counterfactuals Using Sum-Product Networks25 Jan 2024
- 2023Tractable Control for Autoregressive Language Generation15 Apr 2023
- 2023Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition27 Feb 2023
- 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits16 Feb 2023
- 2023Probabilistic Circuits That Know What They Don't Know13 Feb 2023
14 more
- 2022DeeProb-kit: a Python Library for Deep Probabilistic Modelling8 Dec 2022
- 2022Sparse Probabilistic Circuits via Pruning and Growing22 Nov 2022
- 2022Concrete Score Matching: Generalized Score Matching for Discrete Data2 Nov 2022
- 2022Scaling Up Probabilistic Circuits by Latent Variable Distillation10 Oct 2022
- 2022Certified Data Removal in Sum-Product Networks4 Oct 2022
- 2022Outlier Explanation via Sum-Product Networks18 Jul 2022
- 2022Variational Flow Graphical Model6 Jul 2022
- 2022Training and Inference on Any-Order Autoregressive Models the Right Way26 May 2022
- 2022Tractable Boolean and Arithmetic Circuits7 Feb 2022
- 2021Explaining Deep Tractable Probabilistic Models: The sum-product network case19 Oct 2021
- 2021Exchangeability-Aware Sum-Product Networks11 Oct 2021
- 2021Tractable Regularization of Probabilistic Circuits4 Jun 2021
- 2021Fast Private Parameter Learning and Inference for Sum-Product Networks15 Apr 2021
- 2021A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queries11 Feb 2021
- 2022Concrete Score Matching: Generalized Score Matching for Discrete Datacited by 144
- 2023Tractable Control for Autoregressive Language Generationcited by 65
- 2022Training and Inference on Any-Order Autoregressive Models the Right Waycited by 64
- 2021Tractable Regularization of Probabilistic Circuitscited by 39
- 2022Scaling Up Probabilistic Circuits by Latent Variable Distillationcited by 35
- 2024Scaling Tractable Probabilistic Circuits: A Systems Perspectivecited by 23
- 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuitscited by 19
- 2022Sparse Probabilistic Circuits via Pruning and Growingcited by 17
- 2023Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisitioncited by 17
- 2025A Survey on Active Feature Acquisition Strategiescited by 16
- 2022Tractable Boolean and Arithmetic Circuitscited by 9
- 2021A Compositional Atlas of Tractable Circuit Operations: From Simple Transformations to Complex Information-Theoretic Queriescited by 7
12 most cited of 26 All 26 (JSON)
- 2026Diverse and Plausible Algorithmic Recourse via Tractable Recourse Distributions5 Aug 2026
- 2026The Expressivity Boundary of Probabilistic Circuits: A Comparison with Large Language Models13 May 2026
- 2025Tractable Probabilistic Models for Investment Planning17 Nov 2025
- 2025Counterfactual Explanations in Medical Imaging: Exploring SPN-Guided Latent Space Manipulation25 Jul 2025
- 2025Rethinking Probabilistic Circuit Parameter Learning26 May 2025
- 2025A Survey on Active Feature Acquisition Strategies16 Feb 2025
- 2024Scaling Tractable Probabilistic Circuits: A Systems Perspective2 Jun 2024
- 2024Generating Likely Counterfactuals Using Sum-Product Networks25 Jan 2024
- 2023Tractable Control for Autoregressive Language Generation15 Apr 2023
- 2023Acquisition Conditioned Oracle for Nongreedy Active Feature Acquisition27 Feb 2023
- 2023Understanding the Distillation Process from Deep Generative Models to Tractable Probabilistic Circuits16 Feb 2023
- 2023Probabilistic Circuits That Know What They Don't Know13 Feb 2023
12 newest of 26 All 26 (JSON)