The pywmi Framework and Toolbox for Probabilistic Inference using Weighted Model Integration

Kolb, Samuel; Morettin, Paolo; Martires, Pedro Zuidberg Dos; Sommavilla, Francesco; Passerini, Andrea; Sebastiani, Roberto; Raedt, Luc De

doi:10.24963/ijcai.2019/946

Cited by 7 publications

(7 citation statements)

References 3 publications

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“…This is also true for Sampo, the first MC-based WMI algorithm presented in [Zuidberg Dos Martires et al, 2019]. Investigating ad-hoc MC integration techniques is, however, a promising future research direction, especially as [Kolb et al, 2019a].…”

Section: Integrationmentioning

confidence: 91%

“…Following observations made by Kolb et al [2019a], we reformulate weighted model integration using a weight function with no (hidden) combinatorics. Pulling out the combinatorics of the weight function foreshadows the separation of the WMI problem into a combinatorics problem and an integration problem (cf.…”

Section: A Canonical Formulationmentioning

confidence: 99%

“…In Equation 4we see the two sub-problems that make up WMI: 1) finding all disjoint regions encoded in the support φ(x, b) and 2) integrating out the continuous variables over these regions. Kolb et al [2019a] dubbed the region finding problem λ-SMT. In the case of exclusively linear constraints, the regions form convex polytopes.…”

Section: A Canonical Formulationmentioning

confidence: 99%

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Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Morettin

Martires

Kolb

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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Real world decision making problems often involve both discrete and continuous variables and require a combination of probabilistic and deterministic knowledge. Stimulated by recent advances in automated reasoning technology, hybrid (discrete+continuous) probabilistic reasoning with constraints has emerged as a lively and fast growing research field. In this paper we provide a survey of existing techniques for hybrid probabilistic inference with logic and algebraic constraints. We leverage weighted model integration as a unifying formalism and discuss the different paradigms that have been used as well as the expressivity-efficiency trade-offs that have been investigated. We conclude the survey with a comparative overview of existing implementations and a critical discussion of open challenges and promising research directions.

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Section: Integrationmentioning

confidence: 91%

Section: A Canonical Formulationmentioning

confidence: 99%

Section: A Canonical Formulationmentioning

confidence: 99%

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Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Morettin

Martires

Kolb

et al. 2021

Proceedings of the Thirtieth International Joint Conference on Artificial Intelligence

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“…While the content of this thesis focuses on theory, I also contributed to pywmi [50] 1 , a Python3 library that uni es the technical e orts of di erent research groups into a single framework for WMI modelling and inference.…”

Section: Contributionsmentioning

confidence: 99%

Learning and Reasoning in Hybrid Structured Spaces

Morettin

2022

Frontiers in Artificial Intelligence and Applications

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Many real world AI applications involve reasoning on both continuous and discrete variables, while requiring some level of symbolic reasoning that can provide guarantees on the system's behaviour. Unfortunately, most of the existing probabilistic models do not e ciently support hard constraints or they are limited to purely discrete or continuous scenarios. Weighted Model Integration (WMI) is a recent and general formalism that enables probabilistic modeling and inference in hybrid structured domains. A di erence of WMI-based inference algorithms with respect to most alternatives is that probabilities are computed inside a structured support involving both logical and algebraic relationships between variables. While some progress has been made in the last years and the topic is increasingly gaining interest from the community, research in this area is at an early stage. These aspects motivate the study of hybrid and symbolic probabilistic models and the development of scalable inference procedures and e ective learning algorithms in these domains. This PhD Thesis embodies my e ort in studying scalable reasoning and learning techniques in the context of WMI. Now that's almost over, I can say it has been a fun ride. This crazy-fast, colorful journey wouldn't have been the same without the wonderful people I met along the way. Thank you Andrea, thank you Roberto for your kindness and patience in guiding me through these challenging years. Doing a PhD under your supervision has been a life-changing experience and one of the best decisions I've ever made. Life in Trento wouldn't have been as joyful without Marco, Stefano, Dragone, Gianni, Luca, Gianluca and the whole SML family, Edoardo, Zaki, Alessandra, Daniele, Sivam, Genc, Mesay.. I couldn't hope for more supportive and easy-going pals to hang with. I would like to thank Luc, Samuel, Guy, Antonio, Zhe, Fanqi and all the people I met during my visits at KU Leuven and UCLA. Thank you for being so welcoming, working with you was a pleasure and a privilege.

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“…As already discussed, MP-MI shares the same complexity as SMI in that its worst-case complexity is exponential in the primal graph treewidth and diameter. Many recent efforts in WMI converged in the pywmi [20] python framework.…”

Section: Related Workmentioning

confidence: 99%

Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing

Zeng,

Yan,

Morettin

et al. 2019

Preprint

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Weighted model integration (WMI) is a very appealing framework for probabilistic inference: it allows to express the complex dependencies of real-world hybrid scenarios where variables are heterogeneous in nature (both continuous and discrete) via the language of Satisfiability Modulo Theories (SMT); as well as computing probabilistic queries with complex logical constraints. Recent work has shown WMI inference to be reducible to a model integration (MI) problem, under some assumptions, thus effectively allowing hybrid probabilistic reasoning by volume computations. In this paper, we introduce a novel formulation of MI via a message passing scheme that allows to efficiently compute the marginal densities and statistical moments of all the variables in linear time. As such, we are able to amortize inference for rich MI queries when they conform to the problem structure, here represented as the primal graph associated to the SMT formula. Furthermore, we theoretically trace the tractability boundaries of exact MI. Indeed, we prove that in terms of the structural requirements on the primal graph that make our MI algorithm tractable -bounding its diameter and treewidth -the bounds are not only sufficient, but necessary for tractable inference via MI.

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The pywmi Framework and Toolbox for Probabilistic Inference using Weighted Model Integration

Cited by 7 publications

References 3 publications

Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Hybrid Probabilistic Inference with Logical and Algebraic Constraints: a Survey

Learning and Reasoning in Hybrid Structured Spaces

Hybrid Probabilistic Inference with Logical Constraints: Tractability and Message Passing

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