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1. Efficient Inference for Untied MLNs

   https://doi.org/10.24963/ijcai.2017/644  

   Sarkhel, Somdeb ; Venugopal, Deepak ; Ruozzi, Nicholas ; Gogate, Vibhav ( August 2017 , Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence)

   We address the problem of scaling up local-search or sampling-based inference in Markov logic networks (MLNs) that have large shared sub-structures but no (or few) tied weights. Such untied MLNs are ubiquitous in practical applications. However, they have very few symmetries, and as a result lifted inference algorithms--the dominant approach for scaling up inference--perform poorly on them. The key idea in our approach is to reduce the hard, time-consuming sub-task in sampling algorithms, computing the sum of weights of features that satisfy a full assignment, to the problem of computing a set of partition functions of graphical models, each defined over the logical variables in a first-order formula. The importance of this reduction is that when the treewidth of all the graphical models is small, it yields an order of magnitude speedup. When the treewidth is large, we propose an over-symmetric approximation and experimentally demonstrate that it is both fast and accurate.
2. Correlated Equilibria for Approximate Variational Inference in MRFs

   Ortiz, Luis E. ; Wang, Boshen ; Gong, Ze ( January 2020 , Proceedings of Machine Learning Research)

   Jaeger, Manfred ; Nielsen, Thomas Dyhre (Ed.)

   Almost all of the work in graphical models for game theory has mirrored previous work in probabilistic graphical models. Our work considers the opposite direction: Taking advantage of advances in equilibrium computation for probabilistic inference. In particular, we present formulations of inference problems in Markov random fields (MRFs) as computation of equilibria in a certain class of game-theoretic graphical models. While some previous work explores this direction, we still lack a more precise connection between variational probabilistic inference in MRFs and correlated equilibria. This paper sharpens the connection, which helps us exploit relatively more recent theoretical and empirical results from the literature on algorithmic and computational game theory on the tractable, polynomial-time computation of exact or approximate correlated equilibria in graphical games with arbitrary, loopy graph structure. Our work discusses how to design new algorithms with equally tractable guarantees for the computation of approximate variational inference in MRFs. In addition, inspired by a previously stated game-theoretic view of tree-reweighted message-passing techniques for belief inference as a zero-sum game, we propose a different, general-sum potential game to design approximate fictitious-play techniques. Empirical evaluations on synthetic experiments and on an application to soft de-noising on real-world image datasets illustrate the performance ofmore »our proposed approach and shed some light on the conditions under which the resulting belief inference algorithms may be most effective relative to standard state-of-the-art methods.« less
3. Fine-Grained Explanations Using Markov Logic

   Al-Farabi, K.M. ; Sarkhel, S. ; Dey, S. ; Venugopal, D. ( January 2019 , Fine-Grained Explanations Using Markov LogicMachine Learning and Knowledge Discovery in Databases)

   Explaining the results of Machine learning algorithms is crucial given the rapid growth and potential applicability of these methods in critical domains including healthcare, defense, autonomous driving, etc. In this paper, we address this problem in the context of Markov Logic Networks (MLNs) which are highly expressive statistical relational models that combine first-order logic with probabilistic graphical models. MLNs in general are known to be interpretable models, i.e., MLNs can be understood more easily by humans as compared to models learned by approaches such as deep learning. However, at the same time, it is not straightforward to obtain human-understandable explanations specific to an observed inference result (e.g. marginal probability estimate). This is because, the MLN provides a lifted interpretation, one that generalizes to all possible worlds/instantiations, which are not query/evidence specific. In this paper, we extract grounded-explanations, i.e., explanations defined w.r.t specific inference queries and observed evidence. We extract these explanations from importance weights defined over the MLN formulas that encode the contribution of formulas towards the final inference results. We validate our approach in real world problems related to analyzing reviews from Yelp, and show through user-studies that our explanations are richer than state-of-the-art non-relational explainers such as LIMEmore ».« less
4. Shapley Values and Meta-Explanations for Probabilistic Graphical Model Inference

   https://doi.org/10.1145/3340531.3411881  

   Liu, Yifei ; Chen, Chao ; Liu, Yazheng ; Zhang, Xi ; Xie, Sihong ( October 2020 , Proceedings of the 29th ACM International Conference on Information and Knowledge Management (CIKM'2020))

   Probabilistic graphical models, such as Markov random fields (MRF), exploit dependencies among random variables to model a rich family of joint probability distributions. Inference algorithms, such as belief propagation (BP), can effectively compute the marginal posteriors for decision making. Nonetheless, inferences involve sophisticated probability calculations and are difficult for humans to interpret. Among all existing explanation methods for MRFs, no method is designed for fair attributions of an inference outcome to elements on the MRF where the inference takes place. Shapley values provide rigorous attributions but so far have not been studied on MRFs. We thus define Shapley values for MRFs to capture both probabilistic and topological contributions of the variables on MRFs. We theoretically characterize the new definition regarding independence, equal contribution, additivity, and submodularity. As brute-force computation of the Shapley values is challenging, we propose GraphShapley, an approximation algorithm that exploits the decomposability of Shapley values, the structure of MRFs, and the iterative nature of BP inference to speed up the computation. In practice, we propose meta-explanations to explain the Shapley values and make them more accessible and trustworthy to human users. On four synthetic and nine real-world MRFs, we demonstrate that GraphShapley generates sensible and practical explanations.
5. Negative Weights in Hinge-Loss Markov Random Fields.

   Charles Dickens, Eriq Augustine ( July 2021 , Workshop on Tractable Probabilistic Modeling (TPM))

   Probabilistic soft logic (PSL) is a framework for instantiating probabilistic graphical models (PGM) representing complex relational data. Weighted first-order logical statements are used as templates for creating potential functions which define the PGM density. Traditionally, PSL constrains weights to be non-negative to ensure maximum a posteriori (MAP) inference is a tractable convex optimization problem. We propose three novel approaches to extending PSL's expressivity to allow negative weights. Notably, we propose the use of Gödel logic for defining potentials from negatively weighted rules. This method improves upon prior work on this topic by preserving both the convexity and scale of the MAP inference problem. Moreover, we show where each of the five methods discussed in this paper overlap and where they most differ. All negative methods are implemented in PSL, and we introduce a tunable synthetic dataset designed to empirically compare the performance of predictions.