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Templated graphical models (TGMs) encode model structure using rules that capture recurring relationships between multiple random variables. While the rules in TGMs are interpretable, it is not clear how they can be used to generate explanations for the individual predictions of the model. Further, learning these rules from data comes with high computational costs: it typically requires an expensive combinatorial search over the space of rules and repeated optimization over rule weights. In this work, we propose a new structure learning algorithm, Explainable Structured Model Search (ESMS), that learns a templated graphical model and an explanation framework for its predictions. ESMS uses a novel search procedure to efficiently search the space of models and discover models that trade-off predictive accuracy and explainability. We introduce the notion of relational stability and prove that our proposed explanation framework is stable. Further, our proposed piecewise pseudolikelihood (PPLL) objective does not require re-optimizing the rule weights across models during each iteration of the search. In our empirical evaluation on three realworld datasets, we show that our proposed approach not only discovers models that are explainable, but also significantly outperforms existing state-out-the-art structure learning approaches. 

Abstract Statistical relational learning (SRL) frameworks are effective at defining probabilistic models over complex relational data. They often use weighted first-order logical rules where the weights of the rules govern probabilistic interactions and are usually learned from data. Existing weight learning approaches typically attempt to learn a set of weights that maximizes some function of data likelihood; however, this does not always translate to optimal performance on a desired domain metric, such as accuracy or F1 score. In this paper, we introduce a taxonomy of search-based weight learning approaches for SRL frameworks that directly optimize weights on a chosen domain performance metric. To effectively apply these search-based approaches, we introduce a novel projection, referred to as scaled space (SS), that is an accurate representation of the true weight space. We show that SS removes redundancies in the weight space and captures the semantic distance between the possible weight configurations. In order to improve the efficiency of search, we also introduce an approximation of SS which simplifies the process of sampling weight configurations. We demonstrate these approaches on two state-of-the-art SRL frameworks: Markov logic networks and probabilistic soft logic. We perform empirical evaluation on five real-world datasets and evaluate them each on two different metrics. We also compare them against four other weight learning approaches. Our experimental results show that our proposed search-based approaches outperform likelihood-based approaches and yield up to a 10% improvement across a variety of performance metrics. Further, we perform an extensive evaluation to measure the robustness of our approach to different initializations and hyperparameters. The results indicate that our approach is both accurate and robust. 

Constant communities, i.e., groups of vertices that are always clustered together, independent of the community detection algorithm used, are necessary for reducing the inherent stochasticity of community detection results. Current methods for identifying constant communities require multiple runs of community detection algorithm(s). This process is extremely time consuming and not scalable to large networks. We propose a novel approach for finding the constant communities, by transforming the problem to a binary classification of edges. We apply the Otsu method from image thresholding to classify edges based on whether they are always within a community or not. Our algorithm does not require any explicit detection of communities and can thus scale to very large networks of the order of millions of vertices. Our results on real-world graphs show that our method is significantly faster and the constant communities produced have higher accuracy (as per F1 and NMI scores) than state-of-the-art baseline methods. 

Statistical relational learning (SRL) and graph neural networks (GNNs) are two powerful approaches for learning and inference over graphs. Typically, they are evaluated in terms of simple metrics such as accuracy over individual node labels. Complexaggregate graph queries(AGQ) involving multiple nodes, edges, and labels are common in the graph mining community and are used to estimate important network properties such as social cohesion and influence. While graph mining algorithms support AGQs, they typically do not take into account uncertainty, or when they do, make simplifying assumptions and do not build full probabilistic models. In this paper, we examine the performance of SRL and GNNs on AGQs over graphs with partially observed node labels. We show that, not surprisingly, inferring the unobserved node labels as a first step and then evaluating the queries on the fully observed graph can lead to sub-optimal estimates, and that a better approach is to compute these queries as an expectation under the joint distribution. We propose a sampling framework to tractably compute the expected values of AGQs. Motivated by the analysis of subgroup cohesion in social networks, we propose a suite of AGQs that estimate the community structure in graphs. In our empirical evaluation, we show that by estimating these queries as an expectation, SRL-based approaches yield up to a 50-fold reduction in average error when compared to existing GNN-based approaches.

 

Statistical relational learning models are powerful tools that combine ideas from first-order logic with probabilistic graphical models to represent complex dependencies. Despite their success in encoding large problems with a compact set of weighted rules, performing inference over these models is often challenging. In this paper, we show how to effectively combine two powerful ideas for scaling inference for large graphical models. The first idea, lifted inference, is a wellstudied approach to speeding up inference in graphical models by exploiting symmetries in the underlying problem. The second idea is to frame Maximum a posteriori (MAP) inference as a convex optimization problem and use alternating direction method of multipliers (ADMM) to solve the problem in parallel. A well-studied relaxation to the combinatorial optimization problem defined for logical Markov random fields gives rise to a hinge-loss Markov random field (HLMRF) for which MAP inference is a convex optimization problem. We show how the formalism introduced for coloring weighted bipartite graphs using a color refinement algorithm can be integrated with the ADMM optimization technique to take advantage of the sparse dependency structures of HLMRFs. Our proposed approach, lifted hinge-loss Markov random fields (LHL-MRFs), preserves the structure of the original problem after lifting and solves lifted inference as distributed convex optimization with ADMM. In our empirical evaluation on real-world problems, we observe up to a three times speed up in inference over HL-MRFs.