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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. 

Abstract 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. 

We study the classic problem of subgraph counting, where we wish to determine the number of occurrences of a fixed pattern graph H in an input graph G of n vertices. Our focus is on bounded degeneracy inputs, a rich family of graph classes that also characterizes real-world massive networks. Building on the seminal techniques introduced by Chiba-Nishizeki (SICOMP 1985), a recent line of work has built subgraph counting algorithms for bounded degeneracy graphs. Assuming fine-grained complexity conjectures, there is a complete characterization of patterns H for which linear time subgraph counting is possible. For every r ≥ 6, there exists an H with r vertices that cannot be counted in linear time. In this paper, we initiate a study of subquadratic algorithms for subgraph counting on bounded degeneracy graphs. We prove that when H has at most 9 vertices, subgraph counting can be done in Õ(n^{5/3}) time. As a secondary result, we give improved algorithms for counting cycles of length at most 10. Previously, no subquadratic algorithms were known for the above problems on bounded degeneracy graphs. Our main conceptual contribution is a framework that reduces subgraph counting in bounded degeneracy graphs to counting smaller hypergraphs in arbitrary graphs. We believe that our results will help build a general theory of subgraph counting for bounded degeneracy graphs. 

In this work, we examine online collective inference, the problem of maintaining and performing inference over a sequence of evolving graphical models. We utilize templated graphical models (TGM), a general class of graphical models expressed via templates and instantiated with data. A key challenge is minimizing the cost of instantiating the updated model. To address this, we define a class of exact and approximate context-aware methods for updating an existing TGM. These methods avoid a full re-instantiation by using the context of the updates to only add relevant components to the graphical model. Further, we provide stability bounds for the general online inference problem and regret bounds for a proposed approximation. Finally, we implement our approach in probabilistic soft logic, and test it on several online collective inference tasks. Through these experiments we verify the bounds on regret and stability, and show that our approximate online approach consistently runs two to five times faster than the offline alternative while, surprisingly, maintaining the quality of the predictions. 

Abstract We extend classical ideal point estimation to allow voters to have different preferences when voting in different domains—for example, when voting on agricultural policy than when voting on defense policy. Our scaling procedure results in estimated ideal points on a common scale. As a result, we are able to directly compare a member’s revealed preferences across different domains of voting (different sets of motions) to assess if, for example, a member votes more conservatively on agriculture motions than on defense. In doing so, we are able to assess the extent to which voting behavior of an individual voter is consistent with a uni-dimensional spatial model—if a member has the same preferences in all domains. The key novelty is to estimate rather than assume the identity of “stayers”—voters whose revealed preference is constant across votes. Our approach offers methodology for investigating the relationship between the basic space and issue space in legislative voting (Poole 2007). There are several methodological advantages to our approach. First, our model allows for testing sharp hypotheses. Second, the methodology developed can be understood as a kind of partial-pooling model for item response theory scaling, resulting in less uncertainty of estimates. Related, our estimation method provides a principled and unified approach to the issue of “granularity” (i.e., the level of aggregation) in the analysis of roll-call data (Crespin and Rohde 2010; Roberts et al. 2016). We illustrate the model by estimating U.S. House of Representatives members’ revealed preferences in different policy domains, and identify several other potential applications of the model including: studying the relationship between committee and floor voting behavior; and investigating constituency influence and representation. 

Causal inference is at the heart of empirical research in natu- ral and social sciences and is critical for scientific discovery and informed decision making. The gold standard in causal inference is performing randomized controlled trials; unfortu- nately these are not always feasible due to ethical, legal, or cost constraints. As an alternative, methodologies for causal inference from observational data have been developed in sta- tistical studies and social sciences. However, existing meth- ods critically rely on restrictive assumptions such as the study population consisting of homogeneous elements that can be represented in a single flat table, where each row is referred to as a unit. In contrast, in many real-world set- tings, the study domain naturally consists of heterogeneous elements with complex relational structure, where the data is naturally represented in multiple related tables. In this paper, we present a formal framework for causal inference from such relational data. We propose a declarative language called CaRL for capturing causal background knowledge and assumptions, and specifying causal queries using simple Datalog-like rules. CaRL provides a foundation for infer- ring causality and reasoning about the effect of complex interventions in relational domains. We present an extensive experimental evaluation on real relational data to illustrate the applicability of CaRL in social sciences and healthcare.