RockIt is a maximum a-posteriori (MAP) query engine for statistical relational models. MAP inference in graphical models is an optimization problem which can be compiled to integer linear programs (ILPs). We describe several advances in translating MAP queries to ILP instances and present the novel meta-algorithm cutting plane aggregation (CPA). CPA exploits local context-specific symmetries and bundles up sets of linear constraints. The resulting counting constraints lead to more compact ILPs and make the symmetry of the ground model more explicit to state-of-the-art ILP solvers. Moreover, RockIt parallelizes most parts of the MAP inference pipeline taking advantage of ubiquitous shared-memory multi-core architectures. We report on extensive experiments with Markov logic network (MLN) benchmarks showing that RockIt outperforms the state-of-the-art systems Alchemy, Markov TheBeast, and Tuffy both in terms of efficiency and quality of results.
MAP queries in SRL models can be formulated as integer linear programs (ILPs). In this context, cutting plane inference (CPI) solving multiple smaller ILPs in several iterations has shown remarkable performance @cite_37 . In each CPI iteration, only the ground formulas violated by the current intermediate solution are added to the ILP formulation until no violated ground formulas remain. Since CPI ground formulas satisfied by the evidence, it can be seen as a generalization of pre-processing approaches that count the formulas satisfied by the evidence @cite_19 . In the context of max-margin weight learning for MLNs @cite_22 the MAP query was formulated as a linear relaxation of an ILP and a rounding procedure was applied to extract an approximate MAP state. 's ILP formulation requires less constraints for ground clauses with negative weights and it combines CPI with cutting plane aggregation.
@cite_19 @cite_37 @cite_22
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In this work we present Cutting Plane Inference (CPI), a Maximum A Posteriori (MAP) inference method for Statistical Relational Learning. Framed in terms of Markov Logic and inspired by the Cutting Plane Method, it can be seen as a meta algorithm that instantiates small parts of a large and complex Markov Network and then solves these using a conventional MAP method. We evaluate CPI on two tasks, Semantic Role Labelling and Joint Entity Resolution, while plugging in two different MAP inference methods: the current method of choice for MAP inference in Markov Logic, MaxWalkSAT, and Integer Linear Programming. We observe that when used with CPI both methods are significantly faster than when used alone. In addition, CPI improves the accuracy of MaxWalkSAT and maintains the exactness of Integer Linear Programming. Many probabilistic inference tasks involve summations over exponentially large sets. Recently, it has been shown that these problems can be reduced to solving a polynomial number of MAP inference queries for a model augmented with randomly generated parity constraints. By exploiting a connection with max-likelihood decoding of binary codes, we show that these optimizations are computationally hard. Inspired by iterative message passing decoding algorithms, we propose an Integer Linear Programming (ILP) formulation for the problem, enhanced with new sparsification techniques to improve decoding performance. By solving the ILP through a sequence of LP relaxations, we get both lower and upper bounds on the partition function, which hold with high probability and are much tighter than those obtained with variational methods. The computation of prime implicants has several and significant applications in different areas, including automated reasoning, non-monotonic reasoning, electronic design automation, among others. The authors describe a new model and algorithm for computing minimum-size prime implicants of propositional formulas. The proposed approach is based on creating an integer linear program (ILP) formulation for computing the minimum-size prime implicant, which simplifies existing formulations. In addition, they introduce two new algorithms for solving ILPs, both of which are built on top of an algorithm for propositional satisfiability (SAT). Given the organization of the proposed SAT algorithm, the resulting ILP procedures implement powerful search pruning techniques, including a non-chronological backtracking search strategy, clause recording procedures and identification of necessary assignments. Experimental results, obtained on several benchmark examples, indicate that the proposed model and algorithms are significantly more efficient than other existing solutions. Temporal annotations of facts are a key component both for building a high-accuracy knowledge base and for answering queries over the resulting temporal knowledge base with high precision and recall. In this paper, we present a temporal-probabilistic database model for cleaning uncertain temporal facts obtained from information extraction methods. Specifically, we consider a combination of temporal deduction rules, temporal consistency constraints and probabilistic inference based on the common possible-worlds semantics with data lineage, and we study the theoretical properties of this data model. We further develop a query engine which is capable of scaling to very large temporal knowledge bases, with nearly interactive query response times over millions of uncertain facts and hundreds of thousands of grounded rules. Our experiments over two real-world datasets demonstrate the increased robustness of our approach compared to related techniques based on constraint solving via Integer Linear Programming (ILP) and probabilistic inference via Markov Logic Networks (MLNs). We are also able to show that our runtime performance is more than competitive to current ILP solvers and the fastest available, probabilistic but non-temporal, database engines.