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Register a new userRockIt: Exploiting Parallelism and Symmetry for MAP Inference in Statistical Relational Models
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Jan Noessner
Publication date
2013
fields
Informatics Engineering
and research's language is
English
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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.
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Finding the best model that describes a high dimensional dataset, is a daunting task. For binary data, we show that this becomes feasible, if the search is restricted to simple models. These models -- that we call Minimally Complex Models (MCMs) -- are simple because they are composed of independent components of minimal complexity, in terms of description length. Simple models are easy to infer and to sample from. In addition, model selection within the MCMs class is invariant with respect to changes in the representation of the data. They portray the structure of dependencies among variables in a simple way. They provide robust predictions on dependencies and symmetries, as illustrated in several examples. MCMs may contain interactions between variables of any order. So, for example, our approach reveals whether a dataset is appropriately described by a pairwise interaction model.
The rules of d-separation provide a framework for deriving conditional independence facts from model structure. However, this theory only applies to simple directed graphical models. We introduce relational d-separation, a theory for deriving conditional independence in relational models. We provide a sound, complete, and computationally efficient method for relational d-separation, and we present empirical results that demonstrate effectiveness.
Entity resolution, the problem of identifying the underlying entity of references found in data, has been researched for many decades in many communities. A common theme in this research has been the importance of incorporating relational features into the resolution process. Relational entity resolution is particularly important in knowledge graphs (KGs), which have a regular structure capturing entities and their interrelationships. We identify three major problems in KG entity resolution: (1) intra-KG reference ambiguity; (2) inter-KG reference ambiguity; and (3) ambiguity when extending KGs with new facts. We implement a framework that generalizes across these three settings and exploits this regular structure of KGs. Our framework has many advantages over custom solutions widely deployed in industry, including collective inference, scalability, and interpretability. We apply our framework to two real-world KG entity resolution problems, ambiguity in NELL and merging data from Freebase and MusicBrainz, demonstrating the importance of relational features.
We develop a general framework for MAP estimation in discrete and Gaussian graphical models using Lagrangian relaxation techniques. The key idea is to reformulate an intractable estimation problem as one defined on a more tractable graph, but subject to additional constraints. Relaxing these constraints gives a tractable dual problem, one defined by a thin graph, which is then optimized by an iterative procedure. When this iterative optimization leads to a consistent estimate, one which also satisfies the constraints, then it corresponds to an optimal MAP estimate of the original model. Otherwise there is a ``duality gap, and we obtain a bound on the optimal solution. Thus, our approach combines convex optimization with dynamic programming techniques applicable for thin graphs. The popular tree-reweighted max-product (TRMP) method may be seen as solving a particular class of such relaxations, where the intractable graph is relaxed to a set of spanning trees. We also consider relaxations to a set of small induced subgraphs, thin subgraphs (e.g. loops), and a connected tree obtained by ``unwinding cycles. In addition, we propose a new class of multiscale relaxations that introduce ``summary variables. The potential benefits of such generalizations include: reducing or eliminating the ``duality gap in hard problems, reducing the number or Lagrange multipliers in the dual problem, and accelerating convergence of the iterative optimization procedure.
Explainability is essential for autonomous vehicles and other robotics systems interacting with humans and other objects during operation. Humans need to understand and anticipate the actions taken by the machines for trustful and safe cooperation. In this work, we aim to enable the explainability of an autonomous driving system at the design stage by incorporating expert domain knowledge into the model. We propose Grounded Relational Inference (GRI). It models an interactive systems underlying dynamics by inferring an interaction graph representing the agents relations. We ensure an interpretable interaction graph by grounding the relational latent space into semantic behaviors defined with expert domain knowledge. We demonstrate that it can model interactive traffic scenarios under both simulation and real-world settings, and generate interpretable graphs explaining the vehicles behavior by their interactions.
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