Modelling problems containing a mixture of Boolean and numerical variables is a long-standing interest of Artificial Intelligence. However, performing inference and learning in hybrid domains is a particularly daunting task. The ability to model this kind of domains is crucial in "learning to design" tasks, that is, learning applications where the goal is to learn from examples how to perform automatic de novo design of novel objects. In this paper we present Structured Learning Modulo Theories, a max-margin approach for learning in hybrid domains based on Satisfiability Modulo Theories, which allows to combine Boolean reasoning and optimization over continuous linear arithmetical constraints. The main idea is to leverage a state-of-the-art generalized Satisfiability Modulo Theory solver for implementing the inference and separation oracles of Structured Output SVMs. We validate our method on artificial and real world scenarios.
While a number of efficient lifted-inference algorithms have been developed for Relational Continuous Models @cite_57 @cite_61 @cite_5 , performing inference over joint continuous-discrete relational domains is still a challenge. The few existing attempts aim at extending statistical relational learning methods to the hybrid domain.
@cite_57 @cite_5 @cite_61
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Hybrid continuous-discrete models naturally represent many real-world applications in robotics, finance, and environmental engineering. Inference with large-scale models is challenging because relational structures deteriorate rapidly during inference with observations. The main contribution of this paper is an efficient relational variational inference algorithm that factors largescale probability models into simpler variational models, composed of mixtures of iid (Bernoulli) random variables. The algorithm takes probability relational models of largescale hybrid systems and converts them to a close-to-optimal variational models. Then, it efficiently calculates marginal probabilities on the variational models by using a latent (or lifted) variable elimination or a lifted stochastic sampling. This inference is unique because it maintains the relational structure upon individual observations and during inference steps. Relational Continuous Models (RCMs) represent joint probability densities over attributes of objects, when the attributes have continuous domains. With relational representations, they can model joint probability distributions over large numbers of variables compactly in a natural way. This paper presents a new exact lifted inference algorithm for RCMs, thus it scales up to large models of real world applications. The algorithm applies to Relational Pairwise Models which are (relational) products of potentials of arity 2. Our algorithm is unique in two ways. First, it substantially improves the efficiency of lifted inference with variables of continuous domains. When a relational model has Gaussian potentials, it takes only linear-time compared to cubic time of previous methods. Second, it is the first exact inference algorithm which handles RCMs in a lifted way. The algorithm is illustrated over an example from econometrics. Experimental results show that our algorithm outperforms both a ground-level inference algorithm and an algorithm built with previously-known lifted methods. A standard pipeline for statistical relational learning involves two steps: one first constructs the knowledge base (KB) from text, and then performs the learning and reasoning tasks using probabilistic first-order logics. However, a key issue is that information extraction (IE) errors from text affect the quality of the KB, and propagate to the reasoning task. In this paper, we propose a statistical relational learning model for joint information extraction and reasoning. More specifically, we incorporate context-based entity extraction with structure learning (SL) in a scalable probabilistic logic framework. We then propose a latent context invention (LCI) approach to improve the performance. In experiments, we show that our approach outperforms state-of-the-art baselines over three real-world Wikipedia datasets from multiple domains; that joint learning and inference for IE and SL significantly improve both tasks; that latent context invention further improves the results. We present a novel approach to relation extraction that integrates information across documents, performs global inference and requires no labelled text. In particular, we tackle relation extraction and entity identification jointly. We use distant supervision to train a factor graph model for relation extraction based on an existing knowledge base (Freebase, derived in parts from Wikipedia). For inference we run an efficient Gibbs sampler that leads to linear time joint inference. We evaluate our approach both for an indomain (Wikipedia) and a more realistic out-of-domain (New York Times Corpus) setting. For the in-domain setting, our joint model leads to 4 higher precision than an isolated local approach, but has no advantage over a pipeline. For the out-of-domain data, we benefit strongly from joint modelling, and observe improvements in precision of 13 over the pipeline, and 15 over the isolated baseline.