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Added by
Johannes Textor
Publication date
2015
fields
Informatics Engineering
and research's language is
English
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We consider graphs that represent pairwise marginal independencies amongst a set of variables (for instance, the zero entries of a covariance matrix for normal data). We characterize the directed acyclic graphs (DAGs) that faithfully explain a given set of independencies, and derive algorithms to efficiently enumerate such structures. Our results map out the space of faithful causal models for a given set of pairwise marginal independence relations. This allows us to show the extent to which causal inference is possible without using conditional independence tests.
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Our goal is to learn a semantic parser that maps natural language utterances into executable programs when only indirect supervision is available: examples are labeled with the correct execution result, but not the program itself. Consequently, we must search the space of programs for those that output the correct result, while not being misled by spurious programs: incorrect programs that coincidentally output the correct result. We connect two common learning paradigms, reinforcement learning (RL) and maximum marginal likelihood (MML), and then present a new learning algorithm that combines the strengths of both. The new algorithm guards against spurious programs by combining the systematic search traditionally employed in MML with the randomized exploration of RL, and by updating parameters such that probability is spread more evenly across consistent programs. We apply our learning algorithm to a new neural semantic parser and show significant gains over existing state-of-the-art results on a recent context-dependent semantic parsing task.
The Rao-Blackwell theorem is utilized to analyze and improve the scalability of inference in large probabilistic models that exhibit symmetries. A novel marginal density estimator is introduced and shown both analytically and empirically to outperform standard estimators by several orders of magnitude. The developed theory and algorithms apply to a broad class of probabilistic models including statistical relational models considered not susceptible to lifted probabilistic inference.
We study computational aspects of relational marginal polytopes which are statistical relational learning counterparts of marginal polytopes, well-known from probabilistic graphical models. Here, given some first-order logic formula, we can define its relational marginal statistic to be the fraction of groundings that make this formula true in a given possible world. For a list of first-order logic formulas, the relational marginal polytope is the set of all points that correspond to the expected values of the relational marginal statistics that are realizable. In this paper, we study the following two problems: (i) Do domain-liftability results for the partition functions of Markov logic networks (MLNs) carry over to the problem of relational marginal polytope construction? (ii) Is the relational marginal polytope containment problem hard under some plausible complexity-theoretic assumptions? Our positive results have consequences for lifted weight learning of MLNs. In particular, we show that weight learning of MLNs is domain-liftable whenever the computation of the partition function of the respective MLNs is domain-liftable (this result has not been rigorously proven before).
We propose a novel parameterized family of Mixed Membership Mallows Models (M4) to account for variability in pairwise comparisons generated by a heterogeneous population of noisy and inconsistent users. M4 models individual preferences as a user-specific probabilistic mixture of shared latent Mallows components. Our key algorithmic insight for estimation is to establish a statistical connection between M4 and topic models by viewing pairwise comparisons as words, and users as documents. This key insight leads us to explore Mallows components with a separable structure and leverage recent advances in separable topic discovery. While separability appears to be overly restrictive, we nevertheless show that it is an inevitable outcome of a relatively small number of latent Mallows components in a world of large number of items. We then develop an algorithm based on robust extreme-point identification of convex polygons to learn the reference rankings, and is provably consistent with polynomial sample complexity guarantees. We demonstrate that our new model is empirically competitive with the current state-of-the-art approaches in predicting real-world preferences.
The ability to hypothesise, develop abstract concepts based on concrete observations and apply these hypotheses to justify future actions has been paramount in human development. An existing line of research in outfitting intelligent machines with abstract reasoning capabilities revolves around the Ravens Progressive Matrices (RPM). There have been many breakthroughs in supervised approaches to solving RPM in recent years. However, this process requires external assistance, and thus it cannot be claimed that machines have achieved reasoning ability comparable to humans. Namely, humans can solve RPM problems without supervision or prior experience once the RPM rule that relations can only exist row/column-wise is properly introduced. In this paper, we introduce a pairwise relations discriminator (PRD), a technique to develop unsupervised models with sufficient reasoning abilities to tackle an RPM problem. PRD reframes the RPM problem into a relation comparison task, which we can solve without requiring the labelling of the RPM problem. We can identify the optimal candidate by adapting the application of PRD to the RPM problem. Our approach, the PRD, establishes a new state-of-the-art unsupervised learning benchmark with an accuracy of 55.9% on the I-RAVEN, presenting a significant improvement and a step forward in equipping machines with abstract reasoning.
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