Combinatory Categorial Grammar (CCG) is a lexicalized grammar formalism in which words are associated with categories that, in combination with a small universal set of rules, specify the syntactic configurations in which they may occur. Categories are selected from a large, recursively-defined set; this leads to high word-to-category ambiguity, which is one of the primary factors that make learning CCG parsers difficult, especially in the face of little data. Previous work has shown that learning sequence models for CCG tagging can be improved by using linguistically-motivated prior probability distributions over potential categories. We extend this approach to the task of learning a CCG parser from weak supervision. We present a Bayesian formulation for CCG parser induction that assumes only supervision in the form of an incomplete tag dictionary mapping some word types to sets of potential categories. Our approach outperforms a baseline model trained with uniform priors by exploiting universal, intrinsic properties of the CCG formalism to bias the model toward simpler, more cross-linguistically common categories.

We present a probabilistic approach to shape decomposition that creates a skeleton-based shape representation of a 3D object while simultaneously decomposing it into constituent parts. Our approach probabilistically combines two prominent threads from the shape literature: skeleton-based (medial axis) representations of shape, and part-based representations of shape, in which shapes are combinations of primitive parts. Our approach recasts skeleton-based shape representation as a mixture estimation problem, allowing us to apply probabilistic estimation techniques to the problem of 3D shape decomposition, extending earlier work on the 2D case. The estimated 3D shape decompositions approximate human shape decomposition judgments. We present a tractable implementation of the framework, which begins by over-segmenting objects at concavities, and then probabilistically merges them to create a distribution over possible decompositions. This results in a hierarchy of decompositions at different structural scales, again closely matching known properties of human shape representation. The probabilistic estimation procedures that arise naturally in the model allow effective prediction of missing parts. We present results on shapes from a standard database illustrating the effectiveness of the approach.

Object recognition systems can be unreliable when run in isolation depending on only image based features, but their performance can be improved when taking scene context into account. In this paper, we present techniques to model and infer object labels in real scenes based on a variety of spatial relations — geometric features which capture how objects co-occur — and compare their efficacy in the context of augmenting perception based object classification in real-world table-top scenes. We utilise a long-term dataset of office table-tops for qualitatively comparing the performances of these techniques. On this dataset, we show that more intricate techniques, have a superior performance but do not generalise well on small training data. We also show that techniques using coarser information perform crudely but sufficiently well in standalone scenarios and generalise well on small training data. We conclude the paper, expanding on the insights we have gained through these comparisons and comment on a few fundamental topics with respect to long-term autonomous robots.

How should we gather information to make effective decisions? A classical answer to this fundamental problem is given by the decision-theoretic value of information. Unfortunately, optimizing this objective is intractable, and myopic (greedy) approximations are known to perform poorly. In this paper, we introduce DiRECt, an efficient yet near-optimal algorithm for nonmyopically optimizing value of information. Crucially, DiRECt uses a novel surrogate objective that is: (1) aligned with the value of information problem (2) efficient to evaluate and (3) adaptive submodular. This latter property enables us to utilize an efficient greedy optimization while providing strong approximation guarantees. We demonstrate the utility of our approach on four diverse case-studies: touch-based robotic localization, comparison-based preference learning, wild-life conservation management, and preference elicitation in behavioral economics. In the first application, we demonstrate DiRECt in closed-loop on an actual robotic platform.

There are many criteria for measuring the value of information (VOI), each based on a different principle that is usually suitable for specific applications. We propose a new criterion for measuring the value of information, which values information that leads to robust decisions (i.e., ones that are unlikely to change due to new information). We also introduce an algorithm for Naive Bayes networks that selects features with maximal VOI under the new criteria. We discuss the application of the new criteria to classification tasks, showing how it can be used to tradeoff the budget, allotted for acquiring information, with the classification accuracy. In particular, we show empirically that the new criteria can reduce the expended budget significantly while reducing the classification accuracy only slightly. We also show empirically that the new criterion leads to decisions that are much more robust than those based on traditional VOI criteria, such as information gain and classification loss. This make the new criteria particularly suitable for certain decision making applications.

We examine the inferential complexity of Bayesian networks specified through logical constructs. We first consider simple propositional languages, and then move to relational languages. We examine both the combined complexity of inference (as network size and evidence size are not bounded) and the data complexity of inference (where network size is bounded); we also examine the connection to liftability through domain complexity. Combined and data complexity of several inference problems are presented, ranging from polynomial to exponential classes.

The main computational bottleneck in various sampling based and local-search based inference algorithms for Markov logic networks (e.g., Gibbs sampling, MC-SAT, MaxWalksat, etc.) is computing the number of groundings of a first-order formula that are true given a truth assignment to all of its ground atoms. We reduce this problem to the problem of counting the number of solutions of a constraint satisfaction problem (CSP) and show that during their execution, both sampling based and local-search based algorithms repeatedly solve dynamic versions of this counting problem. Deriving from the vast amount of literature on CSPs and graphical models, we propose an exact junction-tree based algorithm for computing the number of solutions of the dynamic CSP, analyze its properties, and show how it can be used to improve the computational complexity of Gibbs sampling and MaxWalksat. Empirical tests on a variety of benchmarks clearly show that our new approach is several orders of magnitude more scalable than existing approaches.

Quantile regression deals with the problem of computing robust estimators when the conditional mean and standard deviation of the predicted function are inadequate to capture its variability. The technique has an extensive list of applications, including health sciences, ecology and finance. In this work we present a non-parametric method of inferring quantiles and derive a novel Variational Bayesian (VB) approximation to the marginal likelihood, leading to an elegant Expectation Maximisation algorithm for learning the model. Our method is nonparametric, has strong convergence guarantees, and can deal with nonsymmetric quantiles seamlessly. We compare the method to other parametric and non-parametric Bayesian techniques, and alternative approximations based on expectation propagation demonstrating the benefits of our framework in toy problems and real datasets.

We consider the problem of, given a probabilistic model on a set of random variables, how to add a new variable that depends on the other variables, without changing the original distribution. In particular, we consider relational models (such as Markov logic networks (MLNs)), where we cannot directly define conditional probabilities. In relational models, there may be an unbounded number of parents in the grounding, and conditional distributions need to be defined in terms of aggregators. The question we ask is whether and when it is possible to represent conditional probabilities at all in various relational models. Some aggregators have been shown to be representable by MLNs, by adding auxiliary variables; however it was unknown whether they could be defined without auxiliary variables. For other aggregators, it was not known whether they can be represented by MLNs at all. We obtained surprisingly strong negative results on the capability of flexible undirected relational models such as MLNs to represent aggregators without affecting the original model's distribution. We provide a map of what aspects of the models, including the use of auxiliary variables and quantifiers, result in the ability to represent various aggregators. In addition, we provide proof techniques which can be used to facilitate future theoretic results on relational models, and demonstrate them on relational logistic regression (RLR).

The hierarchical Dirichlet process (HDP) is a powerful nonparametric Bayesian approach to modeling groups of data which allows the mixture components in each group to be shared. However, in many cases the groups themselves are also in latent groups (categories) which may impact the modeling a lot. In order to utilize the unknown category information of grouped data, we present the hybrid nested/ hierarchical Dirichlet process (hNHDP), a prior that blends the desirable aspects of both the HDP and the nested Dirichlet Process (NDP). Specifically, we introduce a clustering structure for the groups. The prior distribution for each cluster is a realization of a Dirichlet process. Moreover, the set of cluster-specific distributions can share part of atoms between groups, and the shared atoms and specific atoms are generated separately. We apply the hNHDP to document modeling and bring in a mechanism to identify discriminative words and topics. We derive an efficient Markov chain Monte Carlo scheme for posterior inference and present experiments on document modeling.