Coverage functions are an important class of discrete functions that capture laws of diminishing returns. In this paper, we propose a new problem of learning time-varying coverage functions which arise naturally from applications in social network analysis, machine learning, and algorithmic game theory. We develop a novel parametrization of the time-varying coverage function by illustrating the connections with counting processes. We present an efficient algorithm to learn the parameters by maximum likelihood estimation, and provide a rigorous theoretic analysis of its sample complexity. Empirical experiments from information diffusion in social network analysis demonstrate that with few assumptions about the underlying diffusion process, our method performs significantly better than existing approaches on both synthetic and real world data.

Previous theoretical and experimental work on optimal decision-making was restricted to the artificial setting of a reliability of the momentary sensory evidence that remained constant within single trials. The work presented here describes the computation and characterization of optimal decision-making in the more realistic case of an evidence reliability that varies across time even within a trial. It shows that, in this case, the optimal behavior is determined by a bound in the decision maker's belief that depends only on the current, but not the past, reliability. We furthermore demonstrate that simpler heuristics fail to match the optimal performance for certain characteristics of the process that determines the time-course of this reliability, causing a drop in reward rate by more than 50%.

We present an algorithm for finding a chordal Markov network that maximizes any given decomposable scoring function. The algorithm is based on a recursive characterization of clique trees, and it runs in O(4^n) time for n vertices. On an eight-vertex benchmark instance, our implementation turns out to be about ten million times faster than a recently proposed, constraint satisfaction based algorithm (Corander et al., NIPS 2013). Within a few hours, it is able to solve instances up to 18 vertices, and beyond if we restrict the maximum clique size. We also study the performance of a recent integer linear programming algorithm (Bartlett and Cussens, UAI 2013). Our results suggest that, unless we bound the clique sizes, currently only the dynamic programming algorithm is guaranteed to solve instances with around 15 or more vertices.

We investigate architectures of discriminatively trained deep Convolutional Networks (ConvNets) for action recognition in video. The challenge is to capture the complementary information on appearance from still frames and motion between frames. We also aim to generalise the best performing hand-crafted features within a data-driven learning framework. Our contribution is three-fold. First, we propose a two-stream ConvNet architecture which incorporates spatial and temporal networks. Second, we demonstrate that a ConvNet trained on multi-frame dense optical flow is able to achieve very good performance in spite of limited training data. Finally, we show that multi-task learning, applied to two different action classification datasets, can be used to increase the amount of training data and improve the performance on both. Our architecture is trained and evaluated on the standard video actions benchmarks of UCF-101 and HMDB-51, where it is competitive with the state of the art. It also exceeds by a large margin previous attempts to use deep nets for video classification.

Implementing inference procedures for each new probabilistic model is timeconsuming anderror-prone. Probabilistic programming addresses this problem by allowing a user to specify the model and then automatically generating the inference procedure. To make this practical it is important to generate high performance inferencecode. In turn, on modern architectures, high performance requires parallel execution. In this paper we present Augur, a probabilistic modeling language and compiler for Bayesian networks designed to make effective use of data-parallel architectures such as GPUs. We show that the compiler can generate data-parallel inference code scalable to thousands of GPU cores by making use of the conditional independence relationships in the Bayesian network.

A new Bayesian formulation is developed for nonlinear support vector machines (SVMs), based on a Gaussian process and with the SVM hinge loss expressed as a scaled mixture of normals. We then integrate the Bayesian SVM into a factor model, in which feature learning and nonlinear classifier design are performed jointly; almost all previous work on such discriminative feature learning has assumed a linear classifier. Inference is performed with expectation conditional maximization (ECM) and Markov Chain Monte Carlo (MCMC). An extensive set of experiments demonstrate the utility of using a nonlinear Bayesian SVM within discriminative feature learning and factor modeling, from the standpoints of accuracy and interpretability

We analyse a plug-in estimator for a large class of integral functionals of one or more continuous probability densities. This class includes important families of entropy, divergence, mutual information, and their conditional versions. For densities on the d-dimensional unit cube [0,1]^d that lie in a beta-Holder smoothness class, we prove our estimator converges at the rate O(n^(1/(beta+d))). Furthermore, we prove that the estimator obeys an exponential concentration inequality about its mean, whereas most previous related results have bounded only expected error of estimators. Finally, we demonstrate our bounds to the case of conditional Renyi mutual information.

Accurate and efficient analysis of multivariate spatio-temporal data is critical in climatology, geology, and sociology applications. Existing models usually assume simple inter-dependence among variables, space, and time, and are computationally expensive. We propose a unified low rank tensor learning framework for multivariate spatio-temporal analysis, which can conveniently incorporate different properties in spatio-temporal data, such as spatial clustering and shared structure among variables. We demonstrate how the general framework can be applied to cokriging and forecasting tasks, and develop an efficient greedy algorithm to solve the resulting optimization problem with convergence guarantee. We conduct experiments on both synthetic datasets and real application datasets to demonstrate that our method is not only significantly faster than existing methods but also achieves lower estimation error.

State of the art statistical estimators for high-dimensional problems take the form of regularized, and hence non-smooth, convex programs. A key facet of thesestatistical estimation problems is that these are typically not strongly convex under a high-dimensional sampling regime when the Hessian matrix becomes rank-deficient. Under vanilla convexity however, proximal optimization methods attain only a sublinear rate. In this paper, we investigate a novel variant of strong convexity, which we call Constant Nullspace Strong Convexity (CNSC), where we require that the objective function be strongly convex only over a constant subspace. As we show, the CNSC condition is naturally satisfied by high-dimensional statistical estimators. We then analyze the behavior of proximal methods under this CNSC condition: we show global linear convergence of Proximal Gradient and local quadratic convergence of Proximal Newton Method, when the regularization function comprising the statistical estimator is decomposable. We corroborate our theory via numerical experiments, and show a qualitative difference in the convergence rates of the proximal algorithms when the loss function does satisfy the CNSC condition.

We propose a multimodal retrieval procedure based on latent feature models. The procedure consists of a nonparametric Bayesian framework for learning underlying semantically meaningful abstract features in a multimodal dataset, a probabilistic retrieval model that allows cross-modal queries and an extension model for relevance feedback. Experiments on two multimodal datasets, PASCAL-Sentence and SUN-Attribute, demonstrate the effectiveness of the proposed retrieval procedure in comparison to the state-of-the-art algorithms for learning binary codes.