We show an efficient algorithm for the following problem: Given uniformly random points from an arbitrary n-dimensional simplex, estimate the simplex. The size of the sample and the number of arithmetic operations of our algorithm are polynomial in n. This answers a question of Frieze, Jerrum and Kannan [FJK]. Our result can also be interpreted as efficiently learning the intersection of n+1 half-spaces in R^n in the model where the intersection is bounded and we are given polynomially many uniform samples from it. Our proof uses the local search technique from Independent Component Analysis (ICA), also used by [FJK]. Unlike these previous algorithms, which were based on analyzing the fourth moment, ours is based on the third moment. We also show a direct connection between the problem of learning a simplex and ICA: a simple randomized reduction to ICA from the problem of learning a simplex. The connection is based on a known representation of the uniform measure on a simplex. Similar representations lead to a reduction from the problem of learning an affine transformation of an n-dimensional l_p ball to ICA.

We aim to reduce the burden of programming and deploying autonomous systems to work in concert with people in time-critical domains, such as military field operations and disaster response. Deployment plans for these operations are frequently negotiated on-the-fly by teams of human planners. A human operator then translates the agreed upon plan into machine instructions for the robots. We present an algorithm that reduces this translation burden by inferring the final plan from a processed form of the human team's planning conversation. Our approach combines probabilistic generative modeling with logical plan validation used to compute a highly structured prior over possible plans. This hybrid approach enables us to overcome the challenge of performing inference over the large solution space with only a small amount of noisy data from the team planning session. We validate the algorithm through human subject experimentation and show we are able to infer a human team's final plan with 83% accuracy on average. We also describe a robot demonstration in which two people plan and execute a first-response collaborative task with a PR2 robot. To the best of our knowledge, this is the first work that integrates a logical planning technique within a generative model to perform plan inference.

We study the problem of learning with label proportions in which the training data is provided in groups and only the proportion of each class in each group is known. We propose a new method called proportion-SVM, or $\propto$SVM, which explicitly models the latent unknown instance labels together with the known group label proportions in a large-margin framework. Unlike the existing works, our approach avoids making restrictive assumptions about the data. The $\propto$SVM model leads to a non-convex integer programming problem. In order to solve it efficiently, we propose two algorithms: one based on simple alternating optimization and the other based on a convex relaxation. Extensive experiments on standard datasets show that $\propto$SVM outperforms the state-of-the-art, especially for larger group sizes.

We propose a technique for increasing the efficiency of gradient-based inference and learning in Bayesian networks with multiple layers of continuous latent vari- ables. We show that, in many cases, it is possible to express such models in an auxiliary form, where continuous latent variables are conditionally deterministic given their parents and a set of independent auxiliary variables. Variables of mod- els in this auxiliary form have much larger Markov blankets, leading to significant speedups in gradient-based inference, e.g. rapid mixing Hybrid Monte Carlo and efficient gradient-based optimization. The relative efficiency is confirmed in ex- periments.

Optimal transportation distances are a fundamental family of parameterized distances for histograms. Despite their appealing theoretical properties, excellent performance in retrieval tasks and intuitive formulation, their computation involves the resolution of a linear program whose cost is prohibitive whenever the histograms' dimension exceeds a few hundreds. We propose in this work a new family of optimal transportation distances that look at transportation problems from a maximum-entropy perspective. We smooth the classical optimal transportation problem with an entropic regularization term, and show that the resulting optimum is also a distance which can be computed through Sinkhorn-Knopp's matrix scaling algorithm at a speed that is several orders of magnitude faster than that of transportation solvers. We also report improved performance over classical optimal transportation distances on the MNIST benchmark problem.

Online learning with delayed feedback has received increasing attention recently due to its several applications in distributed, web-based learning problems. In this paper we provide a systematic study of the topic, and analyze the effect of delay on the regret of online learning algorithms. Somewhat surprisingly, it turns out that delay increases the regret in a multiplicative way in adversarial problems, and in an additive way in stochastic problems. We give meta-algorithms that transform, in a black-box fashion, algorithms developed for the non-delayed case into ones that can handle the presence of delays in the feedback loop. Modifications of the well-known UCB algorithm are also developed for the bandit problem with delayed feedback, with the advantage over the meta-algorithms that they can be implemented with lower complexity.

We introduce the Randomized Dependence Coefficient (RDC), a measure of non-linear dependence between random variables of arbitrary dimension based on the Hirschfeld-Gebelein-R\'enyi Maximum Correlation Coefficient. RDC is defined in terms of correlation of random non-linear copula projections; it is invariant with respect to marginal distribution transformations, has low computational cost and is easy to implement: just five lines of R code, included at the end of the paper.

Consider a movie recommendation system where apart from the ratings information, side information such as user's age or movie's genre is also available. Unlike standard matrix completion, in this setting one should be able to predict inductively on new users/movies. In this paper, we study the problem of inductive matrix completion in the exact recovery setting. That is, we assume that the ratings matrix is generated by applying feature vectors to a low-rank matrix and the goal is to recover back the underlying matrix. Furthermore, we generalize the problem to that of low-rank matrix estimation using rank-1 measurements. We study this generic problem and provide conditions that the set of measurements should satisfy so that the alternating minimization method (which otherwise is a non-convex method with no convergence guarantees) is able to recover back the {\em exact} underlying low-rank matrix. In addition to inductive matrix completion, we show that two other low-rank estimation problems can be studied in our framework: a) general low-rank matrix sensing using rank-1 measurements, and b) multi-label regression with missing labels. For both the problems, we provide novel and interesting bounds on the number of measurements required by alternating minimization to provably converges to the {\em exact} low-rank matrix. In particular, our analysis for the general low rank matrix sensing problem significantly improves the required storage and computational cost than that required by the RIP-based matrix sensing methods \cite{RechtFP2007}. Finally, we provide empirical validation of our approach and demonstrate that alternating minimization is able to recover the true matrix for the above mentioned problems using a small number of measurements.

Probabilistic programming allows specification of probabilistic models in a declarative manner. Recently, several new software systems and languages for probabilistic programming have been developed on the basis of newly developed and improved methods for approximate inference in probabilistic models. In this contribution a probabilistic model for an idealized dark matter localization problem is described. We first derive the probabilistic model for the inference of dark matter locations and masses, and then show how this model can be implemented using BUGS and Infer.NET, two software systems for probabilistic programming. Finally, the different capabilities of both systems are discussed. The presented dark matter model includes mainly non-conjugate factors, thus, it is difficult to implement this model with Infer.NET.

The accurate prediction of time-changing covariances is an important problem in the modeling of multivariate financial data. However, some of the most popular models suffer from a) overfitting problems and multiple local optima, b) failure to capture shifts in market conditions and c) large computational costs. To address these problems we introduce a novel dynamic model for time-changing covariances. Over-fitting and local optima are avoided by following a Bayesian approach instead of computing point estimates. Changes in market conditions are captured by assuming a diffusion process in parameter values, and finally computationally efficient and scalable inference is performed using particle filters. Experiments with financial data show excellent performance of the proposed method with respect to current standard models.