As a model for an on-line classification setting we consider a stochastic process $(X_{-n},Y_{-n})_{n}$, the present time-point being denoted by 0, with observables $ \ldots,X_{-n},X_{-n+1},\ldots, X_{-1}, X_0$ from which the pattern $Y_0$ is to be inferred. So in this classification setting, in addition to the present observation $X_0$ a number $l$ of preceding observations may be used for classification, thus taking a possible dependence structure into account as it occurs e.g. in an ongoing classification of handwritten characters. We treat the question how the performance of classifiers is improved by using such additional information. For our analysis, a hidden Markov model is used. Letting $R_l$ denote the minimal risk of misclassification using $l$ preceding observations we show that the difference $\sup_k |R_l - R_{l+k}|$ decreases exponentially fast as $l$ increases. This suggests that a small $l$ might already lead to a noticeable improvement. To follow this point we look at the use of past observations for kernel classification rules. Our practical findings in simulated hidden Markov models and in the classification of handwritten characters indicate that using $l=1$, i.e. just the last preceding observation in addition to $X_0$, can lead to a substantial reduction of the risk of misclassification. So, in the presence of stochastic dependencies, we advocate to use $ X_{-1},X_0$ for finding the pattern $Y_0$ instead of only $X_0$ as one would in the independent situation.

In this paper, we look to address the problem of estimating the dynamic direction of arrival (DOA) of a narrowband signal impinging on a sensor array from the far field. The initial estimate is made using a Bayesian compressive sensing (BCS) framework and then tracked using a Bayesian compressed sensing Kalman filter (BCSKF). The BCS framework splits the angular region into N potential DOAs and enforces a belief that only a few of the DOAs will have a non-zero valued signal present. A BCSKF can then be used to track the change in the DOA using the same framework. There can be an issue when the DOA approaches the endfire of the array. In this angular region current methods can struggle to accurately estimate and track changes in the DOAs. To tackle this problem, we propose changing the traditional sparse belief associated with BCS to a belief that the estimated signals will match the predicted signals given a known DOA change. This is done by modelling the difference between the expected sparse received signals and the estimated sparse received signals as a Gaussian distribution. Example test scenarios are provided and comparisons made with the traditional BCS based estimation method. They show that an improvement in estimation accuracy is possible without a significant increase in computational complexity.

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally infeasible. The recently proposed stochastic gradient Langevin dynamics (SGLD) method circumvents this problem in three ways: it generates proposed moves using only a subset of the data, it skips the Metropolis-Hastings accept-reject step, and it uses sequences of decreasing step sizes. In \cite{TehThierryVollmerSGLD2014}, we provided the mathematical foundations for the decreasing step size SGLD, including consistency and a central limit theorem. However, in practice the SGLD is run for a relatively small number of iterations, and its step size is not decreased to zero. The present article investigates the behaviour of the SGLD with fixed step size. In particular we characterise the asymptotic bias explicitly, along with its dependence on the step size and the variance of the stochastic gradient. On that basis a modified SGLD which removes the asymptotic bias due to the variance of the stochastic gradients up to first order in the step size is derived. Moreover, we are able to obtain bounds on the finite-time bias, variance and mean squared error (MSE). The theory is illustrated with a Gaussian toy model for which the bias and the MSE for the estimation of moments can be obtained explicitly. For this toy model we study the gain of the SGLD over the standard Euler method in the limit of large data sets.

This paper addresses the problem of neighborhood selection for Gaussian graphical models. We present two heuristic algorithms: a forward-backward greedy algorithm for general Gaussian graphical models based on mutual information test, and a threshold-based algorithm for walk summable Gaussian graphical models. Both algorithms are shown to be structurally consistent, and efficient. Numerical results show that both algorithms work very well.

Transferring knowledge across a sequence of related tasks is an important challenge in reinforcement learning (RL). Despite much encouraging empirical evidence, there has been little theoretical analysis. In this paper, we study a class of lifelong RL problems: the agent solves a sequence of tasks modeled as finite Markov decision processes (MDPs), each of which is from a finite set of MDPs with the same state/action sets and different transition/reward functions. Motivated by the need for cross-task exploration in lifelong learning, we formulate a novel online coupon-collector problem and give an optimal algorithm. This allows us to develop a new lifelong RL algorithm, whose overall sample complexity in a sequence of tasks is much smaller than single-task learning, even if the sequence of tasks is generated by an adversary. Benefits of the algorithm are demonstrated in simulated problems, including a recently introduced human-robot interaction problem.

Classification and clustering are both important topics in statistical learning. A natural question herein is whether predefined classes are really different from one another, or whether clusters are really there. Specifically, we may be interested in knowing whether the two classes defined by some class labels (when they are provided), or the two clusters tagged by a clustering algorithm (where class labels are not provided), are from the same underlying distribution. Although both are challenging questions for the high-dimensional, low-sample size data, there has been some recent development for both. However, when it is costly to manually place labels on observations, it is often that only a small portion of the class labels is available. In this article, we propose a significance analysis approach for such type of data, namely partially labeled data. Our method makes use of the whole data and tries to test the class difference as if all the labels were observed. Compared to a testing method that ignores the label information, our method provides a greater power, meanwhile, maintaining the size, illustrated by a comprehensive simulation study. Theoretical properties of the proposed method are studied with emphasis on the high-dimensional, low-sample size setting. Our simulated examples help to understand when and how the information extracted from the labeled data can be effective. A real data example further illustrates the usefulness of the proposed method.

In this paper we develop a statistical theory and an implementation of deep learning (DL) models. We show that an elegant variable splitting scheme for the alternating direction method of multipliers (ADMM) optimises a deep learning objective. We allow for non-smooth non-convex regularisation penalties to induce sparsity in parameter weights. We provide a link between traditional shallow layer statistical models such as principal component and sliced inverse regression and deep layer models. We also define the degrees of freedom of a deep learning predictor and a predictive MSE criteria to perform model selection for comparing architecture designs. We focus on deep multiclass logistic learning although our methods apply more generally. Our results suggest an interesting and previously under-exploited relationship between deep learning and proximal splitting techniques. To illustrate our methodology, we provide a multi-class logit classification analysis of Fisher's Iris data where we illustrate the convergence of our algorithm. Finally, we conclude with directions for future research.

Causality has been recently introduced in databases, to model, characterize and possibly compute causes for query results (answers). Connections between query causality and consistency-based diagnosis and database repairs (wrt. integrity constrain violations) have been established in the literature. In this work we establish connections between query causality and abductive diagnosis and the view-update problem. The unveiled relationships allow us to obtain new complexity results for query causality -the main focus of our work- and also for the two other areas.

There is a large variety of objects and appliances in human environments, such as stoves, coffee dispensers, juice extractors, and so on. It is challenging for a roboticist to program a robot for each of these object types and for each of their instantiations. In this work, we present a novel approach to manipulation planning based on the idea that many household objects share similarly-operated object parts. We formulate the manipulation planning as a structured prediction problem and design a deep learning model that can handle large noise in the manipulation demonstrations and learns features from three different modalities: point-clouds, language and trajectory. In order to collect a large number of manipulation demonstrations for different objects, we developed a new crowd-sourcing platform called Robobarista. We test our model on our dataset consisting of 116 objects with 249 parts along with 250 language instructions, for which there are 1225 crowd-sourced manipulation demonstrations. We further show that our robot can even manipulate objects it has never seen before.

Continuous vector representations of words and objects appear to carry surprisingly rich semantic content. In this paper, we advance both the conceptual and theoretical understanding of word embeddings in three ways. First, we ground embeddings in semantic spaces studied in cognitive-psychometric literature and introduce new evaluation tasks. Second, in contrast to prior work, we take metric recovery as the key object of study, unify existing algorithms as consistent metric recovery methods based on co-occurrence counts from simple Markov random walks, and propose a new recovery algorithm. Third, we generalize metric recovery to graphs and manifolds, relating co-occurence counts on random walks in graphs and random processes on manifolds to the underlying metric to be recovered, thereby reconciling manifold estimation and embedding algorithms. We compare embedding algorithms across a range of tasks, from nonlinear dimensionality reduction to three semantic language tasks, including analogies, sequence completion, and classification.