We consider a planning problem where the dynamics and rewards of the environment depend on a hidden static parameter referred to as the context. The objective is to learn a strategy that maximizes the accumulated reward across all contexts. The new model, called Contextual Markov Decision Process (CMDP), can model a customer's behavior when interacting with a website (the learner). The customer's behavior depends on gender, age, location, device, etc. Based on that behavior, the website objective is to determine customer characteristics, and to optimize the interaction between them. Our work focuses on one basic scenario--finite horizon with a small known number of possible contexts. We suggest a family of algorithms with provable guarantees that learn the underlying models and the latent contexts, and optimize the CMDPs. Bounds are obtained for specific naive implementations, and extensions of the framework are discussed, laying the ground for future research.

There has been an explosion of interest in functional Magnetic Resonance Imaging (MRI) during the past two decades. Naturally, this has been accompanied by many major advances in the understanding of the human connectome. These advances have served to pose novel challenges as well as open new avenues for research. One of the most promising and exciting of such avenues is the study of functional MRI in real-time. Such studies have recently gained momentum and have been applied in a wide variety of settings; ranging from training of healthy subjects to self-regulate neuronal activity to being suggested as potential treatments for clinical populations. To date, the vast majority of these studies have focused on a single region at a time. This is due in part to the many challenges faced when estimating dynamic functional connectivity networks in real-time. In this work we propose a novel methodology with which to accurately track changes in functional connectivity networks in real-time. We adapt the recently proposed SINGLE algorithm for estimating sparse and temporally homo- geneous dynamic networks to be applicable in real-time. The proposed method is applied to motor task data from the Human Connectome Project as well as to real-time data ob- tained while exploring a virtual environment. We show that the algorithm is able to estimate significant task-related changes in network structure quickly enough to be useful in future brain-computer interface applications.

Ranking is a key aspect of many applications, such as information retrieval, question answering, ad placement and recommender systems. Learning to rank has the goal of estimating a ranking model automatically from training data. In practical settings, the task often reduces to estimating a rank functional of an object with respect to a query. In this paper, we investigate key issues in designing an effective learning to rank algorithm. These include data representation, the choice of rank functionals, the design of the loss function so that it is correlated with the rank metrics used in evaluation. For the loss function, we study three techniques: approximating the rank metric by a smooth function, decomposition of the loss into a weighted sum of element-wise losses and into a weighted sum of pairwise losses. We then present derivations of piecewise losses using the theory of high-order Markov chains and Markov random fields. In experiments, we evaluate these design aspects on two tasks: answer ranking in a Social Question Answering site, and Web Information Retrieval.

We propose a framework for distributed robust statistical learning on {\em big contaminated data}. The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of magnitude. We analyze the robustness property of DRL, showing that DRL not only preserves the robustness of the base robust learning method, but also tolerates contaminations on a constant fraction of results from computing nodes (node failures). More precisely, even in presence of the most adversarial outlier distribution over computing nodes, DRL still achieves a breakdown point of at least $ \lambda^*/2 $, where $ \lambda^* $ is the break down point of corresponding centralized algorithm. This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of $ k $ when $ k $ computing nodes are used. We then specialize the DRL framework for two concrete cases: distributed robust principal component analysis and distributed robust regression. We demonstrate the efficiency and the robustness advantages of DRL through comprehensive simulations and predicting image tags on a large-scale image set.

Recommender systems, medical diagnosis, network security, etc., require on-going learning and decision-making in real time. These -- and many others -- represent perfect examples of the opportunities and difficulties presented by Big Data: the available information often arrives from a variety of sources and has diverse features so that learning from all the sources may be valuable but integrating what is learned is subject to the curse of dimensionality. This paper develops and analyzes algorithms that allow efficient learning and decision-making while avoiding the curse of dimensionality. We formalize the information available to the learner/decision-maker at a particular time as a context vector which the learner should consider when taking actions. In general the context vector is very high dimensional, but in many settings, the most relevant information is embedded into only a few relevant dimensions. If these relevant dimensions were known in advance, the problem would be simple -- but they are not. Moreover, the relevant dimensions may be different for different actions. Our algorithm learns the relevant dimensions for each action, and makes decisions based in what it has learned. Formally, we build on the structure of a contextual multi-armed bandit by adding and exploiting a relevance relation. We prove a general regret bound for our algorithm whose time order depends only on the maximum number of relevant dimensions among all the actions, which in the special case where the relevance relation is single-valued (a function), reduces to $\tilde{O}(T^{2(\sqrt{2}-1)})$; in the absence of a relevance relation, the best known contextual bandit algorithms achieve regret $\tilde{O}(T^{(D+1)/(D+2)})$, where $D$ is the full dimension of the context vector.

Gaussian Mixture Models (GMM) have found many applications in density estimation and data clustering. However, the model does not adapt well to curved and strongly nonlinear data. Recently there appeared an improvement called AcaGMM (Active curve axis Gaussian Mixture Model), which fits Gaussians along curves using an EM-like (Expectation Maximization) approach. Using the ideas standing behind AcaGMM, we build an alternative active function model of clustering, which has some advantages over AcaGMM. In particular it is naturally defined in arbitrary dimensions and enables an easy adaptation to clustering of complicated datasets along the predefined family of functions. Moreover, it does not need external methods to determine the number of clusters as it automatically reduces the number of groups on-line.

We study the following generalized matrix rank estimation problem: given an $n \times n$ matrix and a constant $c \geq 0$, estimate the number of eigenvalues that are greater than $c$. In the distributed setting, the matrix of interest is the sum of $m$ matrices held by separate machines. We show that any deterministic algorithm solving this problem must communicate $\Omega(n^2)$ bits, which is order-equivalent to transmitting the whole matrix. In contrast, we propose a randomized algorithm that communicates only $\widetilde O(n)$ bits. The upper bound is matched by an $\Omega(n)$ lower bound on the randomized communication complexity. We demonstrate the practical effectiveness of the proposed algorithm with some numerical experiments.

Multi-output Gaussian processes (MOGP) are probability distributions over vector-valued functions, and have been previously used for multi-output regression and for multi-class classification. A less explored facet of the multi-output Gaussian process is that it can be used as a generative model for vector-valued random fields in the context of pattern recognition. As a generative model, the multi-output GP is able to handle vector-valued functions with continuous inputs, as opposed, for example, to hidden Markov models. It also offers the ability to model multivariate random functions with high dimensional inputs. In this report, we use a discriminative training criteria known as Minimum Classification Error to fit the parameters of a multi-output Gaussian process. We compare the performance of generative training and discriminative training of MOGP in emotion recognition, activity recognition, and face recognition. We also compare the proposed methodology against hidden Markov models trained in a generative and in a discriminative way.

Massively multitask neural architectures provide a learning framework for drug discovery that synthesizes information from many distinct biological sources. To train these architectures at scale, we gather large amounts of data from public sources to create a dataset of nearly 40 million measurements across more than 200 biological targets. We investigate several aspects of the multitask framework by performing a series of empirical studies and obtain some interesting results: (1) massively multitask networks obtain predictive accuracies significantly better than single-task methods, (2) the predictive power of multitask networks improves as additional tasks and data are added, (3) the total amount of data and the total number of tasks both contribute significantly to multitask improvement, and (4) multitask networks afford limited transferability to tasks not in the training set. Our results underscore the need for greater data sharing and further algorithmic innovation to accelerate the drug discovery process.

We give two provably accurate feature-selection techniques for the linear SVM. The algorithms run in deterministic and randomized time respectively. Our algorithms can be used in an unsupervised or supervised setting. The supervised approach is based on sampling features from support vectors. We prove that the margin in the feature space is preserved to within $\epsilon$-relative error of the margin in the full feature space in the worst-case. In the unsupervised setting, we also provide worst-case guarantees of the radius of the minimum enclosing ball, thereby ensuring comparable generalization as in the full feature space and resolving an open problem posed in Dasgupta et al. We present extensive experiments on real-world datasets to support our theory and to demonstrate that our method is competitive and often better than prior state-of-the-art, for which there are no known provable guarantees.