Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the same distribution and for the case where there exists some mismatch between training and test distributions. We confirm the theoretical results by designing feature selection algorithms using the criteria from these bounds and by evaluating the algorithms on a series of pathological speech classification tasks.

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.

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.

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.

Typical dimensionality reduction (DR) methods are often data-oriented, focusing on directly reducing the number of random variables (features) while retaining the maximal variations in the high-dimensional data. In unsupervised situations, one of the main limitations of these methods lies in their dependency on the scale of data features. This paper aims to address the problem from a new perspective and considers model-oriented dimensionality reduction in parameter spaces of binary multivariate distributions. Specifically, we propose a general parameter reduction criterion, called Confident-Information-First (CIF) principle, to maximally preserve confident parameters and rule out less confident parameters. Formally, the confidence of each parameter can be assessed by its contribution to the expected Fisher information distance within the geometric manifold over the neighbourhood of the underlying real distribution. We then revisit Boltzmann machines (BM) from a model selection perspective and theoretically show that both the fully visible BM (VBM) and the BM with hidden units can be derived from the general binary multivariate distribution using the CIF principle. This can help us uncover and formalize the essential parts of the target density that BM aims to capture and the non-essential parts that BM should discard. Guided by the theoretical analysis, we develop a sample-specific CIF for model selection of BM that is adaptive to the observed samples. The method is studied in a series of density estimation experiments and has been shown effective in terms of the estimate accuracy.

A relatively recent advance in cognitive neuroscience has been multi-voxel pattern analysis (MVPA), which enables researchers to decode brain states and/or the type of information represented in the brain during a cognitive operation. MVPA methods utilize machine learning algorithms to distinguish among types of information or cognitive states represented in the brain, based on distributed patterns of neural activity. In the current investigation, we propose a new approach for representation of neural data for pattern analysis, namely a Mesh Learning Model. In this approach, at each time instant, a star mesh is formed around each voxel, such that the voxel corresponding to the center node is surrounded by its p-nearest neighbors. The arc weights of each mesh are estimated from the voxel intensity values by least squares method. The estimated arc weights of all the meshes, called Mesh Arc Descriptors (MADs), are then used to train a classifier, such as Neural Networks, k-Nearest Neighbor, Na\"ive Bayes and Support Vector Machines. The proposed Mesh Model was tested on neuroimaging data acquired via functional magnetic resonance imaging (fMRI) during a recognition memory experiment using categorized word lists, employing a previously established experimental paradigm (\"Oztekin & Badre, 2011). Results suggest that the proposed Mesh Learning approach can provide an effective algorithm for pattern analysis of brain activity during cognitive processing.

Inference and learning of graphical models are both well-studied problems in statistics and machine learning that have found many applications in science and engineering. However, exact inference is intractable in general graphical models, which suggests the problem of seeking the best approximation to a collection of random variables within some tractable family of graphical models. In this paper, we focus on the class of planar Ising models, for which exact inference is tractable using techniques of statistical physics. Based on these techniques and recent methods for planarity testing and planar embedding, we propose a simple greedy algorithm for learning the best planar Ising model to approximate an arbitrary collection of binary random variables (possibly from sample data). Given the set of all pairwise correlations among variables, we select a planar graph and optimal planar Ising model defined on this graph to best approximate that set of correlations. We demonstrate our method in simulations and for the application of modeling senate voting records.

Crowdsourcing provides a popular paradigm for data collection at scale. We study the problem of selecting subsets of workers from a given worker pool to maximize the accuracy under a budget constraint. One natural question is whether we should hire as many workers as the budget allows, or restrict on a small number of top-quality workers. By theoretically analyzing the error rate of a typical setting in crowdsourcing, we frame the worker selection problem into a combinatorial optimization problem and propose an algorithm to solve it efficiently. Empirical results on both simulated and real-world datasets show that our algorithm is able to select a small number of high-quality workers, and performs as good as, sometimes even better than, the much larger crowds as the budget allows.

A crucial task in system identification problems is the selection of the most appropriate model class, and is classically addressed resorting to cross-validation or using order selection criteria based on asymptotic arguments. As recently suggested in the literature, this can be addressed in a Bayesian framework, where model complexity is regulated by few hyperparameters, which can be estimated via marginal likelihood maximization. It is thus of primary importance to design effective optimization methods to solve the corresponding optimization problem. If the unknown impulse response is modeled as a Gaussian process with a suitable kernel, the maximization of the marginal likelihood leads to a challenging nonconvex optimization problem, which requires a stable and effective solution strategy. In this paper we address this problem by means of a scaled gradient projection algorithm, in which the scaling matrix and the steplength parameter play a crucial role to provide a meaningful solution in a computational time comparable with second order methods. In particular, we propose both a generalization of the split gradient approach to design the scaling matrix in the presence of box constraints, and an effective implementation of the gradient and objective function. The extensive numerical experiments carried out on several test problems show that our method is very effective in providing in few tenths of a second solutions of the problems with accuracy comparable with state-of-the-art approaches. Moreover, the flexibility of the proposed strategy makes it easily adaptable to a wider range of problems arising in different areas of machine learning, signal processing and system identification.