We investigate the use of sparse coding and dictionary learning in the context of multitask and transfer learning. The central assumption of our learning method is that the tasks parameters are well approximated by sparse linear combinations of the atoms of a dictionary on a high or infinite dimensional space. This assumption, together with the large quantity of available data in the multitask and transfer learning settings, allows a principled choice of the dictionary. We provide bounds on the generalization error of this approach, for both settings. Numerical experiments on one synthetic and two real datasets show the advantage of our method over single task learning, a previous method based on orthogonal and dense representation of the tasks and a related method learning task grouping.

We study Bayesian optimal control of a general class of smoothly parameterized Markov decision problems. Since computing the optimal control is computationally expensive, we design an algorithm that trades off performance for computational efficiency. The algorithm is a lazy posterior sampling method that maintains a distribution over the unknown parameter. The algorithm changes its policy only when the variance of the distribution is reduced sufficiently. Importantly, we analyze the algorithm and show the precise nature of the performance vs. computation tradeoff. Finally, we show the effectiveness of the method on a web server control application.

A matroid is a notion of independence in combinatorial optimization which is closely related to computational efficiency. In particular, it is well known that the maximum of a constrained modular function can be found greedily if and only if the constraints are associated with a matroid. In this paper, we bring together the ideas of bandits and matroids, and propose a new class of combinatorial bandits, matroid bandits. The objective in these problems is to learn how to maximize a modular function on a matroid. This function is stochastic and initially unknown. We propose a practical algorithm for solving our problem, Optimistic Matroid Maximization (OMM); and prove two upper bounds, gap-dependent and gap-free, on its regret. Both bounds are sublinear in time and at most linear in all other quantities of interest. The gap-dependent upper bound is tight and we prove a matching lower bound on a partition matroid bandit. Finally, we evaluate our method on three real-world problems and show that it is practical.

In this work we propose a simple and easily parallelizable algorithm for multiway graph partitioning. The algorithm alternates between three basic components: diffusing seed vertices over the graph, thresholding the diffused seeds, and then randomly reseeding the thresholded clusters. We demonstrate experimentally that the proper combination of these ingredients leads to an algorithm that achieves state-of-the-art performance in terms of cluster purity on standard benchmarks datasets. Moreover, the algorithm runs an order of magnitude faster than the other algorithms that achieve comparable results in terms of accuracy. We also describe a coarsen, cluster and refine approach similar to GRACLUS and METIS that removes an additional order of magnitude from the runtime of our algorithm while still maintaining competitive accuracy.

In addition to finding meaningful clusters, centroid-based clustering algorithms such as K-means or mean-shift should ideally find centroids that are valid patterns in the input space, representative of data in their cluster. This is challenging with data having a nonconvex or manifold structure, as with images or text. We introduce a new algorithm, Laplacian K-modes, which naturally combines three powerful ideas in clustering: the explicit use of assignment variables (as in K-means); the estimation of cluster centroids which are modes of each cluster's density estimate (as in mean-shift); and the regularizing effect of the graph Laplacian, which encourages similar assignments for nearby points (as in spectral clustering). The optimization algorithm alternates an assignment step, which is a convex quadratic program, and a mean-shift step, which separates for each cluster centroid. The algorithm finds meaningful density estimates for each cluster, even with challenging problems where the clusters have manifold structure, are highly nonconvex or in high dimension. It also provides centroids that are valid patterns, truly representative of their cluster (unlike K-means), and an out-of-sample mapping that predicts soft assignments for a new point.

Stochastic gradient descent algorithms for training linear and kernel predictors are gaining more and more importance, thanks to their scalability. While various methods have been proposed to speed up their convergence, the model selection phase is often ignored. In fact, in theoretical works most of the time assumptions are made, for example, on the prior knowledge of the norm of the optimal solution, while in the practical world validation methods remain the only viable approach. In this paper, we propose a new kernel-based stochastic gradient descent algorithm that performs model selection while training, with no parameters to tune, nor any form of cross-validation. The algorithm builds on recent advancement in online learning theory for unconstrained settings, to estimate over time the right regularization in a data-dependent way. Optimal rates of convergence are proved under standard smoothness assumptions on the target function, using the range space of the fractional integral operator associated with the kernel.

In this paper we develop a dynamic form of Bayesian optimization for machine learning models with the goal of rapidly finding good hyperparameter settings. Our method uses the partial information gained during the training of a machine learning model in order to decide whether to pause training and start a new model, or resume the training of a previously-considered model. We specifically tailor our method to machine learning problems by developing a novel positive-definite covariance kernel to capture a variety of training curves. Furthermore, we develop a Gaussian process prior that scales gracefully with additional temporal observations. Finally, we provide an information-theoretic framework to automate the decision process. Experiments on several common machine learning models show that our approach is extremely effective in practice.

Capturing the compositional process which maps the meaning of words to that of documents is a central challenge for researchers in Natural Language Processing and Information Retrieval. We introduce a model that is able to represent the meaning of documents by embedding them in a low dimensional vector space, while preserving distinctions of word and sentence order crucial for capturing nuanced semantics. Our model is based on an extended Dynamic Convolution Neural Network, which learns convolution filters at both the sentence and document level, hierarchically learning to capture and compose low level lexical features into high level semantic concepts. We demonstrate the effectiveness of this model on a range of document modelling tasks, achieving strong results with no feature engineering and with a more compact model. Inspired by recent advances in visualising deep convolution networks for computer vision, we present a novel visualisation technique for our document networks which not only provides insight into their learning process, but also can be interpreted to produce a compelling automatic summarisation system for texts.

Graphical Models have various applications in science and engineering which include physics, bioinformatics, telecommunication and etc. Usage of graphical models needs complex computations in order to evaluation of marginal functions,so there are some powerful methods including mean field approximation, belief propagation algorithm and etc. Quantum graphical models have been recently developed in context of quantum information and computation, and quantum statistical physics, which is possible by generalization of classical probability theory to quantum theory. The main goal of this paper is preparing a primary generalization of Markov network, as a type of graphical models, to quantum case and applying in quantum statistical physics.We have investigated the Markov network and the role of commuting Hamiltonian terms in conditional independence with simple examples of quantum statistical physics.

Despite the fact that they do not consider the temporal nature of data, classic dimensionality reduction techniques, such as PCA, are widely applied to time series data. In this paper, we introduce a factor decomposition specific for time series that builds upon the Bayesian multivariate autoregressive model and hence evades the assumption that data points are mutually independent. The key is to find a low-rank estimation of the autoregressive matrices. As in the probabilistic version of other factor models, this induces a latent low-dimensional representation of the original data. We discuss some possible generalisations and alternatives, with the most relevant being a technique for simultaneous smoothing and dimensionality reduction. To illustrate the potential applications, we apply the model on a synthetic data set and different types of neuroimaging data (EEG and ECoG).