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 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.

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.

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).

Consider a linear regression model where the design matrix X has n rows and p columns. We assume (a) p is much large than n, (b) the coefficient vector beta is sparse in the sense that only a small fraction of its coordinates is nonzero, and (c) the Gram matrix G = X'X is sparse in the sense that each row has relatively few large coordinates (diagonals of G are normalized to 1). The sparsity in G naturally induces the sparsity of the so-called graph of strong dependence (GOSD). We find an interesting interplay between the signal sparsity and the graph sparsity, which ensures that in a broad context, the set of true signals decompose into many different small-size components of GOSD, where different components are disconnected. We propose Graphlet Screening (GS) as a new approach to variable selection, which is a two-stage Screen and Clean method. The key methodological innovation of GS is to use GOSD to guide both the screening and cleaning. Compared to m-variate brute-forth screening that has a computational cost of p^m, the GS only has a computational cost of p (up to some multi-log(p) factors) in screening. We measure the performance of any variable selection procedure by the minimax Hamming distance. We show that in a very broad class of situations, GS achieves the optimal rate of convergence in terms of the Hamming distance. Somewhat surprisingly, the well-known procedures subset selection and the lasso are rate non-optimal, even in very simple settings and even when their tuning parameters are ideally set.

Space and time are two critical components of many real world systems. For this reason, analysis of anomalies in spatiotemporal data has been a great of interest. In this work, application of tensor decomposition and eigenspace techniques on spatiotemporal hotspot detection is investigated. An algorithm called SST-Hotspot is proposed which accounts for spatiotemporal variations in data and detect hotspots using matching of eigenvector elements of two cases and population tensors. The experimental results reveal the interesting application of tensor decomposition and eigenvector-based techniques in hotspot analysis.

Hotspot detection aims at identifying subgroups in the observations that are unexpected, with respect to the some baseline information. For instance, in disease surveillance, the purpose is to detect sub-regions in spatiotemporal space, where the count of reported diseases (e.g. Cancer) is higher than expected, with respect to the population. The state-of-the-art method for this kind of problem is the Space-Time Scan Statistics (STScan), which exhaustively search the whole space through a sliding window looking for significant spatiotemporal clusters. STScan makes some restrictive assumptions about the distribution of data, the shape of the hotspots and the quality of data, which can be unrealistic for some nontraditional data sources. A novel methodology called EigenSpot is proposed where instead of an exhaustive search over the space, tracks the changes in a space-time correlation structure. Not only does the new approach presents much more computational efficiency, but also makes no assumption about the data distribution, hotspot shape or the data quality. The principal idea is that with the joint combination of abnormal elements in the principal spatial and the temporal singular vectors, the location of hotspots in the spatiotemporal space can be approximated. A comprehensive experimental evaluation, both on simulated and real data sets reveals the effectiveness of the proposed method.

Failure detection in telecommunication networks is a vital task. So far, several supervised and unsupervised solutions have been provided for discovering failures in such networks. Among them unsupervised approaches has attracted more attention since no label data is required. Often, network devices are not able to provide information about the type of failure. In such cases the type of failure is not known in advance and the unsupervised setting is more appropriate for diagnosis. Among unsupervised approaches, Principal Component Analysis (PCA) is a well-known solution which has been widely used in the anomaly detection literature and can be applied to matrix data (e.g. Users-Features). However, one of the important properties of network data is their temporal sequential nature. So considering the interaction of dimensions over a third dimension, such as time, may provide us better insights into the nature of network failures. In this paper we demonstrate the power of three-way analysis to detect events and anomalies in time-evolving network data.

Recovering a large matrix from limited measurements is a challenging task arising in many real applications, such as image inpainting, compressive sensing and medical imaging, and this kind of problems are mostly formulated as low-rank matrix approximation problems. Due to the rank operator being non-convex and discontinuous, most of the recent theoretical studies use the nuclear norm as a convex relaxation and the low-rank matrix recovery problem is solved through minimization of the nuclear norm regularized problem. However, a major limitation of nuclear norm minimization is that all the singular values are simultaneously minimized and the rank may not be well approximated \cite{hu2012fast}. Correspondingly, in this paper, we propose a new multi-stage algorithm, which makes use of the concept of Truncated Nuclear Norm Regularization (TNNR) proposed in \citep{hu2012fast} and Iterative Support Detection (ISD) proposed in \citep{wang2010sparse} to overcome the above limitation. Besides matrix completion problems considered in \citep{hu2012fast}, the proposed method can be also extended to the general low-rank matrix recovery problems. Extensive experiments well validate the superiority of our new algorithms over other state-of-the-art methods.