The statistical leverage scores of a complex matrix $A\in\mathbb{C}^{n\times d}$ record the degree of alignment between col$(A)$ and the coordinate axes in $\mathbb{C}^n$. These score are used in random sampling algorithms for solving certain numerical linear algebra problems. In this paper we present a max-plus algebraic analogue for statistical leverage scores. We show that max-plus statistical leverage scores can be used to calculate the exact asymptotic behavior of the conventional statistical leverage scores of a generic matrices of Puiseux series and also provide a novel way to approximate the conventional statistical leverage scores of a fixed or complex matrix. The advantage of approximating a complex matrices scores with max-plus scores is that the max-plus scores can be computed very quickly. This approximation is typically accurate to within an order or magnitude and should be useful in practical problems where the true scores are known to vary widely.

We study fast learning rates when the losses are not necessarily bounded and may have a distribution with heavy tails. To enable such analyses, we introduce two new conditions: (i) the envelope function $\sup_{f \in \mathcal{F}}|\ell \circ f|$, where $\ell$ is the loss function and $\mathcal{F}$ is the hypothesis class, exists and is $L^r$-integrable, and (ii) $\ell$ satisfies the multi-scale Bernstein's condition on $\mathcal{F}$. Under these assumptions, we prove that learning rate faster than $O(n^{-1/2})$ can be obtained and, depending on $r$ and the multi-scale Bernstein's powers, can be arbitrarily close to $O(n^{-1})$. We then verify these assumptions and derive fast learning rates for the problem of vector quantization by $k$-means clustering with heavy-tailed distributions. The analyses enable us to obtain novel learning rates that extend and complement existing results in the literature from both theoretical and practical viewpoints.

There is a growing interest in joint multi-subject fMRI analysis. The challenge of such analysis comes from inherent anatomical and functional variability across subjects. One approach to resolving this is a shared response factor model. This assumes a shared and time synchronized stimulus across subjects. Such a model can often identify shared information, but it may not be able to pinpoint with high resolution the spatial location of this information. In this work, we examine a searchlight based shared response model to identify shared information in small contiguous regions (searchlights) across the whole brain. Validation using classification tasks demonstrates that we can pinpoint informative local regions.

Thanks to the rise of wearable and connected devices, sensor-generated time series comprise a large and growing fraction of the world's data. Unfortunately, extracting value from this data can be challenging, since sensors report low-level signals (e.g., acceleration), not the high-level events that are typically of interest (e.g., gestures). We introduce a technique to bridge this gap by automatically extracting examples of real-world events in low-level data, given only a rough estimate of when these events have taken place. By identifying sets of features that repeat in the same temporal arrangement, we isolate examples of such diverse events as human actions, power consumption patterns, and spoken words with up to 96% precision and recall. Our method is fast enough to run in real time and assumes only minimal knowledge of which variables are relevant or the lengths of events. Our evaluation uses numerous publicly available datasets and over 1 million samples of manually labeled sensor data.

The number of methods available for classification of multi-label data has increased rapidly over recent years, yet relatively few links have been made with the related task of classification of sequential data. If labels indices are considered as time indices, the problems can often be seen as equivalent. In this paper we detect and elaborate on connections between multi-label methods and Markovian models, and study the suitability of multi-label methods for prediction in sequential data. From this study we draw upon the most suitable techniques from the area and develop two novel competitive approaches which can be applied to either kind of data. We carry out an empirical evaluation investigating performance on real-world sequential-prediction tasks: electricity demand, and route prediction. As well as showing that several popular multi-label algorithms are in fact easily applicable to sequencing tasks, our novel approaches, which benefit from a unified view of these areas, prove very competitive against established methods. Keywords: multi-label classification; problem transformation; sequential data; sequence prediction; Markov models 1. Introduction Multi-label classification is the supervised learning problem where an instance is associated with multiple class variables (i.e., labels), rather than with a single class, as in traditional classification problems. See [1] for a review. Corresponding author, jesse.read@polytechnique.edu Preprint submitted to Pattern Recognition September 29, 2016 labels were modelled independently - at the expense of an increased computational cost. The case of binary labels is most common, where a positive class value denotes the relevance of the label (and the negative or null class denotes irrelevance). Typical examples of binary multi-label classification involve categorizing text documents and images, which can be assigned any subset of a particular label set. For example, an image can be associated with both labels beach and sunset. The multi-label classification paradigm has been successfully considered also in many other domains, such as text, video, audio, and bioinformatics - see [1] and references therein for further examples.

The empirical validation of community detection methods is often based on available annotations on the nodes that serve as putative indicators of the large-scale network structure. Most often, the suitability of the annotations as topological descriptors itself is not assessed, and without this it is not possible to ultimately distinguish between actual shortcomings of the community detection algorithms on one hand, and the incompleteness, inaccuracy or structured nature of the data annotations themselves on the other. In this work we present a principled method to access both aspects simultaneously. We construct a joint generative model for the data and metadata, and a nonparametric Bayesian framework to infer its parameters from annotated datasets. We assess the quality of the metadata not according to its direct alignment with the network communities, but rather in its capacity to predict the placement of edges in the network. We also show how this feature can be used to predict the connections to missing nodes when only the metadata is available, as well as missing metadata. By investigating a wide range of datasets, we show that while there are seldom exact agreements between metadata tokens and the inferred data groups, the metadata is often informative of the network structure nevertheless, and can improve the prediction of missing nodes. This shows that the method uncovers meaningful patterns in both the data and metadata, without requiring or expecting a perfect agreement between the two.

This paper analyzes DONE, an online optimization algorithm that iteratively minimizes an unknown function based on costly and noisy measurements. The algorithm maintains a surrogate of the unknown function in the form of a random Fourier expansion (RFE). The surrogate is updated whenever a new measurement is available, and then used to determine the next measurement point. The algorithm is comparable to Bayesian optimization algorithms, but its computational complexity per iteration does not depend on the number of measurements. We derive several theoretical results that provide insight on how the hyper-parameters of the algorithm should be chosen. The algorithm is compared to a Bayesian optimization algorithm for a benchmark problem and three applications, namely, optical coherence tomography, optical beam-forming network tuning, and robot arm control. It is found that the DONE algorithm is significantly faster than Bayesian optimization in the discussed problems, while achieving a similar or better performance.

Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To reduce the number of parameters to estimate in the model, we propose a non-asymptotic model selection procedure supported by strong theoretical guarantees based on an oracle type inequality and a minimax lower bound. The covariance matrix of the model is approximated by a block-diagonal matrix. The structure of this matrix is detected by thresholding the sample covariance matrix, where the threshold is selected using the slope heuristic. Based on the block-diagonal structure of the covariance matrix, the estimation problem is divided into several independent problems: subsequently, the network of dependencies between variables is inferred using the graphical lasso algorithm in each block. The performance of the procedure is illustrated on simulated data. An application to a real gene expression dataset with a limited sample size is also presented: the dimension reduction allows attention to be objectively focused on interactions among smaller subsets of genes, leading to a more parsimonious and interpretable modular network. Contents 1. Introduction 2 2. A method to detect block-diagonal covariance structure 3 3. Theoretical results for non-asymptotic model selection 5 4. Simulation study 8 4.1.

Recent contributions have framed linear system identification as a nonparametric regularized inverse problem. Relying on $\ell_2$-type regularization which accounts for the stability and smoothness of the impulse response to be estimated, these approaches have been shown to be competitive w.r.t classical parametric methods. In this paper, adopting Maximum Entropy arguments, we derive a new $\ell_2$ penalty deriving from a vector-valued kernel; to do so we exploit the structure of the Hankel matrix, thus controlling at the same time complexity, measured by the McMillan degree, stability and smoothness of the identified models. As a special case we recover the nuclear norm penalty on the squared block Hankel matrix. In contrast with previous literature on reweighted nuclear norm penalties, our kernel is described by a small number of hyper-parameters, which are iteratively updated through marginal likelihood maximization; constraining the structure of the kernel acts as a (hyper)regularizer which helps controlling the effective degrees of freedom of our estimator. To optimize the marginal likelihood we adapt a Scaled Gradient Projection (SGP) algorithm which is proved to be significantly computationally cheaper than other first and second order off-the-shelf optimization methods. The paper also contains an extensive comparison with many state-of-the-art methods on several Monte-Carlo studies, which confirms the effectiveness of our procedure.

Gary Glasberg, executive producer and show runner of CBS' hit "NCIS" and the creator and executive producer of its spinoff, "NCIS: New Orleans," has died. A statement from the network said that Glasberg, who was born in New York City, had died in his sleep. No other information was given. Glasberg joined "NCIS," which revolves around a team of special agents from the Naval Criminal Investigative Service, in 2009 as a co-executive producer and writer. He became its show runner in 2011.