We consider the problem of distributed dictionary learning, where a set of nodes is required to collectively learn a common dictionary from noisy measurements. This approach may be useful in several contexts including sensor networks. Diffusion cooperation schemes have been proposed to solve the distributed linear regression problem. In this work we focus on a diffusion-based adaptive dictionary learning strategy: each node records observations and cooperates with its neighbors by sharing its local dictionary. The resulting algorithm corresponds to a distributed block coordinate descent (alternate optimization). Beyond dictionary learning, this strategy could be adapted to many matrix factorization problems and generalized to various settings. This article presents our approach and illustrates its efficiency on some numerical examples.

We consider the problem of online linear regression on arbitrary deterministic sequences when the ambient dimension d can be much larger than the number of time rounds T. We introduce the notion of sparsity regret bound, which is a deterministic online counterpart of recent risk bounds derived in the stochastic setting under a sparsity scenario. We prove such regret bounds for an online-learning algorithm called SeqSEW and based on exponential weighting and data-driven truncation. In a second part we apply a parameter-free version of this algorithm to the stochastic setting (regression model with random design). This yields risk bounds of the same flavor as in Dalalyan and Tsybakov (2011) but which solve two questions left open therein. In particular our risk bounds are adaptive (up to a logarithmic factor) to the unknown variance of the noise if the latter is Gaussian. We also address the regression model with fixed design.

We introduce a new approach to variable selection, called Predictive Correlation Screening, for predictor design. Predictive Correlation Screening (PCS) implements false positive control on the selected variables, is well suited to small sample sizes, and is scalable to high dimensions. We establish asymptotic bounds for Familywise Error Rate (FWER), and resultant mean square error of a linear predictor on the selected variables. We apply Predictive Correlation Screening to the following two-stage predictor design problem. An experimenter wants to learn a multivariate predictor of gene expressions based on successive biological samples assayed on mRNA arrays. She assays the whole genome on a few samples and from these assays she selects a small number of variables using Predictive Correlation Screening. To reduce assay cost, she subsequently assays only the selected variables on the remaining samples, to learn the predictor coefficients. We show superiority of Predictive Correlation Screening relative to LASSO and correlation learning (sometimes popularly referred to in the literature as marginal regression or simple thresholding) in terms of performance and computational complexity.

The Dirichlet process (DP) is a fundamental mathematical tool for Bayesian nonparametric modeling, and is widely used in tasks such as density estimation, natural language processing, and time series modeling. Although MCMC inference methods for the DP often provide a gold standard in terms asymptotic accuracy, they can be computationally expensive and are not obviously parallelizable. We propose a reparameterization of the Dirichlet process that induces conditional independencies between the atoms that form the random measure. This conditional independence enables many of the Markov chain transition operators for DP inference to be simulated in parallel across multiple cores. Applied to mixture modeling, our approach enables the Dirichlet process to simultaneously learn clusters that describe the data and superclusters that define the granularity of parallelization. Unlike previous approaches, our technique does not require alteration of the model and leaves the true posterior distribution invariant. It also naturally lends itself to a distributed software implementation in terms of Map-Reduce, which we test in cluster configurations of over 50 machines and 100 cores. We present experiments exploring the parallel efficiency and convergence properties of our approach on both synthetic and real-world data, including runs on 1MM data vectors in 256 dimensions.

Approaches for testing sets of variants, such as a set of rare or common variants within a gene or pathway, for association with complex traits are important. In particular, set tests allow for aggregation of weak signal within a set, can capture interplay among variants, and reduce the burden of multiple hypothesis testing. Until now, these approaches did not address confounding by family relatedness and population structure, a problem that is becoming more important as larger data sets are used to increase power. Results: We introduce a new approach for set tests that handles confounders. Our model is based on the linear mixed model and uses two random effects-one to capture the set association signal and one to capture confounders. We also introduce a computational speedup for two-random-effects models that makes this approach feasible even for extremely large cohorts. Using this model with both the likelihood ratio test and score test, we find that the former yields more power while controlling type I error. Application of our approach to richly structured GAW14 data demonstrates that our method successfully corrects for population structure and family relatedness, while application of our method to a 15,000 individual Crohn's disease case-control cohort demonstrates that it additionally recovers genes not recoverable by univariate analysis. Availability: A Python-based library implementing our approach is available at http://mscompbio.codeplex.com

We have developed a method for statistical anomaly detection which has been deployed in a tool for condition monitoring of train fleets. The anomaly detection component helps the operators to quickly find significant deviations from normal behavior and to detect early indications for possible problems. The savings in maintenance costs comes mainly from avoiding costly breakdowns, and have been estimated to several million Euros per year for the tool. In the long run, it is expected that maintenance costs can be reduced with between 5 and 10 % by using the tool.

The Swedish Institute of Computer Science (SICS) has for several years developed methods for statistical anomaly detection based on a framework called Bayesian principal anomaly (Holst and Ekman 2011). In this article we describe a novel application Addtrack is a tool developed originally by Bombardier domain for the anomaly-detection method: condition Transportation for general analysis, monitoring, monitoring of trains (Holst, Ekman, and and visualization of train conditions and Larsen 2006). It is "intelligent" in statistical models. There are currently many the sense that analysis modules, such as the one popular anomaly-detection methods based on described in this article, can be used to preprocess nonparametric models (see, for example, Ahmed, and visualize data sets. Addtrack, including the anomalydetection model is very general since the parametric module described in this article, is forms of the distributions need not be currently deployed in Sweden, India, China, and known.

The process of collecting and organizing sets of observations represents a common theme throughout the history of science. However, despite the ubiquity of scientists measuring, recording, and analyzing the dynamics of different processes, an extensive organization of scientific time-series data and analysis methods has never been performed. Addressing this, annotated collections of over 35 000 real-world and model-generated time series and over 9000 time-series analysis algorithms are analyzed in this work. We introduce reduced representations of both time series, in terms of their properties measured by diverse scientific methods, and of time-series analysis methods, in terms of their behaviour on empirical time series, and use them to organize these interdisciplinary resources. This new approach to comparing across diverse scientific data and methods allows us to organize time-series datasets automatically according to their properties, retrieve alternatives to particular analysis methods developed in other scientific disciplines, and automate the selection of useful methods for time-series classification and regression tasks. The broad scientific utility of these tools is demonstrated on datasets of electroencephalograms, self-affine time series, heart beat intervals, speech signals, and others, in each case contributing novel analysis techniques to the existing literature. Highly comparative techniques that compare across an interdisciplinary literature can thus be used to guide more focused research in time-series analysis for applications across the scientific disciplines.

Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture transient dependencies, such as, gene regulatory dependencies throughout a developmental cycle of an organism. Kolar et al (2010b) proposed a method based on kernel-smoothing l1-penalized logistic regression for estimating time-varying networks from nodal observations collected from a time-series of observational data. In this paper, we establish conditions under which the proposed method consistently recovers the structure of a time-varying network. This work complements previous empirical findings by providing sound theoretical guarantees for the proposed estimation procedure. For completeness, we include numerical simulations in the paper.

We present a new classification method for quasar identification in the EROS-2 and MACHO datasets based on a boosted version of Random Forest classifier. We use a set of variability features including parameters of a continuous auto regressive model. We prove that continuous auto regressive parameters are very important discriminators in the classification process. We create two training sets (one for EROS-2 and one for MACHO datasets) using known quasars found in the LMC. Our model's accuracy in both EROS-2 and MACHO training sets is about 90% precision and 86% recall, improving the state of the art models accuracy in quasar detection. We apply the model on the complete, including 28 million objects, EROS-2 and MACHO LMC datasets, finding 1160 and 2551 candidates respectively. To further validate our list of candidates, we crossmatched our list with a previous 663 known strong candidates, getting 74% of matches for MACHO and 40% in EROS-2. The main difference on matching level is because EROS-2 is a slightly shallower survey which translates to significantly lower signal-to-noise ratio lightcurves.