Distributed Robust Learning

We propose a framework for distributed robust statistical learning on {\em big contaminated data}. The Distributed Robust Learning (DRL) framework can reduce the computational time of traditional robust learning methods by several orders of magnitude. We analyze the robustness property of DRL, showing that DRL not only preserves the robustness of the base robust learning method, but also tolerates contaminations on a constant fraction of results from computing nodes (node failures). More precisely, even in presence of the most adversarial outlier distribution over computing nodes, DRL still achieves a breakdown point of at least $\lambda^*/2$, where $\lambda^*$ is the break down point of corresponding centralized algorithm. This is in stark contrast with naive division-and-averaging implementation, which may reduce the breakdown point by a factor of $k$ when $k$ computing nodes are used. We then specialize the DRL framework for two concrete cases: distributed robust principal component analysis and distributed robust regression. We demonstrate the efficiency and the robustness advantages of DRL through comprehensive simulations and predicting image tags on a large-scale image set.Comment: 18 pages, 2 figure

A survey of outlier detection methodologies

Outlier detection has been used for centuries to detect and, where appropriate, remove anomalous observations from data. Outliers arise due to mechanical faults, changes in system behaviour, fraudulent behaviour, human error, instrument error or simply through natural deviations in populations. Their detection can identify system faults and fraud before they escalate with potentially catastrophic consequences. It can identify errors and remove their contaminating effect on the data set and as such to purify the data for processing. The original outlier detection methods were arbitrary but now, principled and systematic techniques are used, drawn from the full gamut of Computer Science and Statistics. In this paper, we introduce a survey of contemporary techniques for outlier detection. We identify their respective motivations and distinguish their advantages and disadvantages in a comparative review

RNA-Seq optimization with eQTL gold standards.

BackgroundRNA-Sequencing (RNA-Seq) experiments have been optimized for library preparation, mapping, and gene expression estimation. These methods, however, have revealed weaknesses in the next stages of analysis of differential expression, with results sensitive to systematic sample stratification or, in more extreme cases, to outliers. Further, a method to assess normalization and adjustment measures imposed on the data is lacking.ResultsTo address these issues, we utilize previously published eQTLs as a novel gold standard at the center of a framework that integrates DNA genotypes and RNA-Seq data to optimize analysis and aid in the understanding of genetic variation and gene expression. After detecting sample contamination and sequencing outliers in RNA-Seq data, a set of previously published brain eQTLs was used to determine if sample outlier removal was appropriate. Improved replication of known eQTLs supported removal of these samples in downstream analyses. eQTL replication was further employed to assess normalization methods, covariate inclusion, and gene annotation. This method was validated in an independent RNA-Seq blood data set from the GTEx project and a tissue-appropriate set of eQTLs. eQTL replication in both data sets highlights the necessity of accounting for unknown covariates in RNA-Seq data analysis.ConclusionAs each RNA-Seq experiment is unique with its own experiment-specific limitations, we offer an easily-implementable method that uses the replication of known eQTLs to guide each step in one's data analysis pipeline. In the two data sets presented herein, we highlight not only the necessity of careful outlier detection but also the need to account for unknown covariates in RNA-Seq experiments

Recent advances in directional statistics

Mainstream statistical methodology is generally applicable to data observed in Euclidean space. There are, however, numerous contexts of considerable scientific interest in which the natural supports for the data under consideration are Riemannian manifolds like the unit circle, torus, sphere and their extensions. Typically, such data can be represented using one or more directions, and directional statistics is the branch of statistics that deals with their analysis. In this paper we provide a review of the many recent developments in the field since the publication of Mardia and Jupp (1999), still the most comprehensive text on directional statistics. Many of those developments have been stimulated by interesting applications in fields as diverse as astronomy, medicine, genetics, neurology, aeronautics, acoustics, image analysis, text mining, environmetrics, and machine learning. We begin by considering developments for the exploratory analysis of directional data before progressing to distributional models, general approaches to inference, hypothesis testing, regression, nonparametric curve estimation, methods for dimension reduction, classification and clustering, and the modelling of time series, spatial and spatio-temporal data. An overview of currently available software for analysing directional data is also provided, and potential future developments discussed.Comment: 61 page