190 research outputs found

    Fast robust correlation for high-dimensional data

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    The product moment covariance is a cornerstone of multivariate data analysis, from which one can derive correlations, principal components, Mahalanobis distances and many other results. Unfortunately the product moment covariance and the corresponding Pearson correlation are very susceptible to outliers (anomalies) in the data. Several robust measures of covariance have been developed, but few are suitable for the ultrahigh dimensional data that are becoming more prevalent nowadays. For that one needs methods whose computation scales well with the dimension, are guaranteed to yield a positive semidefinite covariance matrix, and are sufficiently robust to outliers as well as sufficiently accurate in the statistical sense of low variability. We construct such methods using data transformations. The resulting approach is simple, fast and widely applicable. We study its robustness by deriving influence functions and breakdown values, and computing the mean squared error on contaminated data. Using these results we select a method that performs well overall. This also allows us to construct a faster version of the DetectDeviatingCells method (Rousseeuw and Van den Bossche, 2018) to detect cellwise outliers, that can deal with much higher dimensions. The approach is illustrated on genomic data with 12,000 variables and color video data with 920,000 dimensions

    Discussion of "The power of monitoring"

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    This is an invited comment on the discussion paper "The power of monitoring: how to make the most of a contaminated multivariate sample" by A. Cerioli, M. Riani, A. Atkinson and A. Corbellini that will appear in the journal Statistical Methods & Applications

    Finding Outliers in Surface Data and Video

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    Surface, image and video data can be considered as functional data with a bivariate domain. To detect outlying surfaces or images, a new method is proposed based on the mean and the variability of the degree of outlyingness at each grid point. A rule is constructed to flag the outliers in the resulting functional outlier map. Heatmaps of their outlyingness indicate the regions which are most deviating from the regular surfaces. The method is applied to fluorescence excitation-emission spectra after fitting a PARAFAC model, to MRI image data which are augmented with their gradients, and to video surveillance data

    Measuring overlap in logistic regression

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    In this paper we show that the recent notion of regression depth can be used as a data-analytic tool to measure the amount of separation between successes and failures in the binary response framework. Extending this algorithm allows us to compute the overlap in data sets which are commonly fitted by logistic regression models. The overlap is the number of observations that would need to be removed to obtain complete or quasicomplete separation, i.e. the situation where the logistic regression parameters are no longer identifiable and the maximum likelihood estimate does not exist. It turns out that the overlap is often quite small
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