Streaming robust covariance estimation and sequential outlier detection

Abstract

Robust estimation of the covariance matrix and outlier detection remain major statistical hurdles, particularly in large datasets where the rate of data contamination increases. The presence of outliers can severely bias parameter estimates and induce a masking effect, whereby some outliers conceal the presence of other outliers, further complicating their detection. Although many approaches have been proposed for covariance estimation and outlier detection, to our knowledge, none of these methods have been implemented in an online setting. In this paper, we focus on online covariance matrix estimation and outlier detection. Specifically, we propose a new method for simultaneously and online estimating the geometric median and variance, which allows us to calculate the Mahalanobis distance for each incoming data point before deciding whether it should be considered an outlier. To mitigate the masking effect, robust estimation techniques for the mean and variance are required. Our approach uses the geometric median for robust estimation of the location and the median covariance matrix for robust estimation of the dispersion parameters. The new online methods proposed for parameter estimation and outlier detection allow real-time identification of outliers as data are observed sequentially. The performance of our methods is demonstrated on simulated and real datasets.