arXiv subjects

Mia Hubert

Publications and source records attributed to Mia Hubert.

27 records · Page 2Linked to original sources

arXiv2018

Robust Monitoring of Time Series with Application to Fraud Detection

Time series often contain outliers and level shifts or structural changes. These unexpected events are of the utmost importance in fraud detection, as they may pinpoint suspicious transactions. The presence of such unusual events can easily mislead conventional time series analysis and yield erroneous conclusions. In this paper we provide a unified framework for detecting outliers and level shifts in short time series that may have a seasonal pattern. The approach combines ideas from the FastLTS algorithm for robust regression with alternating least squares. The double wedge plot is proposed, a graphical display which indicates outliers and potential level shifts. The methodology was developed to detect potential fraud cases in time series of imports into the European Union, and is illustrated on two such series.

stat.CO↗

arXiv2017

Anomaly Detection by Robust Statistics

Real data often contain anomalous cases, also known as outliers. These may spoil the resulting analysis but they may also contain valuable information. In either case, the ability to detect such anomalies is essential. A useful tool for this purpose is robust statistics, which aims to detect the outliers by first fitting the majority of the data and then flagging data points that deviate from it. We present an overview of several robust methods and the resulting graphical outlier detection tools. We discuss robust procedures for univariate, low-dimensional, and high-dimensional data, such as estimating location and scatter, linear regression, principal component analysis, classification, clustering, and functional data analysis. Also the challenging new topic of cellwise outliers is introduced.

stat.ML↗

arXiv2017

Minimum Covariance Determinant and Extensions

The Minimum Covariance Determinant (MCD) method is a highly robust estimator of multivariate location and scatter, for which a fast algorithm is available. Since estimating the covariance matrix is the cornerstone of many multivariate statistical methods, the MCD is an important building block when developing robust multivariate techniques. It also serves as a convenient and efficient tool for outlier detection. The MCD estimator is reviewed, along with its main properties such as affine equivariance, breakdown value, and influence function. We discuss its computation, and list applications and extensions of the MCD in applied and methodological multivariate statistics. Two recent extensions of the MCD are described. The first one is a fast deterministic algorithm which inherits the robustness of the MCD while being almost affine equivariant. The second is tailored to high-dimensional data, possibly with more dimensions than cases, and incorporates regularization to prevent singular matrices.

stat.ME↗

arXiv2017

A Measure of Directional Outlyingness with Applications to Image Data and Video

Functional data covers a wide range of data types. They all have in common that the observed objects are functions of of a univariate argument (e.g. time or wavelength) or a multivariate argument (say, a spatial position). These functions take on values which can in turn be univariate (such as the absorbance level) or multivariate (such as the red/green/blue color levels of an image). In practice it is important to be able to detect outliers in such data. For this purpose we introduce a new measure of outlyingness that we compute at each gridpoint of the functions' domain. The proposed Directional Outlyingness} (DO) measure accounts for skewness in the data and only requires O(n) computation time per direction. We derive the influence function of the DO and compute a cutoff for outlier detection. The resulting heatmap and functional outlier map reflect local and global outlyingness of a function. To illustrate the performance of the method on real data it is applied to spectra, MRI images, and video surveillance data.

stat.ME↗

arXiv2017

Analysis of travel activity determinants using robust statistics

This study investigates travel behavior determinants based on a multiday travel survey conducted in the region of Ghent, Belgium. Due to the limited data reliability of the data sample and the influence of outliers exerted on classical principal component analysis, robust principal component analysis (ROBPCA) is employed in order to reveal the explanatory variables responsible for most of the variability. Interpretation of the results is eased by utilizing ROSPCA. The application of ROSPCA reveals six distinct principal components where each is determined by a few variables. Among others, our results suggest a key role of variable categories such as journey purpose-related impedance and journey inherent constraints. Surprisingly, the variables associated with journey timing turn out to be less important. Finally, our findings reveal the critical role of outliers in travel behavior analysis. This suggests that a systematic understanding of how outliers contribute to observed mobility behavior patterns, as derived from travel surveys, is needed. In this regard, the proposed methods serve for processing raw data typically used in activity-based modelling.

stat.AP↗

arXiv2016

Multivariate and functional classification using depth and distance

We construct classifiers for multivariate and functional data. Our approach is based on a kind of distance between data points and classes. The distance measure needs to be robust to outliers and invariant to linear transformations of the data. For this purpose we can use the bagdistance which is based on halfspace depth. It satisfies most of the properties of a norm but is able to reflect asymmetry when the class is skewed. Alternatively we can compute a measure of outlyingness based on the skew-adjusted projection depth. In either case we propose the DistSpace transform which maps each data point to the vector of its distances to all classes, followed by k-nearest neighbor (kNN) classification of the transformed data points. This combines invariance and robustness with the simplicity and wide applicability of kNN. The proposal is compared with other methods in experiments with real and simulated data.

stat.ME↗

arXiv2016

Finding Outliers in Surface Data and Video

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.

stat.ME↗

arXiv2015

Statistical depth meets computational geometry: a short survey

During the past two decades there has been a lot of interest in developing statistical depth notions that generalize the univariate concept of ranking to multivariate data. The notion of depth has also been extended to regression models and functional data. However, computing such depth functions as well as their contours and deepest points is not trivial. Techniques of computational geometry appear to be well-suited for the development of such algorithms. Both the statistical and the computational geometry communities have done much work in this direction, often in close collaboration. We give a short survey of this work, focusing mainly on depth and multivariate medians, and end by listing some other areas of statistics where computational geometry has been of great help in constructing efficient algorithms.

stat.ME↗

arXiv2008

High-Breakdown Robust Multivariate Methods

When applying a statistical method in practice it often occurs that some observations deviate from the usual assumptions. However, many classical methods are sensitive to outliers. The goal of robust statistics is to develop methods that are robust against the possibility that one or several unannounced outliers may occur anywhere in the data. These methods then allow to detect outlying observations by their residuals from a robust fit. We focus on high-breakdown methods, which can deal with a substantial fraction of outliers in the data. We give an overview of recent high-breakdown robust methods for multivariate settings such as covariance estimation, multiple and multivariate regression, discriminant analysis, principal components and multivariate calibration.

stat.ME↗