Seminar

Peter Filzmoser

Peter Filzmoser
(TU Wien)
Bio Peter Filzmoser is a Professor of Statistics at TU Wien, Austria. He has conducted research in the area of Robust Statistics, including outlier detection, Multivariate Statistics, and Compositional Data Analysis. He contributed to the development of new methods and algorithms for complex data, including high-dimensional data, functional data, and data depending on space/time. He has more than 300 peer reviewed publications, mainly in scientific journals, and he is co-author of 3 books (Springer, Wiley, CRC Press).

Abstract

In multivariate data analysis we consider an observation as a vector, with measurements for each variable. Outlier detection techniques are well established for this case. Here we extend vector-valued observations to matrix-valued objects, and thus the measurements of an observation are arranged in the rows and columns of a matrix. A prominent example for such a data structure are image data, where the pixel information is typically presented in a rectangular matrix. In traditional analyses, the pixel information is converted row-by-row (or column-by-column) to a long vector, which is considered as a row in a high-dimensional matrix of observations. With such a representation, the information about the neighborhood relationships of the pixels is lost.

The concept of matrix-valued data is not new at all, and a prominent distribution in this context is the matrix normal distribution. There are different proposals in the literature on how to estimate the parameters of this distribution. It is also possible to define a Mahalanobis distance, and the concept of robust covariance estimation can be modified to obtain robust estimators for the matrix-valued case. We present an adaptation of the well-known MCD (Minimum Covariance Determinant) estimator to this situation.

Moreover, the concept of Shapley values, which has been successfully used in the context of Explainable AI, is extended in order to explain the reasoning behind the outlyingness.In the context of image data, for example, one can identify outlying images and explain which pixels contribute to this outlyingness. A more detailed background, as well as illustrative examples, will be provided in the presentation.

Schedule

  • Friday 14 February 2025, 11:00-12:00 room seminar 1 @ Povo 0

Details