Soham Sarkar

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https://people.epfl.ch/soham.sarkar?lang=fr

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CovNet: Covariance networks for functional data on multidimensional domains

Victor Panaretos, Soham Sarkar

Covariance estimation is ubiquitous in functional data analysis. Yet, the case of functional observations over multidimensional domains introduces computational and statistical challenges, rendering the standard methods effectively inapplicable. To address this problem, we introduce Covariance Networks (CovNet) as a modelling and estimation tool. The CovNet model is universal-it can be used to approximate any covariance up to desired precision. Moreover, the model can be fitted efficiently to the data and its neural network architecture allows us to employ modern computational tools in the implementation. The CovNet model also admits a closed-form eigendecomposition, which can be computed efficiently, without constructing the covariance itself. This facilitates easy storage and subsequent manipulation of a covariance in the context of the CovNet. We establish consistency of the proposed estimator and derive its rate of convergence. The usefulness of the proposed method is demonstrated via an extensive simulation study and an application to resting state functional magnetic resonance imaging data.

WILEY2022

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On Generalizations of Some Distance Based Classifiers for HDLSS Data

Soham Sarkar

In high dimension, low sample size (HDLSS) settings, classifiers based on Euclidean distances like the nearest neighbor classifier and the average distance classifier perform quite poorly if differences between locations of the underlying populations get masked by scale differences. To rectify this problem, several modifications of these classifiers have been proposed in the literature. However, existing methods are confined to location and scale differences only, and they often fail to discriminate among populations differing outside of the first two moments. In this article, we propose some simple transformations of these classifiers resulting in improved performance even when the underlying populations have the same location and scale. We further propose a generalization of these classifiers based on the idea of grouping of variables. High-dimensional behavior of the proposed classifiers is studied theoretically. Numerical experiments with a variety of simulated examples as well as an extensive analysis of benchmark data sets from three different databases exhibit advantages of the proposed methods.

MICROTOME PUBL2022

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Testing mutual independence among several random vectors of arbitrary dimensions is a challenging problem in Statistics, and it has gained considerable interest in recent years. In this article, we propose some nonparametric tests based on different notions of ranks of nearest neighbour. These proposed tests can be conveniently used for high dimensional data, even when the dimensions of the random vectors are larger than the sample size. We investigate the performance of these tests on several simulated and real data sets and also use them in identifying causal relationships among the random vectors. Our numerical results show that they can outperform state-of-the-art tests in a wide variety of examples.

TAYLOR & FRANCIS LTD2021

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