Related papers: Robust Functional Data Analysis for Discretely Obs…
A data table which is arranged according to two factors can often be considered as a compositional table. An example is the number of unemployed people, split according to gender and age classes. Analyzed as compositions, the relevant…
We develop a new approach for detecting changes in the behavior of stochastic processes and random fields based on tensor product representations such as the Karhunen-Lo\`{e}ve expansion. From the associated eigenspaces of the covariance…
In this paper, by proposing two new kinds of distributional uncertainty sets, we explore robustness of distortion risk measures against distributional uncertainty. To be precise, we first consider a distributional uncertainty set which is…
Robust statistics traditionally focuses on outliers, or perturbations in total variation distance. However, a dataset could be corrupted in many other ways, such as systematic measurement errors and missing covariates. We generalize the…
This paper investigates the problem of making inference about a parametric model for the regression of an outcome variable $Y$ on covariates $(V,L)$ when data are fused from two separate sources, one which contains information only on $(V,…
We study the fundamental problem of high-dimensional mean estimation in a robust model where a constant fraction of the samples are adversarially corrupted. Recent work gave the first polynomial time algorithms for this problem with…
This paper deals with robust marginal estimation under a general regression model when missing data occur in the response and also in some of covariates. The target is a marginal location parameter which is given through an $M-$functional.…
The main focus of this work is on providing a formal definition of statistical depth for functional data on the basis of six properties, recognising topological features such as continuity, smoothness and contiguity. Amongst our depth…
Semi-functional linear regression models postulate a linear relationship between a scalar response and a functional covariate, and also include a non-parametric component involving a univariate explanatory variable. It is of practical…
Machine learning has demonstrated remarkable performance over finite datasets, yet whether the scores over the fixed benchmarks can sufficiently indicate the model's performance in the real world is still in discussion. In reality, an ideal…
In functional data analysis (FDA), covariance function is fundamental not only as a critical quantity for understanding elementary aspects of functional data but also as an indispensable ingredient for many advanced FDA methods. This paper…
This paper introduces the partial Gini covariance, a novel dependence measure that addresses the challenges of high-dimensional inference with heavy-tailed errors, often encountered in fields like finance, insurance, climate, and biology.…
Robust mean estimation is the problem of estimating the mean $\mu \in \mathbb{R}^d$ of a $d$-dimensional distribution $D$ from a list of independent samples, an $\epsilon$-fraction of which have been arbitrarily corrupted by a malicious…
As machine learning models become increasingly prevalent in critical decision-making models and systems in fields like finance, healthcare, etc., ensuring their robustness against adversarial attacks and changes in the input data is…
In this paper, we propose a novel approach to fit a functional linear regression in which both the response and the predictor are functions of a common variable such as time. We consider the case that the response and the predictor…
We study the problem of robustly estimating the posterior distribution for the setting where observed data can be contaminated with potentially adversarial outliers. We propose Rob-ULA, a robust variant of the Unadjusted Langevin Algorithm…
Massive vector field datasets are common in multi-spectral optical and radar sensors, among many other emerging areas of application. We develop a novel stochastic functional (data) analysis approach for detecting anomalies based on the…
It is becoming increasingly apparent that probabilistic approaches can overcome conservatism and computational complexity of the classical worst-case deterministic framework and may lead to designs that are actually safer. In this paper we…
In statistical learning and analysis from shared data, which is increasingly widely adopted in platforms such as federated learning and meta-learning, there are two major concerns: privacy and robustness. Each participating individual…
Nonparametric regression models offer a way to understand and quantify relationships between variables without having to identify an appropriate family of possible regression functions. Although many estimation methods for these models have…