Related papers: Statistical Distances and Their Role in Robustness
Outlier detection algorithms typically assign an outlier score to each observation in a dataset, indicating the degree to which an observation is an outlier. However, these scores are often not comparable across algorithms and can be…
Divergence functions are interesting discrepancy measures. Even though they are not true distances, we can use them to measure how separated two points are. Curiously enough, when they are applied to random variables, they lead to a notion…
The concentration of a distribution toward a lower bound is a conceptually simple property that closely relates to concepts of rarity and poverty, but that lacks a global descriptive statistic. We term this property 'shift' and define it as…
Within the continuous endeavour of improving the efficiency and resilience of air transport, the trend of using concepts and metrics from statistical physics has recently gained momentum. This scientific discipline, which integrates…
The method of statistical differentials, which approximates the mean and variance of transformations of random variables is used in many areas of mathematics. This paper will discuss the conditions under which such an approximation will be…
Rigorous assessment of uncertainty is crucial to the utility of DNS results. Uncertainties in the computed statistics arise from two sources: finite statistical sampling and the discretization of the Navier-Stokes equations. Due to the…
This paper is about how we study statistical methods. As an example, it uses the random regressions model, in which the intercept and slope of cluster-specific regression lines are modeled as a bivariate random effect. Maximizing this…
The aim of this paper is to provide an overview of recent development related to Bregman distances outside its native areas of optimization and statistics. We discuss approaches in inverse problems and image processing based on Bregman…
Constructing a differentially private (DP) estimator requires deriving the maximum influence of an observation, which can be difficult in the absence of exogenous bounds on the input data or the estimator, especially in high dimensional…
Statistical modeling plays a fundamental role in understanding the underlying mechanism of massive data (statistical inference) and predicting the future (statistical prediction). Although all models are wrong, researchers try their best to…
Adversarial robustness refers to a model's ability to resist perturbation of inputs, while distribution robustness evaluates the performance of the model under data shifts. Although both aim to ensure reliable performance, prior work has…
Every scientific endeavour consists of (at least) two components: A hypothesis on the one hand and data on the other. There is always a more or less abstract level - some theory, a set of concepts, certain relations of ideas - and a…
Quantifying robustness in a single measure for the purposes of model selection, development of adversarial training methods, and anticipating trends has so far been elusive. The simplest metric to consider is the number of trainable…
Over the past decade, numerous theories have been proposed to explain the widespread vulnerability of deep neural networks to adversarial evasion attacks. Among these, the theory of non-robust features proposed by Ilyas et al. has been…
Classical results in asymptotic statistics show that the Fisher information matrix controls the difficulty of estimating a statistical model from observed data. In this work, we introduce a companion measure of robustness of an estimation…
Superstatistics is a widely employed tool of non-equilibrium statistical physics which plays an important role in analysis of hierarchical complex dynamical systems. Yet, its "canonical" formulation in terms of a single nuisance parameter…
Robustness to distribution shift and fairness have independently emerged as two important desiderata required of modern machine learning models. While these two desiderata seem related, the connection between them is often unclear in…
This work investigates adversarial training in the context of margin-based linear classifiers in the high-dimensional regime where the dimension $d$ and the number of data points $n$ diverge with a fixed ratio $\alpha = n / d$. We introduce…
Cook's distance [Technometrics 19 (1977) 15-18] is one of the most important diagnostic tools for detecting influential individual or subsets of observations in linear regression for cross-sectional data. However, for many complex data…
In this paper we study some basic properties of strong {\lambda}- statistical convergence of sequences in probabilistic metric (PM) spaces. We also introduce and study the notion of strong {\lambda}-statistically Cauchyness. Further…