Related papers: On relative universality, regression operator, and…

We introduce Fisher consistency in the sense of unbiasedness as a desirable property for estimators of class prior probabilities. Lack of Fisher consistency could be used as a criterion to dismiss estimators that are unlikely to deliver…

Dependence is undoubtedly a central concept in statistics. Though, it proves difficult to locate in the literature a formal definition which goes beyond the self-evident 'dependence = non-independence'. This absence has allowed the term…

Beginning with a discussion of R. A. Fisher's early written remarks that relate to dimension reduction, this article revisits principal components as a reductive method in regression, develops several model-based extensions and ends with…

A universal formulation of uncertainty relations for quantum measurements is presented with additional focus on the representability of quantum observables by classical observables over a given state. Owing to the simplicity and operational…

A very simple example demonstrates that Fisher's application of the conditionality principle to regression ("fixed-$x$ regression"), endorsed by Sprott and many other followers, makes prediction impossible in the context of statistical…

It has been observed that the performances of many high-dimensional estimation problems are universal with respect to underlying sensing (or design) matrices. Specifically, matrices with markedly different constructions seem to achieve…

That science and other domains are now largely data-driven means virtually unlimited opportunities for statisticians. With great power comes responsibility, so it's imperative that statisticians ensure that the methods being developing to…

Fair Machine Learning endeavors to prevent unfairness arising in the context of machine learning applications embedded in society. Despite the variety of definitions of fairness and proposed "fair algorithms", there remain unresolved…

The classical concept of bounded completeness and its relation to sufficiency and ancillarity play a fundamental role in unbiased estimation, unbiased testing, and the validity of inference in the presence of nuisance parameters. In this…

Efficient recovery of a low-dimensional structure from high-dimensional data has been pursued in various settings including wavelet denoising, generalized linear models and low-rank matrix estimation. By thresholding some parameters to…

Gaussian universality results assert that the properties of many estimators remain unchanged when the input data are replaced by Gaussians. Such results have gained popularity in high-dimensional statistics and machine learning, as…

Whole robustness is a nice property to have for statistical models. It implies that the impact of outliers gradually vanishes as they approach plus or minus infinity. So far, the Bayesian literature provides results that ensure whole…

Linear regression is a classical paradigm in statistics. A new look at it is provided via the lens of universal learning. In applying universal learning to linear regression the hypotheses class represents the label $y\in {\cal R}$ as a…

A universal formulation of the quantum uncertainty regarding quantum indeterminacy, quantum measurement, and its inevitable observer effect is presented with additional focus on the representability of quantum observables over a given…

Conformal predictors provide set or functional predictions that are valid under the assumption of randomness, i.e., under the assumption of independent and identically distributed data. The question asked in this paper is whether there are…

The modified universality hypothesis proposed by Jones et al. (2022) suggests that adversarially robust models trained for a given task are highly similar. We revisit the hypothesis and test its generality. While we verify Jones' main claim…

For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…

This work is about understanding the impact of invariance and equivariance on generalisation in supervised learning. We use the perspective afforded by an averaging operator to show that for any predictor that is not equivariant, there is…

We study the universality property of estimators for high-dimensional linear models, which implies that the distribution of estimators is independent of whether the covariates follow a Gaussian distribution. Recent developments in…

In a noiseless linear estimation problem, one aims to reconstruct a vector x* from the knowledge of its linear projections y=Phi x*. There have been many theoretical works concentrating on the case where the matrix Phi is a random i.i.d.…