Related papers: The empirical Christoffel function with applicatio…
Following the theory of information measures based on the cumulative distribution function, we propose the fractional generalized cumulative entropy, and its dynamic version. These entropies are particularly suitable to deal with…
Dealing with massive data is a challenging task for machine learning. An important aspect of machine learning is function approximation. In the context of massive data, some of the commonly used tools for this purpose are sparsity,…
Motivated by the need for efficient estimation of conditional expectations, we consider a least-squares function approximation problem with heavily polluted data. Existing methods that are effective in the small-noise regime are suboptimal…
We study the approximation of a square-integrable function from a finite number of evaluations on a random set of nodes according to a well-chosen distribution. This is particularly relevant when the function is assumed to belong to a…
This paper proposes and analyzes fully data driven methods for inference about the mean function of a stochastic process from a sample of independent trajectories of the process, observed at discrete time points and corrupted by additive…
Asymptotic statistical theory for estimating functions is reviewed in a generality suitable for stochastic processes. Conditions concerning existence of a consistent estimator, uniqueness, rate of convergence, and the asymptotic…
We provide statistical learning guarantees for two unsupervised learning tasks in the context of compressive statistical learning, a general framework for resource-efficient large-scale learning that we introduced in a companion paper.The…
This paper considers inference for conditional moment inequality models using a multiscale statistic. We derive the asymptotic distribution of this test statistic and use the result to propose feasible critical values that have a simple…
We consider empirical measures of $\R^{d}$-valued stochastic process in finite discrete-time. We show that the adapted empirical measure introduced in the recent work \cite{backhoff2022estimating} by Backhoff et al. in compact spaces can be…
We propose a novel family of test statistics to detect the presence of changepoints in a sequence of dependent, possibly multivariate, functional-valued observations. Our approach allows to test for a very general class of changepoints,…
Precise asymptotics for Christoffel functions are established for power type weights on unions of Jordan curves and arcs. The asymptotics involve the equilibrium measure of the support of the measure. The result at the endpoints of arc…
We propose a new perspective for the evaluation of matching procedures by considering the complexity of the function class they belong to. Under this perspective we provide theoretical guarantees on post-matching covariate balance through a…
With the increasing penetration of high-frequency sensors across a number of biological and physical systems, the abundance of the resulting observations offers opportunities for higher statistical accuracy of down-stream estimates, but…
Topological data analysis has emerged as a powerful tool for extracting the metric, geometric and topological features underlying the data as a multi-resolution summary statistic, and has found applications in several areas where data…
There is a mismatch between the standard theoretical analyses of statistical machine learning and how learning is used in practice. The foundational assumption supporting the theory is that we can represent features and models using…
Fisher's criterion is a widely used tool in machine learning for feature selection. For large search spaces, Fisher's criterion can provide a scalable solution to select features. A challenging limitation of Fisher's criterion, however, is…
We review approaches to statistical inference based on randomization. Permutation tests are treated as an important special case. Under a certain group invariance property, referred to as the ``randomization hypothesis,'' randomization…
The recently proposed statistical finite element (statFEM) approach synthesises measurement data with finite element models and allows for making predictions about the unknown true system response. We provide a probabilistic error analysis…
We prove that if a rectangular matrix with uniformly small entries and approximately orthogonal rows is applied to the independent standardized random variables with uniformly bounded third moments, then the empirical CDF of the resulting…
Discrimination in machine learning often arises along multiple dimensions (a.k.a. protected attributes); it is then desirable to ensure \emph{intersectional fairness} -- i.e., that no subgroup is discriminated against. It is known that…