Related papers: Conformal geometry of statistical manifold with ap…

Consider semiparametric estimation where a doubly robust estimating function for a low-dimensional parameter is available, depending on two working models. With high-dimensional data, we develop regularized calibrated estimation as a…

We propose a sequential design method aiming at the estimation of an extreme quantile based on a sample of dichotomic data corresponding to peaks over a given threshold. This study is motivated by an industrial challenge in material…

To analyse a very large data set containing lengthy variables, we adopt a sequential estimation idea and propose a parallel divide-and-conquer method. We conduct several conventional sequential estimation procedures separately, and properly…

Utilizing recently developed abstract notions of sectional curvature, we introduce a method for constructing a curvature-based geometric profile of discrete metric spaces. The curvature concept that we use here captures the metric relations…

The general aim of manifold estimation is reconstructing, by statistical methods, an $m$-dimensional compact manifold $S$ on ${\mathbb R}^d$ (with $m\leq d$) or estimating some relevant quantities related to the geometric properties of $S$.…

We here adapt an extended version of the adaptive cubic regularisation method with dynamic inexact Hessian information for nonconvex optimisation in [3] to the stochastic optimisation setting. While exact function evaluations are still…

Upon a consistent topological statistical theory the application of structural statistics requires a quantification of the proximity structure of model spaces. An important tool to study these structures are Pseudo-Riemannian metrices,…

We study numerical computation of conformal invariants of domains in the complex plane. In particular, we provide an algorithm for computing the conformal capacity of a condenser. The algorithm applies for wide kind of geometries: domains…

A sequential quadratic optimization algorithm for minimizing an objective function defined by an expectation subject to nonlinear inequality and equality constraints is proposed, analyzed, and tested. The context of interest is when it is…

This paper aims to characterize rank-one arithmetic and locally symmetric metrics in the coarsely geometric setting using coarse-geometric commensurators. We provide a positive answer in general under the Hilbert-Smith conjecture and…

We reconsider non-degenerate second order superintegrable systems in dimension two as geometric structures on conformal surfaces. This extends a formalism developed by the authors, initially introduced for (pseudo-)Riemannian manifolds of…

We propose a discrete approach for approximating solutions to the prescribed Gaussian curvature problem in two-dimensional manifolds, based on the notion of discrete conformality. Our approach provides an efficient numerical method to…

We construct efficient robust truncated sequential estimators for the pointwise estimation problem in nonparametric autoregression models with smooth coefficients. For Gaussian models we propose an adaptive procedure based on the…

This paper introduces a framework for uncertainty quantification in regression models defined in metric spaces. Leveraging a newly defined notion of homoscedasticity, we develop a conformal prediction algorithm that offers finite-sample…

Conformal prediction offers finite-sample coverage guarantees under minimal assumptions. However, existing methods treat the entire modeling process as a black box, overlooking opportunities to exploit and understand modular structure. We…

We introduce a new method for two-sample testing of high-dimensional linear regression coefficients without assuming that those coefficients are individually estimable. The procedure works by first projecting the matrices of covariates and…

We show that the definition of a second order superintegrable system on a (pseudo-)Riemannian manifold gives rise to a conformally invariant notion of superintegrability. Conformal equivalence is the natural extension of the well-known…

We consider supervised learning (regression/classification) problems with tensor-valued input. We derive multi-linear sufficient reductions for the regression or classification problem by modeling the conditional distribution of the…

In this paper, we propose new sequential estimation methods based on inclusion principle. The main idea is to reformulate the estimation problems as constructing sequential random intervals and use confidence sequences to control the…

Using systematic calculations in spinor language, we obtain simple descriptions of the second order symmetry operators for the conformal wave equation, the Dirac-Weyl equation and the Maxwell equation on a curved four dimensional Lorentzian…