arXiv research

New Lehmer constants computed for free groups, improving bounds.

Sharp stability of Alexandrov's theorem for $C^1$ domains in the small-excess regime

Study sharp inequalities for perimeter functionals in capillarity and convex cones.

Guts determine the leading coefficients of $L^2$-Alexander torsions for 3-manifolds.

This paper addresses the so-called conformal capacities in $\mathbb R^n$, $n\ge 3$, through comparing three existing definitions (due to Betsakos, Colesanti-Cuoghi, Anderson-Vamananmurthy-Fuglede respectively) and studying their associated iso-capacitary inequalities with connection to half-diameter, mean-width, mean-c…

Quantifies nearly spherical subsets in complex ball geometry.

We study properties of a generalization of the Mahler measure to elements in group rings, in terms of the Lueck-Fuglede-Kadison determinant. Our main focus is the variation of the Mahler measure when the base group is changed. In particular, we study how to obtain the Mahler measure over an infinite group as limit of M…

The aim of this paper is to extend the notion of pseudo harmonic morphism (introduced by Loubeau \cite {Lo}) to the case when the source manifold is an admissible Riemannian polyhedron. We define these maps to be harmonic in the sense of Eells-Fuglede \cite {EF} and pseudo-horizontally weakly conformal in our sense (se…

We continue the study of the variation of the $p$--modulus of a foliation initiated by the first author. We derive the formula for the second variation which allows to study $p$--stable foliations. We obtain some results concerning codimension one $p$--stable foliations. Moreover, we derive the equation for the critica…

The goal of the present paper is to establish some kind of regularity of an energy minimizer map between Riemannian polyhedra. More precisely, we will show the hölder continuity of local energy minimizers between Riemannian polyhedra with the target spaces without focal points. With this new result, we also complete ou…

f-Harmonic maps were first introduced and studied by Lichnerowicz in \cite{Li} (see also Section 10.20 in Eells-Lemaire's report \cite{EL}). In this paper, we study a subclass of f-harmonic maps called f-harmonic morphisms which pull back local harmonic functions to local f-harmonic functions. We prove that a map betwe…

Inspired by the all-important conformal invariance of harmonic maps on two-dimensional domains, this article studies the relationship between biharmonicity and conformality. We first give a characterization of biharmonic morphisms, analogues of harmonic morphisms investigated by Fuglede and Ishihara, which, in particul…

Generalizes crystallographic properties to all dimensions.

New estimators outperform maximum likelihood without hyper-parameter estimation.

New estimator reduces kernel mean estimation error.

Dual Bayesian Affine Estimators for Wiener-type state-space models

Enhances gradient estimates for Hermitian Monge-Ampère equations.

Paper proposes robust estimators for GANs under Wasserstein contamination.

New framework converts offline to online estimation using black-box offline estimators.

Proposes variational autoencoder for efficient MMSE estimation.

Paper improves Fisher information estimation methods.

Proposes a robust estimator for RD designs.

SCOPE estimator improves covariance and precision matrix estimation.

We present a multi-task learning approach to jointly estimate the means of multiple independent data sets. The proposed multi-task averaging (MTA) algorithm results in a convex combination of the single-task maximum likelihood estimates. We derive the optimal minimum risk estimator and the minimax estimator, and show t…

We derive an unbiased estimator for expectations over discrete random variables based on sampling without replacement, which reduces variance as it avoids duplicate samples. We show that our estimator can be derived as the Rao-Blackwellization of three different estimators. Combining our estimator with REINFORCE, we ob…

Obtaining more accurate equity value estimates is the starting point for stock selection, value-based indexing in a noisy market, and beating benchmark indices through tactical style rotation. Unfortunately, discounted cash flow, method of comparables, and fundamental analysis typically yield discrepant valuation estim…

The maximum mean discrepancy (MMD) is a kernel-based distance between probability distributions useful in many applications (Gretton et al. 2012), bearing a simple estimator with pleasing computational and statistical properties. Being able to efficiently estimate the variance of this estimator is very helpful to vario…

Stochastic volatility modelling of financial processes has become increasingly popular. The proposed models usually contain a stationary volatility process. We will motivate and review several nonparametric methods for estimation of the density of the volatility process. Both models based on discretely sampled continuo…

A new copula estimation method using classification.

This paper reviews SDR methods for multivariate response regression.

Density ratio estimation is a vital tool in both machine learning and statistical community. However, due to the unbounded nature of density ratio, the estimation procedure can be vulnerable to corrupted data points, which often pushes the estimated ratio toward infinity. In this paper, we present a robust estimator wh…

TAKDE optimizes kernel density estimation for real-time dynamic processes.

We introduce two new estimators of the bivariate Hurst exponent in the power-law cross-correlations setting -- the cross-periodogram and local $X$-Whittle estimators -- as generalizations of their univariate counterparts. As the spectrum-based estimators are dependent on a part of the spectrum taken into consideration …

Paper bridges score estimation to parameter and density estimation in DDPMs.

New method for fast volatility estimation robust to change points.

ROME improves density estimation for multi-modal, non-normal data.

Paper introduces VDE, a variance-reduced determinant estimator.

New estimator improves mutual information estimation.

Private estimation of many quantiles using differential privacy.

Paper proposes robust LAD estimators for 2D sinusoidal model, proving consistency and normality.

Combines multiple OPE estimators into a more accurate and efficient estimate.

Optimal and safe semi-supervised learning estimator for high-dimensional data.

Improved nonparametric regression with debiasing for root-n consistency.

Estimating boundaries from point clouds with improved accuracy and rigorous error estimates.

Study nonparametric covariance function estimation for noisy data.

We formalize notions of robustness for composite estimators via the notion of a breakdown point. A composite estimator successively applies two (or more) estimators: on data decomposed into disjoint parts, it applies the first estimator on each part, then the second estimator on the outputs of the first estimator. And …

Gradient and Laplacian estimates for complex Monge-Ampère equations found.

Proposes RCL method to improve ATE estimation from observational data.