Related papers: Asymptotic quantization for probability measures o…
We use tools from geometric statistics to analyze the usual estimation procedure of a template shape. This applies to shapes from landmarks, curves, surfaces, images etc. We demonstrate the asymptotic bias of the template shape estimation…
We consider the problem of estimating curvature where the data can be viewed as a noisy sample from an underlying manifold. For manifolds of dimension greater than one there are multiple definitions of local curvature, each suggesting a…
A novel solution to the quantum measurement problem is presented by using a new asymmetric equation that is complementary to the Schr\"odinger equation. Solved for the hydrogen atom, the new equation describes the temporal and spatial…
Asymptotic equivalence theory developed in the literature so far are only for bounded loss functions. This limits the potential applications of the theory because many commonly used loss functions in statistical inference are unbounded. In…
We give a condition on the curvature tensors of Riemannian manifolds that admit Lipschitz approximation by polyhedral metrics with curvature bounded below or above. We show that this condition is also sufficient for the existence of local…
To study a noncompact Riemannian manifold, it is often useful to find a compactification. We discuss several common compactifications and survey some recent results.
The present paper is devoted to the study of mappings with finite distortion on Riemannian manifolds. Theorems on local behavior of generalized quasiisometries with unbounded characteristic of quasiconformality are obtained.
A nonparametric procedure for robust regression estimation and for quantile regression is proposed which is completely data-driven and adapts locally to the regularity of the regression function. This is achieved by considering in each…
Asymptotic expansions are derived for the tail distribution of the product of two correlated normal random variables with non-zero means and arbitrary variances, and more generally the sum of independent copies of such random variables.…
For theoretical approach of quantum measurements it is proposed a set of reconsidered conjectures. The proposed approach implies linear functional transformations for probability density and current but preserves the expressions for…
We present a new framework for statistical inference on Riemannian manifolds that achieves high-order accuracy, addressing the challenges posed by non-Euclidean parameter spaces frequently encountered in modern data science. Our approach…
We study generalizations of Reifenberg's Theorem for measures in $\mathbb R^n$ under assumptions on the Jones' $\beta$-numbers, which appropriately measure how close the support is to being contained in a subspace. Our main results, which…
To begin with, it is pointed out that the form of the quantum probabil- ity formula originates in the very initial state of the object system as seen when the state is expanded with the eigen-projectors of the measured ob- servable. Making…
Bayesian methods are developed for the multivariate nonparametric regression problem where the domain is taken to be a compact Riemannian manifold. In terms of the latter, the underlying geometry of the manifold induces certain symmetries…
Nielsen [quant-ph/0108020] introduced a model of quantum computation by measurement-based simulation of unitary computations. In this model, a consequence of the non-determinism of quantum measurement is the probabilistic termination of…
Using extended Schwinger's quantization approach quantum mechanics on a Riemannian manifold $M$ with a given action of an intransitive group of isometries is developed. It was shown that quantum mechanics can be determined unequivocally…
In this work we study the asymptotic distribution of eigenvalues in one-dimensional open sets. The method of proof is rather elementary, based on the Dirichlet lattice points problem, which enable us to consider sets with infinite measure.…
Concerning quantitative isoperimetry for a weighted Riemannian manifold satisfying $\mathrm{Ric}_{\infty} \ge 1$, we give an $L^1$-estimate exhibiting that the push-forward of the reference measure by the guiding function (arising from the…
In recent years, manifold learning has become increasingly popular as a tool for performing non-linear dimensionality reduction. This has led to the development of numerous algorithms of varying degrees of complexity that aim to recover man…
We continue our study on the logarithmic balanced model metric initiated in our previous work. By a non-trivial refinement of the set of tools developed in our previous work, we are able to confirm partially a conjecture we made in our…