相关论文: Local dimension-free estimates for volumes of subl…
Derivative-free algorithms seek the minimum of a given function based only on function values queried at appropriate points. Although these methods are widely used in practice, their performance is known to worsen as the problem dimension…
In this paper we give a relation between the volume of sublevel sets and the area of level sets using a Gelfand-Leray form. As a consequence, we give an estimation of the volume of sublevel sets. In particular we give a proof of the known…
We show that, in a generic setting, self-affine and almost self-affine measures are exact dimensional, with local dimension equal almost everywhere to the information dimension and given by the zero of a superadditive pressure functional.
We give upper bounds for volume of sublevel sets of real polynomials. Our method is to combine a version of global Lojasiewicz inequality with some well known estimate on volume of tubes around real algebraic sets. Some applications to…
We consider settings where data are available on a nonparametric function and various partial derivatives. Such circumstances arise in practice, for example in the joint estimation of cost and input functions in economics. We show that when…
We present and analyze an algorithm for estimating the size, under a Gaussian or uniform measure, of a localized neighborhood in neural network parameter space with behavior similar to an ``anchor'' point. We refer to this as the "local…
Suppose that $n$ statistical units are observed, each following the model $Y(x_j)=m(x_j)+ \epsilon(x_j),\, j=1,...,N,$ where $m$ is a regression function, $0 \leq x_1 <...<x_N \leq 1$ are observation times spaced according to a sampling…
The local a priori estimate for the finite element approximation is essential for underlying the local and parallel technique. It is well known that the constant coefficients in the inequality is independent of the mesh size. But it is not…
We study the local dimension of the convolution of two measures. We give conditions for bounding the local dimension of the convolution on the basis of the local dimension of one of them. Moreover, we give a formula for the local dimension…
In this paper, we develop a local rank correlation measure which quantifies the performance of dimension reduction methods. The local rank correlation is easily interpretable, and robust against the extreme skewness of nearest neighbor…
We have derived an analytical formulation for estimating the volume of geometries enclosed by implicitly defined surfaces. The novelty of this work is due to two aspects. First we provide a general analytical formulation for all…
For $2\leq p\leq \infty$, we establish dimension-free estimates for discrete dyadic Hardy-Littlewood maximal operators over Euclidean balls on semi-commutative $L_{p}$ space. In particular, when the radius is sufficiently large, these…
Let $D$ be a strictly pseudoconvex domain in $\C^N$ and $X$ a pure-dimensional non-reduced subvariety that behaves well at $\partial D$. We provide $L^p$-estimates of extensions of holomorphic functions defined on $X$.
Concentration inequalities are obtained on Poisson space, for random functionals with finite or infinite variance. In particular, dimension free tail estimates and exponential integrability results are given for the Euclidean norm of…
The level of a function f on an n-dimensional space encloses a region. The volume of a region between two such levels depends on both levels. Fixing one of them the volume becomes a function of the remaining level. We show that if the…
We discuss new proofs, and new forms, of a reverse logarithmic Sobolev inequality, with respect to the standard Gaussian measure, for low complexity functions, measured in terms of Gaussian-width. In particular, we provide a dimension-free…
In this paper, we develop and analyze a rigorous multiscale upscaling method for dual continuum model, which serves as a powerful tool in subsurface formation applications. Our proposed method is capable of identifying different continua…
In this note, we show that the normalized local volume of a non-closed point can be expressed in terms of the normalized local volumes of closed points.
The notion of a local fractional derivative (LFD) was introduced recently for functions of a single variable. LFD was shown to be useful in studying fractional differentiability properties of fractal and multifractal functions. It was…
The local dimension spectrum provides a framework for quantifying the fractal properties of a measure, and it is well understood for non-overlapping self-similar measures. In this article, we study the local dimension spectrum for dominated…