相关论文: Conditional Equi-concentration of Types

Maximum-likelihood exponent maps have been studied as a technique to increase the understanding and improve the fit of power-law exponents to experimental and numerical simulation data, especially when they exhibit both upper and lower…

In algebraic statistics, the maximum likelihood degree of a statistical model refers to the number of solutions (counted with multiplicity) of the score equations over the complex field. In this paper, the maximum likelihood degree of the…

We develop a comprehensive study on sharp potential type Riemannian Sobolev inequalities of order 2 by means of a local geometric Sobolev inequality of same kind and suitable De Giorgi-Nash-Moser estimates. In particular we discuss…

We consider a generic system composed of a fixed number of particles distributed over a finite number of energy levels. We make only general assumptions about system's properties and the entropy. System's constraints other than fixed number…

The purpose of this paper is to characterize the weak efficient solutions, the efficient solutions, and the isolated efficient solutions of a given vector optimization problem with finitely many convex objective functions and infinitely…

Condition numbers of random polynomial systems have been widely studied in the literature under certain coefficient ensembles of invariant type. In this note we introduce a method that allows us to study these numbers for a broad family of…

Max stable laws are limit laws of linearly normalized partial maxima of independent identically distributed random variables. Saeb (2014) proves that the Renyi entropy of order b (b > 1) of linear normalized maximum of iid random variables…

We develop and generalize the theory of extreme value for non-stationary stochastic processes, mostly by weakening the uniform mixing condition that was previously used in this setting. We apply our results to non-autonomous dynamical…

We extend projection theorems concerning Hellinger and Jones et al. divergences to the continuous case. These projection theorems reduce certain estimation problems on generalized exponential models to linear problems. We introduce the…

We study vectors chosen at random from a compact convex polytope in $\mathbb{R}^n$ given by a finite number of linear constraints. We determine which projections of these random vectors are asymptotically normal as $n\to\infty$. Marginal…

We consider statistically independent non-identical subsystems with different entropic indices q1 and q2. A relation between q1, q2 and q' (for the entire system) extends a power law for entropic index as a function of distance r. A few…

We consider the task of estimating a conditional density using i.i.d. samples from a joint distribution, which is a fundamental problem with applications in both classification and uncertainty quantification for regression. For joint…

This paper presents concentration inequalities and laws of large numbers under weak assumptions of irrelevance, expressed through lower and upper expectations. The results are variants and extensions of De Cooman and Miranda's recent…

The main purpose of this paper is to obtain strong laws of large numbers for arrays or weighted sums of random variables under a scenario of dependence. Namely, for triangular arrays $\{X_{n,k}, \, 1 \leqslant k \leqslant n, \, n \geqslant…

When using boundary integral equation methods, we represent solutions of a linear partial differential equation as layer potentials. It is well-known that the approximation of layer potentials using quadrature rules suffer from poor…

In this paper we apply the entropy principle to the relativistic version of the differential equations describing a standard fluid flow, that is, the equations for mass, momentum, and a system for the energy matrix. These are the second…

Algorithms for min-max optimization and variational inequalities are often studied under monotonicity assumptions. Motivated by non-monotone machine learning applications, we follow the line of works [Diakonikolas et al., 2021, Lee and Kim,…

We describe a type system for the linear-algebraic $\lambda$-calculus. The type system accounts for the linear-algebraic aspects of this extension of $\lambda$-calculus: it is able to statically describe the linear combinations of terms…

Consider the continuous greedy paths model: given a $d$-dimensional Poisson point process with positive marks interpreted as masses, let $\mathrm P(\ell)$ denote the maximum mass gathered by a path of length $\ell$ starting from the origin.…

In this paper we generalize the H\'ajek-R\'enyi-Chow maximal inequality for submartingales to $L^p$ type Riesz spaces with conditional expectation operators. As applications we obtain a submartingale convergence theorem and a strong law of…