相关论文: On the accuracy of the poissonisation in the infin…
Maximum entropy estimation is of broad interest for inferring properties of systems across many different disciplines. In this work, we significantly extend a technique we previously introduced for estimating the maximum entropy of a set of…
We prove a.s. (almost sure) unisolvency of interpolation by continuous random sampling with respect to any given density, in spaces of multivariate a.e. (almost everywhere) analytic functions. Examples are given concerning polynomial and…
A space-discretization for the elastic flow of inextensible curves is devised and quasi-optimal convergence of the corresponding semi-discrete problem is proved for a suitable discretization of the nonlinear inextensibility constraint.…
We prove exponential localization for the Schr\"odinger operator with a Poisson random potential at the bottom of the spectrum in any dimension. We also prove exponential localization in a prescribed interval for all large Poisson…
Simulation schemes for probabilistic inference in Bayesian belief networks offer many advantages over exact algorithms; for example, these schemes have a linear and thus predictable runtime while exact algorithms have exponential runtime.…
The problem of integer partitions is addressed using the microcanonical approach which is based on the analogy between this problem in the number theory and the calculation of microstates of a many-boson system. For ordinary…
We prove existence of asymptotic entropy of random walks on regular languages over a finite alphabet and we give formulas for it. Furthermore, we show that the entropy varies real-analytically in terms of probability measures of constant…
Quantization for probability distributions refers broadly to estimating a given probability measure by a discrete probability measure supported by a finite number of points. We consider general geometric approaches to quantization using…
This paper presents a new numerical scheme for simulating stochastic processes specified by their marginal distribution functions and covariance functions. Stochastic samples are firstly generated to automatically satisfy target marginal…
We establish an exact asymptotic formula for the square variation of certain partial sum processes. Let $\{X_{i}\}$ be a sequence of independent, identically distributed mean zero random variables with finite variance $\sigma$ and…
A new equivalence notion between non-stationary subdivision schemes, termed asymptotical similarity, which is weaker than asymptotical equivalence, is introduced and studied. It is known that asymptotical equivalence between a…
We consider an occupancy scheme in which "balls" are identified with $n$ points sampled from the standard exponential distribution, while the role of "boxes" is played by the spacings induced by an independent random walk with positive and…
This work is devoted to the numerical simulation of nonlinear Schr\"odinger and Klein-Gordon equations. We present a general strategy to construct numerical schemes which are uniformly accurate with respect to the oscillation frequency.…
Conformal inference is a versatile tool for building prediction sets in regression or classification. We study the false coverage proportion (FCP) in a simultaneous inference setting with a calibration sample of $n$ points and a test sample…
We prove the unexpected result that almost uniform sampling of independent sets in graphs is possible via a probabilistic polynomial time algorithm. Note that our sampling algorithm (if correct) has extremely surprising consequences; the…
We propose an iterative estimating equations procedure for analysis of longitudinal data. We show that, under very mild conditions, the probability that the procedure converges at an exponential rate tends to one as the sample size…
Most existing algorithms for dictionary learning assume that all entries of the (high-dimensional) input data are fully observed. However, in several practical applications (such as hyper-spectral imaging or blood glucose monitoring), only…
Thompson sampling is an efficient algorithm for sequential decision making, which exploits the posterior uncertainty to address the exploration-exploitation dilemma. There has been significant recent interest in integrating Bayesian neural…
The exact statistics of an arbitrary quantum observable is analytically obtained. Due to the probabilistic nature of a sequence of intermediate measurements and stochastic fluctuations induced by the interaction with the environment, the…
Asymptotics of maximum likelihood estimation for $\alpha$-stable law are analytically investigated with a continuous parameterization. The consistency and asymptotic normality are shown on the interior of the whole parameter space. Although…