相关论文: Some results on the Gittins index for a normal rew…
We introduce and explore an empirical index of increase that works in both deterministic and random environments, thus allowing to assess monotonicity of functions that are prone to random measurement-errors. We prove consistency of the…
This paper develops an optimal Chernoff type bound for the probabilities of large deviations of sums $\sum_{k=1}^n f (X_k)$ where $f$ is a real-valued function and $(X_k)_{k \in \mathbb{Z}_{\ge 0}}$ is a finite state Markov chain with an…
We investigate the effect of explicitly enforcing the Lipschitz continuity of neural networks with respect to their inputs. To this end, we provide a simple technique for computing an upper bound to the Lipschitz constant---for multiple…
In the paper [25], written in collaboration with Gesine Reinert, we proved a universality principle for the Gaussian Wiener chaos. In the present work, we aim at providing an original example of application of this principle in the…
The Gittins policy is a highly general scheduling policy that minimizes a wide variety of mean holding cost metrics in the M/G/1 queue. Perhaps most famously, Gittins minimizes mean response time in the M/G/1 when jobs' service times are…
We revisit the classical theory of linear second-order uniformly elliptic equations in divergence form whose solutions have H\"older continuous gradients, and prove versions of the generalized maximum principle, the $C^{1,\alpha}$-estimate,…
We use Stein's method to provide non asymptotic $L^1$ bounds to the normal for functionals of associated point processes. As for supporting tools, we use the connection between association and $\alpha$-mixing properties that was recently…
Many inference problems, such as sequential decision problems like A/B testing, adaptive sampling schemes like bandit selection, are often online in nature. The fundamental problem for online inference is to provide a sequence of confidence…
We derive convenient uniform concentration bounds and finite sample multivariate normal approximation results for quadratic forms, then describe some applications involving variance components estimation in linear random-effects models.…
We introduce methods to bound the mean of a discrete distribution (or finite population) based on sample data, for random variables with a known set of possible values. In particular, the methods can be applied to categorical data with…
We find explicit and optimal upper bounds for the expected occupation density for an It\^o-process when its drift and diffusion coefficients are unknown under boundedness and ellipticity conditions on the coefficients. This is related to…
We study a problem with three equivalent formulations: describing Gibbs measures for five-vertex model in quadrant; classifying coherent systems on a p-deformation of the Gelfand-Tsetlin graph related to Grothendieck polynomials; finding…
Entropy is being used in physics, mathematics, informatics and in related areas to describe equilibration, dissipation, maximal probability states and optimal compression of information. The Gini index on the other hand is an established…
This paper develops a theory and methodology for estimation of Gini index such that both cost of sampling and estimation error are minimum. Methods in which sample size is fixed in advance, cannot minimize estimation error and sampling cost…
We discuss the identification of a time-dependent potential in a time-fractional diffusion model from a boundary measurement taken at a single point. Theoretically, we establish a conditional Lipschitz stability for this inverse problem.…
We find the value of constants related to constraints in characterization of some known statistical distributions and then we proceed to use the idea behind maximum entropy principle to derive generalized version of this distributions using…
We consider a situation where the distribution of a random variable is being estimated by the empirical distribution of noisy measurements of that variable. This is common practice in, for example, teacher value-added models and other…
We consider the exit problem for a one-dimensional system with random switching near an unstable equilibrium point of the averaged drift. In the infinite switching rate limit, we show that the exit time satisfies a limit theorem with a…
In a classic model analysed by Weitzman an agent is presented with boxes containing prizes. She may open boxes in any order, discover prizes within, and optimally stop. She wishes to maximize the expected value of the greatest prize found,…
We provide a characterization of an optimal stopping time for a class of finite horizon time-inconsistent optimal stopping problems (OSPs) of mean-field type, adapted to the Brownian filtration, including those related to mean-field…