相关论文: Bounding the expectation of the supremum of empiri…

Recently, there has been significant progress in understanding reinforcement learning in discounted infinite-horizon Markov decision processes (MDPs) by deriving tight sample complexity bounds. However, in many real-world applications, an…

We introduce and study a 2-parameter family of unitarily invariant probability measures on the space of infinite Hermitian matrices. We show that the decomposition of a measure from this family on ergodic components is described by a…

Motivated by the statistical and computational challenges of computing Wasserstein distances in high-dimensional contexts, machine learning researchers have defined modified Wasserstein distances based on computing distances between…

This paper studies probabilistic rates of convergence for consensus+innovations type of algorithms in random, generic networks. For each node, we find a lower and also a family of upper bounds on the large deviations rate function, thus…

In this paper, we develop a general approach for probabilistic estimation and optimization. An explicit formula and a computational approach are established for controlling the reliability of probabilistic estimation based on a mixed…

In this paper, we present a nonparametric estimation procedure for the multivariate Hawkes point process. The timeline is cut into bins and -- for each component process -- the number of points in each bin is counted. The distribution of…

Recent advances in probabilistic modelling have led to a large number of simulation-based inference algorithms which do not require numerical evaluation of likelihoods. However, a public benchmark with appropriate performance metrics for…

The Wasserstein distance is an attractive tool for data analysis but statistical inference is hindered by the lack of distributional limits. To overcome this obstacle, for probability measures supported on finitely many points, we derive…

Gaussian Processes (GPs) are widely employed in control and learning because of their principled treatment of uncertainty. However, tracking uncertainty for iterative, multi-step predictions in general leads to an analytically intractable…

We consider random discrepancy under weighted importance sampling of a class of stratified input. We give the expected $L_p-$discrepancy($2\leq p<\infty$) upper bound in weighted form under a class of stratified sampling. This result…

In this paper, we derive an explicit upper bound for the Wasserstein distance between a functional of point processes and a Gaussian distribution. Using Stein's method in conjunction with Malliavin's calculus and the Poisson embedding…

We introduce two kinds of risk measures with respect to some reference probability measure, which both allow for a certain order structure and domination property. Analyzing their relation to each other leads to the question when a certain…

We seek to understand the probability an individual benefits from treatment (PIBT), an inestimable quantity that must be bounded in practice. Given the innate uncertainty in the population-level bounds on PIBT, we seek to better understand…

Sequential estimation of a probability $p$ by means of inverse binomial sampling is considered. For $\mu_1,\mu_2>1$ given, the accuracy of an estimator $\hat{p}$ is measured by the confidence level $P[p/\mu_2\leq\hat{p}\leq p\mu_1]$. The…

Within the calibration of material models, often the numerical results of a simulation model $y$ are compared with the experimental measurements $y^*$. Usually, the differences between measurements and simulation are minimized using least…

This paper focuses on recursive estimation of time varying autoregressive processes in a nonparametric setting. The stability of the model is revisited and uniform results are provided when the time-varying autoregressive parameters belong…

Finding optimal policies for Partially Observable Markov Decision Processes (POMDPs) is challenging due to their uncountable state spaces when transformed into fully observable Markov Decision Processes (MDPs) using belief states.…

We observe a $n$-sample, the distribution of which is assumed to belong, or at least to be close enough, to a given mixture model. We propose an estimator of this distribution that belongs to our model and possesses some robustness…

Gaussian process regression in its most simplified form assumes normal homoscedastic noise and utilizes analytically tractable mean and covariance functions of predictive posterior distribution using Gaussian conditioning. Its…

This paper provides a bound for the supremum of sample averages over a class of functions for a general class of mixing stochastic processes with arbitrary mixing rates. Regardless of the speed of mixing, the bound is comprised of a…