Given samples from an unknown multivariate distribution p, is it possible to distinguish
whether p is the product of its marginals versus p being far from every product distribution …

We address the problem of estimating the mixing time $ t_ {\mathsf {mix}} $ of an arbitrary
ergodic finite Markov chain from a single trajectory of length $ m $. The reversible case was …

This article provides the first procedure for computing a fully data-dependent interval that
traps the mixing time $ t_ {mix} $ of a finite reversible ergodic Markov chain at a prescribed …

The spectral gap ⋆ of a finite, ergodic and reversible Markov chain is an important
parameter measuring the asymptotic rate of convergence. In applications, the transition …

Abstract The mixing time $ t_ {\mathsf {mix}} $ of an ergodic Markov chain measures the rate
of convergence towards its stationary distribution $\boldsymbol {\pi} $. We consider the …

In this paper we discuss the problem of estimating graph parameters from a random walk
with restarts. In this setting, an algorithm observes the trajectory of a random walk over an …

We show that the minimax sample complexity for estimating the pseudo-spectral gap γ ps of
an ergodic Markov chain in constant multiplicative error is of the order of Θ˜(1 γ ps π⋆) …

Entropy estimation is one of the prototypical problems in distribution property testing. To
consistently estimate the Shannon entropy of a distribution on $ S $ elements with …

In a groundbreaking work, Schmidt-Hieber (2020) proved the minimax optimality of deep
neural networks with ReLu activation for least-square regression estimation over a large …

We introduce a novel statistical measure for MCMC-mean estimation, the inter-trace
variance ${\rm trv}^{(\tau_ {rel})}({\cal M}, f) $, which depends on a Markov chain ${\cal M} …