This paper establishes Hoeffding's lemma and inequality for bounded functions of general-
state-space and not necessarily reversible Markov chains. The sharpness of these results is …

We establish Bernstein's inequalities for functions of general (general-state-space and
possibly non-reversible) Markov chains. These inequalities achieve sharp variance proxies …

Abstract We give Hoeffding-and Bernstein-type concentration inequalities for the largest
eigenvalue of sums of random matrices arising from a Markov chain. We consider time …

We propose a novel approach to concentration for non-independent random variables. The
main idea is to “pretend” that the random variables are independent and pay a multiplicative …

We consider adaptive increasingly rare Markov chain Monte Carlo (AIR MCMC), which is an
adaptive MCMC method, where the adaptation concerning the past happens less and less …

Gibbs samplers are preeminent Markov chain Monte Carlo algorithms used in computational
physics and statistical computing. Yet, their most fundamental properties, such as relations …

High-dimensional linear regression has been intensively studied in the community of
statistics in the last two decades. For the convenience of theoretical analyses, classical …

We establish non-asymptotic error bounds for the classical Maximal Likelihood Estimation of
the transition matrix of a given Markov chain. Meanwhile, in the reversible case, we propose …

We investigate online maximum cardinality matching, a central problem in ad allocation. In
this problem, users are revealed sequentially, and each new user can be paired with any …

This paper studies Hoeffding's inequality for Markov chains under the generalized
concentrability condition defined via integral probability metric (IPM). The generalized …