相关论文: Convergence properties of pseudo-marginal Markov c…
In this paper, we propose a variance reduction approach for Markov chains based on additive control variates and the minimization of an appropriate estimate for the asymptotic variance. We focus on the particular case when control variates…
The aim of this note is to investigate the concentration properties of unbounded functions of geometrically ergodic Markov chains. We derive concentration properties of centered functions with respect to the square of the Lyapunov's…
A key goal in the design of probabilistic inference algorithms is identifying and exploiting properties of the distribution that make inference tractable. Lifted inference algorithms identify symmetry as a property that enables efficient…
Markov chains can be used to generate samples whose distribution approximates a given target distribution. The quality of the samples of such Markov chains can be measured by the discrepancy between the empirical distribution of the samples…
We establish an ordering criterion for the asymptotic variances of two consistent Markov chain Monte Carlo (MCMC) estimators: an importance sampling (IS) estimator, based on an approximate reversible chain and subsequent IS weighting, and a…
Markov chain Monte Carlo (MCMC) is an established approach for uncertainty quantification and propagation in scientific applications. A key challenge in applying MCMC to scientific domains is computation: the target density of interest is…
The reinforcement learning algorithm SARSA combined with linear function approximation has been shown to converge for infinite horizon discounted Markov decision problems (MDPs). In this paper, we investigate the convergence of the…
The asymptotic behavior of the stochastic gradient algorithm with a biased gradient estimator is analyzed. Relying on arguments based on the dynamic system theory (chain-recurrence) and the differential geometry (Yomdin theorem and…
Adaptive Markov chain Monte Carlo (MCMC) algorithms, which automatically tune their parameters based on past samples, have proved extremely useful in practice. The self-tuning mechanism makes them `non-Markovian', which means that their…
Markov chain Monte Carlo samplers produce dependent streams of variates drawn from the limiting distribution of the Markov chain. With this as motivation, we introduce novel univariate kernel density estimators which are appropriate for the…
We consider periodic Markov chains with absorption. Applying to iterates of this periodic Markov chain criteria for the exponential convergence of conditional distributions of aperiodic absorbed Markov chains, we obtain exponential…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
In this work, we examine sampling problems with non-smooth potentials. We propose a novel Markov chain Monte Carlo algorithm for sampling from non-smooth potentials. We provide a non-asymptotical analysis of our algorithm and establish a…
Most Markov chain Monte Carlo methods operate in discrete time and are reversible with respect to the target probability. Nevertheless, it is now understood that the use of non-reversible Markov chains can be beneficial in many contexts. In…
In any Markov chain Monte Carlo analysis, rapid convergence of the chain to its target probability distribution is of practical and theoretical importance. A chain that converges at a geometric rate is geometrically ergodic. In this paper,…
Performing numerical integration when the integrand itself cannot be evaluated point-wise is a challenging task that arises in statistical analysis, notably in Bayesian inference for models with intractable likelihood functions. Markov…
We prove finite sample complexities for sequential Monte Carlo (SMC) algorithms which require only local mixing times of the associated Markov kernels. Our bounds are particularly useful when the target distribution is multimodal and global…
We propose an extragradient method with stepsizes bounded away from zero for stochastic variational inequalities requiring only pseudo-monotonicity. We provide convergence and complexity analysis, allowing for an unbounded feasible set,…
An irreversible Markov-chain Monte Carlo (MCMC) algorithm with skew detailed balance conditions originally proposed by Turitsyn et al. is extended to general discrete systems on the basis of the Metropolis-Hastings scheme. To evaluate the…
We consider the stochastic variational inequality problem in which the map is expectation-valued in a component-wise sense. Much of the available convergence theory and rate statements for stochastic approximation schemes are limited to…