Related papers: Adaptive estimation for bifurcating Markov chains
We present an algorithm for learning mixtures of Markov chains and Markov decision processes (MDPs) from short unlabeled trajectories. Specifically, our method handles mixtures of Markov chains with optional control input by going through a…
We consider general Markov processes with absorption and provide criteria ensuring the exponential convergence in total variation of the distribution of the process conditioned not to be absorbed. The first one is based on two-sided…
Understanding stochastic gradient descent (SGD) and its variants is essential for machine learning. However, most of the preceding analyses are conducted under amenable conditions such as unbiased gradient estimator and bounded objective…
In the first part of this paper we study approximations of trajectories of Piecewise Deter-ministic Processes (PDP) when the flow is not explicit by the thinning method. We also establish a strong error estimate for PDPs as well as a weak…
In this paper, we quantify the impact of using non-convergent Markov chains to train Energy-Based models (EBMs). In particular, we show analytically that EBMs trained with non-persistent short runs to estimate the gradient can perfectly…
In this paper we deal with the regression problem in a random design setting. We investigate asymptotic optimality under minimax point of view of various Bayesian rules based on warped wavelets and show that they nearly attain optimal…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
We present a simulation methodology for Bayesian estimation of rate parameters in Markov jump processes arising for example in stochastic kinetic models. To handle the problem of missing components and measurement errors in observed data,…
We consider whether ergodic Markov chains with bounded step size remain bounded in probability when their transitions are modified by an adversary on a bounded subset. We provide counterexamples to show that the answer is no in general, and…
The Pseudo-Marginal (PM) algorithm is a popular Markov chain Monte Carlo (MCMC) method used to sample from a target distribution when its density is inaccessible, but can be estimated with a non-negative unbiased estimator. Its performance…
Monte Carlo methods -- such as Markov chain Monte Carlo (MCMC) and piecewise deterministic Markov process (PDMP) samplers -- provide asymptotically exact estimators of expectations under a target distribution. There is growing interest in…
We prove an invariance principle for non-stationary random processes and establish a rate of convergence under a new type of mixing condition. The dependence is exponentially decaying in the gap between the past and the future and is…
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…
Many exact Markov chain Monte Carlo algorithms have been developed for posterior inference in Bayesian nonparametric models which involve infinite-dimensional priors. However, these methods are not generic and special methodology must be…
In this paper we develop a statistical estimation technique to recover the transition kernel $P$ of a Markov chain $X=(X_m)_{m \in \mathbb N}$ in presence of censored data. We consider the situation where only a sub-sequence of $X$ is…
In this paper we propose a novel variance reduction approach for additive functionals of Markov chains based on minimization of an estimate for the asymptotic variance of these functionals over suitable classes of control variates. A…
We study nonparametric regression over Besov spaces from noisy observations under sub-exponential noise, aiming to achieve minimax-optimal guarantees on the integrated squared error that hold with high probability and adapt to the unknown…
This paper proposes a new randomized strategy for adaptive MCMC using Bayesian optimization. This approach applies to non-differentiable objective functions and trades off exploration and exploitation to reduce the number of potentially…
We provide a novel method for sensitivity analysis of parametric robust Markov chains. These models incorporate parameters and sets of probability distributions to alleviate the often unrealistic assumption that precise probabilities are…
This paper presents a nonparametric method for estimating the conditional density associated to the jump rate of a piecewise-deterministic Markov process. In our framework, the estimation needs only one observation of the process within a…