arXiv research

Study on gradient descent in Hilbert spaces with Markov chains, focusing on mixing coefficients.

Unbiased gradient estimation for Markov chains

Study nonparametric estimator for Markov chain transition matrices in offline setting.

Identity testing for reversible Markov chains without symmetry assumption.

Study on financial systems using perturbed unimodal maps with heteroscedastic noise.

New algorithm clusters trajectories from multiple Markov chains with near-optimal error.

The paper studies how quickly samples from Langevin dynamics become independent.

Enhanced Markov chain sampler learns network statistics faster.

Stochastic kernel based dimensionality reduction approaches have become popular in the last decade. The central component of many of these methods is a symmetric kernel that quantifies the vicinity between pairs of data points and a kernel-induced Markov chain on the data. Typically, the Markov chain is fully specified…

In his 2011 work, Maas has shown that the law of any time-reversible continuous-time Markov chain with finite state space evolves like a gradient flow of the relative entropy with respect to its stationary distribution. In this work we show the converse to the above by showing that if the relative law of a Markov chain…

Estimates Markov chain variance efficiently without storing samples.

New method trains Markov kernels for efficient sampling.

Develops CLTs for Markov chain transition probabilities and policies.

Efficiently samples multimodal distributions using data-based initialization.

GenDICE estimates stationary values from offline data.

In this paper we propose an efficient variance reduction approach for additive functionals of Markov chains relying on a novel discrete time martingale representation. Our approach is fully non-asymptotic and does not require the knowledge of the stationary distribution (and even any type of ergodicity) or specific str…

A new model BGAR(1) improves temporal NMF for time series data.

Paper proves CLT for quantile SGD with constant learning rate.

Exponential inequalities are main tools in machine learning theory. To prove exponential inequalities for non i.i.d random variables allows to extend many learning techniques to these variables. Indeed, much work has been done both on inequalities and learning theory for time series, in the past 15 years. However, for …

A low-rank tensor model simplifies multi-dimensional Markov chains.

Paper improves Oja's algorithm for Markovian data streams.

The Riemannian barycentre is one of the most widely used statistical descriptors for probability distributions on Riemannian manifolds. At present, existing algorithms are able to compute the Riemannian barycentre of a probability distribution, only if i.i.d. samples of this distribution are readily available. However,…

Graphical models are popular statistical tools which are used to represent dependent or causal complex systems. Statistically equivalent causal or directed graphical models are said to belong to a Markov equivalent class. It is of great interest to describe and understand the space of such classes. However, with curren…

Uniform TD(0) bound derived for function approximation with Markov noise.

Markov chain Monte Carlo (MCMC) algorithms are ubiquitous in probability theory in general and in machine learning in particular. A Markov chain is devised so that its stationary distribution is some probability distribution of interest. Then one samples from the given distribution by running the Markov chain for a "lo…

Neural Markov models improve time series analysis by balancing deep learning and classical models.

The paper develops a stationary-distribution theory for Random Forest ensemble size selection.

This article considers a model for alternative processes for securities prices and compares this model with actual return data of several securities. The distributions of returns that appear in the model can be Gaussian as well as non-Gaussian; in particular they may have two peaks. We consider a discrete Markov chain …

Optimizes consumption under regime-switching economic states with risk-sensitive preferences.

Estimates missing mass in Markovian sequences with linear runtime and near-optimal risk.

Optimal sequential testing for Markovian data with lower and upper bounds.

We propose a novel framework of estimating systemic risk measures and risk allocations based on Markov chain Monte Carlo (MCMC) methods. We consider a class of allocations whose jth component can be written as some risk measure of the jth conditional marginal loss distribution given the so-called crisis event. By consi…

This paper analyzes the bias of inexact MCMC methods in high dimensions.

Recent works propose using the discriminator of a GAN to filter out unrealistic samples of the generator. We generalize these ideas by introducing the implicit Metropolis-Hastings algorithm. For any implicit probabilistic model and a target distribution represented by a set of samples, implicit Metropolis-Hastings oper…

We provide conditions for the existence and the unicity of strictly stationary solutions of the usual Dynamic Conditional Correlation GARCH models (DCC-GARCH). The proof is based on Tweedie's (1988) criteria, after having rewritten DCC-GARCH models as nonlinear Markov chains. Moreover, we study the existence of their f…

Stochastic normalizing flows use SDEs for efficient training and sampling.

Study online learning in RKHS with dependent processes, focusing on \(β\)- and \(φ\)-mixing.

Scalable method learns context-specific models for hundreds of variables.

The paper analyzes fixed step-size SA schemes on Riemannian manifolds.

Generative Stochastic Networks (GSNs) have been recently introduced as an alternative to traditional probabilistic modeling: instead of parametrizing the data distribution directly, one parametrizes a transition operator for a Markov chain whose stationary distribution is an estimator of the data generating distributio…

Estimating the entropy based on data is one of the prototypical problems in distribution property testing and estimation. For estimating the Shannon entropy of a distribution on $S$ elements with independent samples, [Paninski2004] showed that the sample complexity is sublinear in $S$, and [Valiant--Valiant2011] showed…

The paper analyzes convergence rates of Langevin dynamics and Proximal Sampler using $Φ$-divergence.

New method adapts to unknown mixing time in stochastic optimization.

Study analyzes stock order transitions during US-China trade war using Markov chains.

A Markov Chain approach for aligning generative models from pairwise human preferences.

Study analyzes price change patterns across different market capitalizations using Markov chains.

Markov chain Monte Carlo (MCMC) algorithms are simple and extremely powerful techniques to sample from almost arbitrary distributions. The flaw in practice is that it can take a large and/or unknown amount of time to converge to the stationary distribution. This paper gives sufficient conditions to guarantee that univa…

This work provides a simplified proof of the statistical minimax optimality of (iterate averaged) stochastic gradient descent (SGD), for the special case of least squares. This result is obtained by analyzing SGD as a stochastic process and by sharply characterizing the stationary covariance matrix of this process. The…