Reduces identity testing of reversible Markov chains to simpler symmetric chain tests.
problem Testing identity of reversible Markov chains from a single trajectory.
method Using lumping-congruent Markov embeddings, the problem is simplified to testing symmetric chains over a larger state space.
result Achieves state-of-the-art sample complexity for identity testing.
Stochastic gradient methods are the workhorse (algorithms) of large-scale optimization problems in machine learning, signal processing, and other computational sciences and engineering. This paper studies Markov chain gradient descent, a variant of stochastic gradient descent where the random samples are taken on the t…
Identity testing for reversible Markov chains without symmetry assumption.
problem Identity testing of reversible Markov chains.
method Using distance notion from Daskalakis et al. [2018a], testing without symmetry assumption.
result It is possible to perform identity testing under weaker assumption of reversibility.
Extended elliptical slice sampling for infinite-dimensional spaces, proving reversibility.
problem Proving reversibility of elliptical slice sampling in infinite-dimensional spaces.
method Extended elliptical slice sampling to infinite-dimensional separable Hilbert spaces, providing an alternative proof of reversibility.
result The approach yields a positive semi-definite Markov operator, proving reversibility.
New method trains Markov kernels for efficient sampling.
problem Efficient sampling from complex probability distributions.
method Adversarial learning of involutive Metropolis-Hastings kernels.
result Minimizes total variation distance to empirical data.
Study shows TD(0) with linear approx. converges for reversible Markov chains.
problem TD(0) divergence with off-policy and function approximation.
method Analyzes standard TD(0) with reversible Markov chains, adapting stochastic approximation framework.
result Establishes convergence with probability one for projected Bellman error = 0.
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…
A new sampler improves the inference of causal structures from observational data.
problem Inferring causal relationships from observational data when DAGs are Markov equivalent.
method Developed a non-reversible Markov chain, Causal Zig-Zag sampler, targeting Markov Equivalence Classes of DAGs.
result The sampler improves mixing and offers efficient algorithms for DAG inference.
New MCMC method for complex models with large variables.
problem Inference on posterior model probabilities in large model spaces.
method Reversible genetically modified mode jumping Markov chain Monte Carlo (GMJMCMC).
result Introduced a proper MCMC with correct limiting distribution.
We study the problem of hypothesis testing between two discrete distributions, where we only have access to samples after the action of a known reversible Markov chain, playing the role of noise. We derive instance-dependent minimax rates for the sample complexity of this problem, and show how its dependence in time is…
The paper proves inequalities for Steklov eigenvalues on finite graphs.
problem Eigenvalues of Laplacians for reversible Markov chains and Steklov eigenvalues.
method Generalized Cheeger inequalities, convergence results, and resolvent convergence.
result Sharp estimate for the first non-trivial Steklov eigenvalue.
Estimates Markov chain mixing time from a single trajectory.
problem Estimating mixing time of Markov chains from a single trajectory.
method Contraction with respect to total variation, inspired by Wolfer's contraction coefficient.
result Improved confidence intervals and instance-dependent rates for estimating Markov chains.
We present a nonparametric prior over reversible Markov chains. We use completely random measures, specifically gamma processes, to construct a countably infinite graph with weighted edges. By enforcing symmetry to make the edges undirected we define a prior over random walks on graphs that results in a reversible Mark…
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…
Bayesian method selects interacting regions in Markov models.
problem Estimating interacting regions in Markov Random Fields.
method Reversible Jump Monte Carlo Markov Chain algorithm with pseudoposteriors.
result Proposed method accurately selects interacting regions in simulations and real data.
HDT improves MCMC on graphs with history-dependent sampling.
problem Efficient sampling from target distributions on general graphs with low computational overhead.
method History-driven target (HDT) framework that replaces the original target distribution with a history-dependent one.
result Near-zero variance performance and scalability to large graphs with memory-efficient implementation.
This article provides the first procedure for computing a fully data-dependent interval that traps the mixing time tmix of a finite reversible ergodic Markov chain at a prescribed confidence level. The interval is computed from a single finite-length sample path from the Markov chain, and does not require t…
A new sampler speeds up Bayesian mixture models.
problem Sampling from Bayesian finite mixture models is slow and hard.
method Introduces a non-reversible sampling scheme for Bayesian finite mixture models.
result The new sampler outperforms classical samplers in many scenarios, especially during convergence.
New algorithms learn Ising models from minimal observation of configuration changes.
problem Learning Ising models from the evolution of Markov chains with minimal observation.
method Developed algorithms that efficiently learn Ising models from minimal observation of configuration changes.
result First algorithms that efficiently learn Ising models in a more realistic observation model.
This paper develops tools for nonreversible MCMC with convergence guarantees.
problem Designing nonreversible MCMC kernels with convergence guarantees.
method Develops tools for nonreversible Markov kernels using conditional invertible transforms.
result Ensures nonreversible kernels have the desired invariance property and lead to convergent algorithms.
We address the problem of estimating the mixing time tmix of an arbitrary ergodic finite-state Markov chain from a single trajectory of length m. The reversible case was addressed by Hsu et al. [2019], who left the general case as an open problem. In the reversible case, the analysis is greatly facilita…
CD learning is shown to be an adversarial game for fitting models.
problem Difficulty in understanding the convergence properties of CD learning.
method Presented an alternative derivation of CD without approximation, showing it as a time-reversal adversarial game.
result CD is an adversarial learning procedure where a discriminator tries to classify time-reversed Markov chains.
BINDy uses Bayesian methods to identify nonlinear dynamics from data.
problem Learning sparse representations of complex dynamics from data.
method Bayesian treatment of dictionary learning system identification using reversible-jump Markov-chain Monte-Carlo.
result BINDy produces models that are sparse in model space rather than parameter space.
Let K be an irreducible and reversible Markov kernel on a finite set X. We construct a metric W on the set of probability measures on X and show that with respect to this metric, the law of the continuous time Markov chain evolves as the gradient flow of the entropy. This result is a discrete counterpart of the Wassers…
New PDMP samplers tackle variable selection in models.
problem Jointly explore model space and parameter space.
method Develop reversible jump PDMP samplers.
result New samplers mix better and are more efficient.
We introduce a new geometric approach that constructs a transition kernel of Markov chain. Our method always minimizes the average rejection rate and even reduce it to zero in many relevant cases, which cannot be achieved by conventional methods, such as the Metropolis-Hastings algorithm or the heat bath algorithm (Gib…
The article examines entropy-information inequalities for continuous-time Markov chains under curvature-dimension conditions.
problem Proving Li-Yau inequalities and modified logarithmic Sobolev inequalities for reversible Markov chains.
method Introducing the CDΥ(κ,F) condition and deriving entropy-information inequalities. result Derives functional inequalities relating entropy to Fisher information.
The spectral gap γ of a finite, ergodic, and reversible Markov chain is an important parameter measuring the asymptotic rate of convergence. In applications, the transition matrix P may be unknown, yet one sample of the chain up to a fixed time n may be observed. We consider here the problem of estimating γ fro…
We consider the problem of estimating from sample paths the absolute spectral gap γ∗ of a reversible, irreducible and aperiodic Markov chain (Xt)t∈N over a finite state space Ω. We propose the UCPI (Upper Confidence Power Iteration) algorithm for this problem, a low-complexity algorithm …
Study non-negative curvature Markov chains, proving entropy contraction.
problem Prove entropy contraction for Markov chains with non-negative curvature.
method Prove 1-step contraction in Wasserstein distance implies 1-step contraction in relative entropy.
result Prove MLSI with constant equal to minimal rate increment for mean-field zero-range process.
Sampling the parameters of high-dimensional Continuous Time Markov Chains (CTMC) is a challenging problem with important applications in many fields of applied statistics. In this work a recently proposed type of non-reversible rejection-free Markov Chain Monte Carlo (MCMC) sampler, the Bouncy Particle Sampler (BPS), i…
Bayesian symbolic regression uncovers missing physics from data with uncertainty quantification.
problem Incomplete knowledge of physical laws from experimental data.
method Bayesian symbolic regression using Reversible Jump Markov Chain Monte Carlo.
result Uncertainty quantification in recovered model structures.
Paper improves Oja's algorithm for Markovian data streams.
problem Estimating the top eigenvector of a covariance matrix from Markovian data.
method Improves Oja's algorithm for streaming PCA with Markovian dependence.
result First sharp rate for Oja's algorithm on entire data stream, removing sample size dependence.
A new two-step MH method for Bayesian EL computation.
problem Complex likelihood support in Bayesian EL.
method Hierarchical Metropolis Hastings with reversible jump MCMC.
result Improved sampling from BayesEL posteriors.
Continuous time framework for discrete data denoising models.
problem Efficient training and sampling for discrete data denoising models.
method Formulated as Continuous Time Markov Chains (CTMCs), efficient training using continuous time ELBO, high-dimensional CTMC simulation, novel theoretical error bound.
result Continuous time treatment enables novel theoretical error bound between generated and true data distributions.
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…
New algorithm improves sampling from constrained spaces.
problem Sampling from constrained spaces efficiently.
method Metropolis-adjusted Mirror Langevin algorithm.
result Unbiased sampling with improved mixing time.
MetFlow combines MCMC and VI efficiently for better inference.
problem Combining MCMC and VI for efficient inference.
method Introduces MetFlow, a novel MCMC algorithm with Normalizing Flows, and a new method to combine it with VI.
result MetFlow produces expressive variational families with improved computational efficiency.
New algorithm broadens BART models applicability.
problem Limited applicability of Bayesian additive regression trees (BART) models due to conditional conjugacy.
method Introduces a reversible jump Markov chain Monte Carlo algorithm for generalized BART models.
result Extends BART models to arbitrary generalized BART models without conditional conjugacy.
We propose a novel reversible jump Markov chain Monte Carlo (MCMC) simulated annealing algorithm to optimize radial basis function (RBF) networks. This algorithm enables us to maximize the joint posterior distribution of the network parameters and the number of basis functions. It performs a global search in the joint …
Enhances RJMCMC efficiency with non-linear transport-based proposals.
problem Designing efficient RJMCMC proposals for complex models.
method Applies non-linear transport-based approach to construct efficient transdimensional jumps.
result Acceptance probability depends only on model probabilities when exact transports are used.
In this paper we build on previous work which uses inferences techniques, in particular Markov Chain Monte Carlo (MCMC) methods, to solve parameterized control problems. We propose a number of modifications in order to make this approach more practical in general, higher-dimensional spaces. We first introduce a new tar…
The paper extends game theory using Hodge theory on graphs.
problem Generalizing Shapley's value allocation formula for cooperative games on graphs.
method Connecting stochastic path integrals to Hodge-theoretic Poisson's equations on graphs.
result The value allocation operator is the solution to Poisson's equation in combinatorial Hodge theory.
This paper studies the optimal VIX futures trading problems under a regime-switching model. We consider the VIX as mean reversion dynamics with dependence on the regime that switches among a finite number of states. For the trading strategies, we analyze the timings and sequences of the investor's market participation,…
Directed acyclic graphs are the basic representation of the structure underlying Bayesian networks, which represent multivariate probability distributions. In many practical applications, such as the reverse engineering of gene regulatory networks, not only the estimation of model parameters but the reconstruction of t…
The book covers scalable MCMC methods for Bayesian learning.
problem Scalability issues in Bayesian learning with large datasets.
method Advanced MCMC algorithms, including stochastic gradient, non-reversible, and continuous time methods.
result Substantial advances in practical and theoretical Bayesian computation.
A new Monte Carlo sampling method derived from reverse diffusion.
problem Sampling from complex distributions, especially multi-modal ones.
method Transforming score matching into mean estimation; estimating means of regularized posterior distributions.
result rdMC can approximate sampling with any desired accuracy and is significantly faster than MCMC for complex distributions.
The paper provides mean-square error bounds for stochastic approximation algorithms.
problem Error bounds for recursive equations with Markovian disturbances.
method Analysis of mean-square error for stochastic approximation algorithms.
result Mean-square error achieves the optimal rate of O(1/n) under certain conditions.