Related papers: Convergence of Contrastive Divergence Algorithm in…

We consider adaptive increasingly rare Markov chain Monte Carlo (MCMC) algorithms, which are adaptive MCMC methods, where the adaptation concerning the "past'' happens less and less frequently over time. Under a contraction assumption with…

By exploiting the property that the RBM log-likelihood function is the difference of convex functions, we formulate a stochastic variant of the difference of convex functions (DC) programming to minimize the negative log-likelihood.…

We consider the classical problem of learning, with arbitrary accuracy, the natural parameters of a $k$-parameter truncated \textit{minimal} exponential family from i.i.d. samples in a computationally and statistically efficient manner. We…

We study the problem of sampling from a distribution $\target$ using the Langevin Monte Carlo algorithm and provide rate of convergences for this algorithm in terms of Wasserstein distance of order $2$. Our result holds as long as the…

Stochastic gradient descent in continuous time (SGDCT) provides a computationally efficient method for the statistical learning of continuous-time models, which are widely used in science, engineering, and finance. The SGDCT algorithm…

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the…

Learning RBMs using standard algorithms such as CD(k) involves gradient descent on the negative log-likelihood. One of the terms in the gradient, which involves expectation w.r.t. the model distribution, is intractable and is obtained…

Contrastive decoding (CD) (Li et al., 2023) improves the next-token distribution of a large expert language model (LM) using a small amateur LM. Although CD is applied to various LMs and domains to enhance open-ended text generation, it is…

We consider off-policy temporal-difference (TD) learning methods for policy evaluation in Markov decision processes with finite spaces and discounted reward criteria, and we present a collection of convergence results for several…

We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To…

The learning of domain-invariant representations in the context of domain adaptation with neural networks is considered. We propose a new regularization method that minimizes the discrepancy between domain-specific latent feature…

Convergence rate analysis for general state-space Markov chains is fundamentally important in areas such as Markov chain Monte Carlo and algorithmic analysis (for computing explicit convergence bounds). This problem, however, is notoriously…

Temporal difference (TD) learning is a fundamental algorithm for estimating value functions in reinforcement learning. Recent finite-time analyses of TD with linear function approximation quantify its theoretical convergence rate. However,…

The cyclic block coordinate descent-type (CBCD-type) methods, which performs iterative updates for a few coordinates (a block) simultaneously throughout the procedure, have shown remarkable computational performance for solving strongly…

Applying standard Markov chain Monte Carlo (MCMC) algorithms to large data sets is computationally expensive. Both the calculation of the acceptance probability and the creation of informed proposals usually require an iteration through the…

We demonstrate the use of a variational method to determine a quantitative lower bound on the rate of convergence of Markov Chain Monte Carlo (MCMC) algorithms as a function of the target density and proposal density. The bound relies on…

Expectation maximization (EM) is the default algorithm for fitting probabilistic models with missing or latent variables, yet we lack a full understanding of its non-asymptotic convergence properties. Previous works show results along the…

Energy-based learning algorithms are alternatives to backpropagation and are well-suited to distributed implementations in analog electronic devices. However, a rigorous theory of convergence is lacking. We make a first step in this…

Restricted Boltzmann Machines (RBMs) are general unsupervised learning devices to ascertain generative models of data distributions. RBMs are often trained using the Contrastive Divergence learning algorithm (CD), an approximation to the…

In this paper, we establish new convergence results for the quantized distributed gradient descent and suggest a novel strategy of choosing the stepsizes for the high-performance of the algorithm. Under the strongly convexity assumption on…