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The Metropolis-Adjusted Langevin Algorithm (MALA) is a widely used Markov Chain Monte Carlo (MCMC) method for sampling from high-dimensional distributions. However, MALA relies on differentiability assumptions that restrict its…
Although with progress in introducing auxiliary amortized inference models, learning discrete latent variable models is still challenging. In this paper, we show that the annoying difficulty of obtaining reliable stochastic gradients for…
The Metropolis-adjusted Langevin (MALA) algorithm is a sampling algorithm that incorporates the gradient of the logarithm of the target density in its proposal distribution. In an earlier joint work \citet{pill:stu:12}, the author had…
Latent class model (LCM), which is a finite mixture of different categorical distributions, is one of the most widely used models in statistics and machine learning fields. Because of its non-continuous nature and the flexibility in shape,…
Energy-based models (EBMs) are generative models inspired by statistical physics with a wide range of applications in unsupervised learning. Their performance is best measured by the cross-entropy (CE) of the model distribution relative to…
Variational autoencoders (VAEs) are popular likelihood-based generative models which can be efficiently trained by maximizing an Evidence Lower Bound (ELBO). There has been much progress in improving the expressiveness of the variational…
Uncertainty estimation is a key issue when considering the application of deep neural network methods in science and engineering. In this work, we introduce a novel algorithm that quantifies epistemic uncertainty via Monte Carlo sampling…
This paper presents a new Metropolis-adjusted Langevin algorithm (MALA) that uses convex analysis to simulate efficiently from high-dimensional densities that are log-concave, a class of probability distributions that is widely used in…
We consider a recently proposed class of MCMC methods which uses proximity maps instead of gradients to build proposal mechanisms which can be employed for both differentiable and non-differentiable targets. These methods have been shown to…
The expectation maximization (EM) algorithm is a widespread method for empirical Bayesian inference, but its expectation step (E-step) is often intractable. Employing a stochastic approximation scheme with Markov chain Monte Carlo (MCMC)…
Structured Latent Attribute Models (SLAMs) are a family of discrete latent variable models widely used in education, psychology, and epidemiology to model multivariate categorical data. A SLAM assumes that multiple discrete latent…
Latent variable models (LVMs) represent observed variables by parameterized functions of latent variables. Prominent examples of LVMs for unsupervised learning are probabilistic PCA or probabilistic SC which both assume a weighted linear…
Markov Chain Monte Carlo (MCMC) is one of the most powerful methods to sample from a given probability distribution, of which the Metropolis Adjusted Langevin Algorithm (MALA) is a variant wherein the gradient of the distribution is used…
We propose a modified version of the three-step estimation method for the latent class model with covariates, which may be used to estimate latent Markov models for longitudinal data. The three-step estimation approach we propose is based…
The Laplace approximation (LA) has been proposed as a method for approximating the marginal likelihood of statistical models with latent variables. However, the approximate maximum likelihood estimators (MLEs) based on the LA are often…
Stochastic approximation methods play a central role in maximum likelihood estimation problems involving intractable likelihood functions, such as marginal likelihoods arising in problems with missing or incomplete data, and in parametric…
It has been shown that the nonreversible overdamped Langevin dynamics enjoy better convergence properties in terms of spectral gap and asymptotic variance than the reversible one. In this article we propose a variance reduction method for…
The Metropolis-adjusted Langevin algorithm (MALA) is a Metropolis-Hastings method for approximate sampling from continuous distributions. We derive upper bounds for the contraction rate in Kantorovich-Rubinstein-Wasserstein distance of the…
Latent Gaussian models have a rich history in statistics and machine learning, with applications ranging from factor analysis to compressed sensing to time series analysis. The classical method for maximizing the likelihood of these models…
We introduce an approach based on mirror descent and sequential Monte Carlo (SMC) to perform joint parameter inference and posterior estimation in latent variable models. This approach is based on minimisation of a functional over the…