Related papers: Adaptive Variational Inference in Probabilistic Gr…
We introduce an adaptive sampling method for the Deep Ritz method aimed at solving partial differential equations (PDEs). Two deep neural networks are used. One network is employed to approximate the solution of PDEs, while the other one is…
We develop a framework for incorporating structured graphical models in the \emph{encoders} of variational autoencoders (VAEs) that allows us to induce interpretable representations through approximate variational inference. This allows us…
The Tweedie Compound Poisson-Gamma model is routinely used for modeling non-negative continuous data with a discrete probability mass at zero. Mixed models with random effects account for the covariance structure related to the grouping…
Training deep generative models with maximum likelihood remains a challenge. The typical workaround is to use variational inference (VI) and maximize a lower bound to the log marginal likelihood of the data. Variational auto-encoders (VAEs)…
Likelihood-free Bayesian inference algorithms are popular methods for calibrating the parameters of complex, stochastic models, required when the likelihood of the observed data is intractable. These algorithms characteristically rely…
Deriving Bayesian inference for exponential random graph models (ERGMs) is a challenging "doubly intractable" problem as the normalizing constants of the likelihood and posterior density are both intractable. Markov chain Monte Carlo (MCMC)…
We study two free energy approximations (Bethe and plaquette-CVM) for the Random Field Ising Model in two dimensions. We compare results obtained by these two methods in single instances of the model on the square grid, showing the…
Variational approximation methods have proven to be useful for scaling Bayesian computations to large data sets and highly parametrized models. Applying variational methods involves solving an optimization problem, and recent research in…
Structural equation models are commonly used to capture the relationship between sets of observed and unobservable variables. Traditionally these models are fitted using frequentist approaches but recently researchers and practitioners have…
We develop flexible methods of deriving variational inference for models with complex latent variable structure. By splitting the variables in these models into "global" parameters and "local" latent variables, we define a class of…
Envelope models provide a sufficient dimension reduction framework for multivariate regression analysis. Bayesian inference for these models has been developed primarily using Markov chain Monte Carlo (MCMC) methods. Specifically, Gibbs…
The Variational Autoencoder (VAE) is a powerful framework for learning probabilistic latent variable generative models. However, typical assumptions on the approximate posterior distribution of the encoder and/or the prior, seriously…
This article is concerned with the mathematical analysis of a family of adaptive importance sampling algorithms applied to diffusion processes. These methods, referred to as Adaptive Biasing Potential methods, are designed to efficiently…
Well-calibrated probabilistic regression models are a crucial learning component in robotics applications as datasets grow rapidly and tasks become more complex. Unfortunately, classical regression models are usually either probabilistic…
We consider the closely related problems of sampling from a distribution known up to a normalizing constant, and estimating said normalizing constant. We show how variational autoencoders (VAEs) can be applied to this task. In their…
Probabilistic graphical models with frustration exhibit rugged energy landscapes that trap iterative optimization dynamics. These landscapes are shaped not only by local interactions, but crucially also by the global loop structure of the…
A common method for assessing validity of Bayesian sampling or approximate inference methods makes use of simulated data replicates for parameters drawn from the prior. Under continuity assumptions, quantiles of functions of the simulated…
Current methods for learning graphical models with latent variables and a fixed structure estimate optimal values for the model parameters. Whereas this approach usually produces overfitting and suboptimal generalization performance,…
A scheme to provide various mean-field-type approximation algorithms is presented by employing the Bethe free energy formalism to a family of replicated systems in conjunction with analytical continuation with respect to the number of…
Many modern unsupervised or semi-supervised machine learning algorithms rely on Bayesian probabilistic models. These models are usually intractable and thus require approximate inference. Variational inference (VI) lets us approximate a…