Related papers: Bayesian variational inference for exponential ran…
Variational inference, as an alternative to Markov chain Monte Carlo sampling, has played a transformative role in enabling scalable computation for complex Bayesian models. Nevertheless, existing approaches often depend on either rigid…
Modelling random dynamical systems in continuous time, diffusion processes are a powerful tool in many areas of science. Model parameters can be estimated from time-discretely observed processes using Markov chain Monte Carlo (MCMC) methods…
Variational Bayes (VB) is a popular tool for Bayesian inference in statistical modeling. Recently, some VB algorithms are proposed to handle intractable likelihoods with applications such as approximate Bayesian computation. In this paper,…
Mean-field variational inference is a method for approximate Bayesian posterior inference. It approximates a full posterior distribution with a factorized set of distributions by maximizing a lower bound on the marginal likelihood. This…
Estimating hidden processes from non-linear noisy observations is particularly difficult when the parameters of these processes are not known. This paper adopts a machine learning approach to devise variational Bayesian inference for such…
We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…
It has become increasingly easy nowadays to collect approximate posterior samples via fast algorithms such as variational Bayes, but concerns exist about the estimation accuracy. It is tempting to build solutions that exploit approximate…
Gaussian variational approximation is a popular methodology to approximate posterior distributions in Bayesian inference especially in high dimensional and large data settings. To control the computational cost while being able to capture…
Achieving robust uncertainty quantification for deep neural networks represents an important requirement in many real-world applications of deep learning such as medical imaging where it is necessary to assess the reliability of a neural…
This paper presents a detailed theoretical analysis of the three stochastic approximation proximal gradient algorithms proposed in our companion paper [49] to set regularization parameters by marginal maximum likelihood estimation. We prove…
Latent Gaussian models (LGMs) are perhaps the most commonly used class of models in statistical applications. Nevertheless, in areas ranging from longitudinal studies in biostatistics to geostatistics, it is easy to find datasets that…
This paper examines Bayesian belief network inference using simulation as a method for computing the posterior probabilities of network variables. Specifically, it examines the use of a method described by Henrion, called logic sampling,…
Non-Gaussian likelihoods are essential for modelling complex real-world observations but pose significant computational challenges in learning and inference. Even with Gaussian priors, non-Gaussian likelihoods often lead to analytically…
In many domains, we are interested in analyzing the structure of the underlying distribution, e.g., whether one variable is a direct parent of the other. Bayesian model-selection attempts to find the MAP model and use its structure to…
Variable selection is a key issue when analyzing high-dimensional data. The explosion of data with large sample sizes and dimensionality brings new challenges to this problem in both inference accuracy and computational complexity. To…
Researchers increasingly wish to estimate time-varying parameter (TVP) regressions which involve a large number of explanatory variables. Including prior information to mitigate over-parameterization concerns has led to many using Bayesian…
Variational inference is a powerful tool for approximate inference, and it has been recently applied for representation learning with deep generative models. We develop the variational Gaussian process (VGP), a Bayesian nonparametric…
The Laplace approximation has been one of the workhorses of Bayesian inference. It often delivers good approximations in practice despite the fact that it does not strictly take into account where the volume of posterior density lies.…
Increasingly complex datasets pose a number of challenges for Bayesian inference. Conventional posterior sampling based on Markov chain Monte Carlo can be too computationally intensive, is serial in nature and mixes poorly between posterior…
Bayesian inference promises to ground and improve the performance of deep neural networks. It promises to be robust to overfitting, to simplify the training procedure and the space of hyperparameters, and to provide a calibrated measure of…