Related papers: Mixed Variational Inference
Popular deterministic approximations of posterior distributions from, e.g. the Laplace method, variational Bayes and expectation-propagation, generally rely on symmetric approximating families, often taken to be Gaussian. This choice…
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…
We consider Bayesian variable selection in sparse high-dimensional regression, where the number of covariates $p$ may be large relative to the samples size $n$, but at most a moderate number $q$ of covariates are active. Specifically, we…
Laplace approximations are popular techniques for endowing deep networks with epistemic uncertainty estimates as they can be applied without altering the predictions of the trained network, and they scale to large models and datasets. While…
Deep Gaussian processes provide a flexible approach to probabilistic modelling of data using either supervised or unsupervised learning. For tractable inference approximations to the marginal likelihood of the model must be made. The…
Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…
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,…
We show how to use a variational approximation to the logistic function to perform approximate inference in Bayesian networks containing discrete nodes with continuous parents. Essentially, we convert the logistic function to a Gaussian,…
Markov chain Monte Carlo (MCMC) methods remain the mainstay of Bayesian estimation of structural equation models (SEM), though they often incur a high computational cost. We present a bespoke approximate Bayesian approach to SEM, drawing on…
Variational inference has become an increasingly attractive fast alternative to Markov chain Monte Carlo methods for approximate Bayesian inference. However, a major obstacle to the widespread use of variational methods is the lack of…
Latent variable models for ordinal data represent a useful tool in different fields of research in which the constructs of interest are not directly observable. In such models, problems related to the integration of the likelihood function…
Using an asymmetric Laplace distribution, which provides a mechanism for Bayesian inference of quantile regression models, we develop a fully Bayesian approach to fitting single-index models in conditional quantile regression. In this work,…
The Bayesian estimation of GARCH-family models has been typically addressed through Monte Carlo sampling. Variational Inference is gaining popularity and attention as a robust approach for Bayesian inference in complex machine learning…
Variational Bayes methods approximate the posterior density by a family of tractable distributions whose parameters are estimated by optimisation. Variational approximation is useful when exact inference is intractable or very costly. Our…
Deep Gaussian Processes (DGPs) are hierarchical generalizations of Gaussian Processes that combine well calibrated uncertainty estimates with the high flexibility of multilayer models. One of the biggest challenges with these models is that…
Many approximate Bayesian inference methods assume a particular parametric form for approximating the posterior distribution. A multivariate Gaussian distribution provides a convenient density for such approaches; examples include the…
Bayesian inference typically requires the computation of an approximation to the posterior distribution. An important requirement for an approximate Bayesian inference algorithm is to output high-accuracy posterior mean and uncertainty…
Modern variational inference (VI) uses stochastic gradients to avoid intractable expectations, enabling large-scale probabilistic inference in complex models. VI posits a family of approximating distributions q and then finds the member of…
Local projections (LPs) are widely used for impulse response analysis, but Bayesian methods face challenges due to the absence of a likelihood function. Existing approaches rely on pseudo-likelihoods, which often result in poorly calibrated…
Quantiles are useful characteristics of random variables that can provide substantial information on distributions compared with commonly used summary statistics such as means. In this paper, we propose a Bayesian quantile trend filtering…