Related papers: Conditionally conjugate mean-field variational Bay…
Surrogate models provide a quick-to-evaluate approximation to complex computational models and are essential for multi-query problems like design optimisation. The inputs of current deterministic computational models are usually…
Spatial count data models are used to explain and predict the frequency of phenomena such as traffic accidents in geographically distinct entities such as census tracts or road segments. These models are typically estimated using Bayesian…
An ordinary differential equation (ODE) model, whose regression curves are a set of solution curves for some ODEs, poses a challenge in parameter estimation. The challenge, due to the frequent absence of analytic solutions and the…
While stochastic variational inference is relatively well known for scaling inference in Bayesian probabilistic models, related methods also offer ways to circumnavigate the approximation of analytically intractable expectations. The key…
Large spatial datasets with non-Gaussian responses are increasingly common in environmental monitoring, ecology, and remote sensing, yet scalable Bayesian inference for such data remains challenging. Markov chain Monte Carlo (MCMC) methods…
Like mean, quantile and variance, mode is also an important measure of central tendency and data summary. Many practical questions often focus on "Which element (gene or file or signal) occurs most often or is the most typical among all…
We introduce the Variational Holder (VH) bound as an alternative to Variational Bayes (VB) for approximate Bayesian inference. Unlike VB which typically involves maximization of a non-convex lower bound with respect to the variational…
In stochastic variational inference, the variational Bayes objective function is optimized using stochastic gradient approximation, where gradients computed on small random subsets of data are used to approximate the true gradient over the…
Variational inference has recently emerged as a popular alternative to the classical Markov chain Monte Carlo (MCMC) in large-scale Bayesian inference. The core idea is to trade statistical accuracy for computational efficiency. In this…
Bayesian approach, as a useful tool for quantifying uncertainties, has been widely used for solving inverse problems of partial differential equations (PDEs). One of the key difficulties for employing Bayesian approach for the issue is how…
We propose a lower bound on the log marginal likelihood of Gaussian process regression models that can be computed without matrix factorisation of the full kernel matrix. We show that approximate maximum likelihood learning of model…
Bayesian inference provides an attractive online-learning framework to analyze sequential data, and offers generalization guarantees which hold even with model mismatch and adversaries. Unfortunately, exact Bayesian inference is rarely…
We develop a variational Bayesian (VB) approach for estimating large-scale dynamic network models in the network autoregression framework. The VB approach allows for the automatic identification of the dynamic structure of such a model and…
Variational Bayes is a popular method for approximate inference but its derivation can be cumbersome. To simplify the process, we give a 3-step recipe to identify the posterior form by explicitly looking for linearity with respect to…
Approximate inference methods like the Laplace method, Laplace approximations and variational methods, amongst others, are popular methods when exact inference is not feasible due to the complexity of the model or the abundance of data. In…
In Bayesian analysis, the posterior follows from the data and a choice of a prior and a likelihood. One hopes that the posterior is robust to reasonable variation in the choice of prior and likelihood, since this choice is made by the…
We introduce the concept of conjugate prior models for a given likelihood function in Bayesian spatial inversion. The conjugate class of prior models can be selection extended and still remain conjugate. We demonstrate the generality of…
Bayesian neural networks (BNNs) hold great promise as a flexible and principled solution to deal with uncertainty when learning from finite data. Among approaches to realize probabilistic inference in deep neural networks, variational Bayes…
Bayesian predictive inference propagates parameter uncertainty to quantities of interest through the posterior-predictive distribution. In practice, this is typically performed using a two-stage procedure: first approximating the posterior…
We develop a version of variational inference for Bayesian count response regression-type models that possesses attractive attributes such as convexity and closed form updates. The convex solution aspect entails numerically stable fitting…