Related papers: Derivation of the Variational Bayes Equations
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
This note is concerned with an accurate and computationally efficient variational bayesian treatment of mixed-effects modelling. We focus on group studies, i.e. empirical studies that report multiple measurements acquired in multiple…
Inference, prediction and control of complex dynamical systems from time series is important in many areas, including financial markets, power grid management, climate and weather modeling, or molecular dynamics. The analysis of such highly…
The use of sophisticated machine learning models for critical decision making is faced with a challenge that these models are often applied as a "black-box". This has led to an increased interest in interpretable machine learning, where…
Variational Bayes (VB) is a critical method in machine learning and statistics, underpinning the recent success of Bayesian deep learning. The natural gradient is an essential component of efficient VB estimation, but it is prohibitively…
In this paper we present applications of methods from wavelet analysis to polynomial approximations for a number of accelerator physics problems. According to variational approach in the general case we have the solution as a…
Bayesian causal discovery benefits from prior information elicited from domain experts, and in heterogeneous domains any prior knowledge would be badly needed. However, so far prior elicitation approaches have assumed a single causal graph…
Bayesian hierarchical linear models provide a natural framework to analyze nested and clustered data. Classical estimation with Markov chain Monte Carlo produces well calibrated posterior distributions but becomes computationally expensive…
Macroscopic equations arising out of stochastic particle systems in detailed balance (called dissipative systems or gradient flows) have a natural variational structure, which can be derived from the large-deviation rate functional for the…
The advances in variational inference are providing promising paths in Bayesian estimation problems. These advances make variational phylogenetic inference an alternative approach to Markov Chain Monte Carlo methods for approximating the…
This paper proposes various new analysis techniques for Bayes networks in which conditional probability tables (CPTs) may contain symbolic variables. The key idea is to exploit scalable and powerful techniques for synthesis problems in…
We consider the applications of a numerical-analytical approach based on multiscale variational wavelet technique to the systems with collective type behaviour described by some forms of Vlasov-Poisson/Maxwell equations. We calculate the…
We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to…
Approximate inference in Bayesian deep networks exhibits a dilemma of how to yield high fidelity posterior approximations while maintaining computational efficiency and scalability. We tackle this challenge by introducing a novel…
This paper develops a Bayesian mechanics for adaptive systems. Firstly, we model the interface between a system and its environment with a Markov blanket. This affords conditions under which states internal to the blanket encode information…
Hawkes processes are often applied to model dependence and interaction phenomena in multivariate event data sets, such as neuronal spike trains, social interactions, and financial transactions. In the nonparametric setting, learning the…
A common impediment in conducting inference for Bayesian nonparametric models is either the need for complex MCMC algorithms and/or computational run-time for large datasets. We propose solutions here for Enriched Dirichlet process mixtures…
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…
In this paper, we consider a generalization of variational calculus which allows us to consider in the same framework different cases of mechanical systems, for instance, Lagrangian mechanics, Hamiltonian mechanics, systems subjected to…
Variational inference uses optimization, rather than integration, to approximate the marginal likelihood, and thereby the posterior, in a Bayesian model. Thanks to advances in computational scalability made in the last decade, variational…