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We introduce Group Spike-and-slab Variational Bayes (GSVB), a scalable method for group sparse regression. A fast co-ordinate ascent variational inference (CAVI) algorithm is developed for several common model families including Gaussian,…
Wasserstein Gradient Flow (WGF) describes the gradient dynamics of probability density within the Wasserstein space. WGF provides a promising approach for conducting optimization over the probability distributions. Numerically approximating…
Mean field games (MFGs) model interactions in large-population multi-agent systems through population distributions. Traditional learning methods for MFGs are based on fixed-point iteration (FPI), where policy updates and induced population…
The Gaussian function (GF) is widely used to explain the behavior or statistical distribution of many natural phenomena as well as industrial processes in different disciplines of engineering and applied science. For example, the GF can be…
Many machine learning problems can be seen as approximating a \textit{target} distribution using a \textit{particle} distribution by minimizing their statistical discrepancy. Wasserstein Gradient Flow can move particles along a path that…
The Stein Variational Gradient Descent (SVGD) algorithm is a deterministic particle method for sampling. However, a mean-field analysis reveals that the gradient flow corresponding to the SVGD algorithm (i.e., the Stein Variational Gradient…
We propose in this work RBM-SVGD, a stochastic version of Stein Variational Gradient Descent (SVGD) method for efficiently sampling from a given probability measure and thus useful for Bayesian inference. The method is to apply the Random…
Gaussian processes (GPs) are a powerful tool for probabilistic inference over functions. They have been applied to both regression and non-linear dimensionality reduction, and offer desirable properties such as uncertainty estimates,…
In the gravitational-wave analysis of pulsar-timing-array datasets, parameter estimation is usually performed using Markov Chain Monte Carlo methods to explore posterior probability densities. We introduce an alternative procedure that…
We consider in this work a system of two stochastic differential equations named the perturbed compositional gradient flow. By introducing a separation of fast and slow scales of the two equations, we show that the limit of the slow motion…
Gaussian Process (GP) models are a powerful tool in probabilistic machine learning with a solid theoretical foundation. Thanks to current advances, modeling complex data with GPs is becoming increasingly feasible, which makes them an…
This article details a novel numerical scheme to approximate gradient flows for optimal transport (i.e. Wasserstein) metrics. These flows have proved useful to tackle theoretically and numerically non-linear diffusion equations that model…
Natural-gradient methods enable fast and simple algorithms for variational inference, but due to computational difficulties, their use is mostly limited to \emph{minimal} exponential-family (EF) approximations. In this paper, we extend…
We introduce a new scalable approximation for Gaussian processes with provable guarantees which hold simultaneously over its entire parameter space. Our approximation is obtained from an improved sample complexity analysis for sparse…
A computational method based on the non-linear Gaussian process (GP), known as deep Gaussian processes (deep GPs) for uncertainty quantification & propagation in modelling of flow through heterogeneous porous media is presented. The method…
The renormalization group plays an essential role in many areas of physics, both conceptually and as a practical tool to determine the long-distance low-energy properties of many systems on the one hand and on the other hand search for…
Stochastic variational inference offers an attractive option as a default method for differentiable probabilistic programming. However, the performance of the variational approach depends on the choice of an appropriate variational family.…
Gaussian processes are a powerful framework for quantifying uncertainty and for sequential decision-making but are limited by the requirement of solving linear systems. In general, this has a cubic cost in dataset size and is sensitive to…
Implicit particle filtering is a sequential Monte Carlo method for data assim- ilation, designed to keep the number of particles manageable by focussing attention on regions of large probability. These regions are found by min- imizing, for…
Approximate inference in high-dimensional, discrete probabilistic models is a central problem in computational statistics and machine learning. This paper describes discrete particle variational inference (DPVI), a new approach that…