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We develop unbiased implicit variational inference (UIVI), a method that expands the applicability of variational inference by defining an expressive variational family. UIVI considers an implicit variational distribution obtained in a…
A Bayesian approach to the classification problem is proposed in which random partitions play a central role. It is argued that the partitioning approach has the capacity to take advantage of a variety of large-scale spatial structures, if…
Online optimization has gained increasing interest due to its capability of tracking real-world streaming data. Although online optimization methods have been widely studied in the setting of frequentist statistics, few works have…
Markov Chain Monte Carlo (MCMC) sampling is computationally expensive, especially for complex models. Alternative methods make simplifying assumptions about the posterior to reduce computational burden, but their impact on predictive…
Bayesian inference for Markov processes has become increasingly relevant in recent years. Problems of this type often have intractable likelihoods and prior knowledge about model rate parameters is often poor. Markov Chain Monte Carlo…
Variational Bayesian (VB) methods produce posterior inference in a time frame considerably smaller than traditional Markov Chain Monte Carlo approaches. Although the VB posterior is an approximation, it has been shown to produce good…
Hierarchical models represent a challenging setting for inference algorithms. MCMC methods struggle to scale to large models with many local variables and observations, and variational inference (VI) may fail to provide accurate…
Semi-implicit variational inference (SIVI) extends traditional variational families with semi-implicit distributions defined in a hierarchical manner. Due to the intractable densities of semi-implicit distributions, classical SIVI often…
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…
We develop a method to combine Markov chain Monte Carlo (MCMC) and variational inference (VI), leveraging the advantages of both inference approaches. Specifically, we improve the variational distribution by running a few MCMC steps. To…
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.…
Probabilistic state estimation is essential for robots navigating uncertain environments. Accurately and efficiently managing uncertainty in estimated states is key to robust robotic operation. However, nonlinearities in robotic platforms…
Variational Bayes (VB) provides a computationally efficient alternative to Markov Chain Monte Carlo, especially for high-dimensional and large-scale inference. However, existing theory on VB primarily focuses on fixed-dimensional settings…
We introduce TrustVI, a fast second-order algorithm for black-box variational inference based on trust-region optimization and the reparameterization trick. At each iteration, TrustVI proposes and assesses a step based on minibatches of…
Variational inference (VI) is a technique to approximate difficult to compute posteriors by optimization. In contrast to MCMC, VI scales to many observations. In the case of complex posteriors, however, state-of-the-art VI approaches often…
Stochastic Natural Gradient Variational Inference (NGVI) is a widely used method for approximating posterior distribution in probabilistic models. Despite its empirical success and foundational role in variational inference, its theoretical…
Variational Bayes (VB) is a recent approximate method for Bayesian inference. It has the merit of being a fast and scalable alternative to Markov Chain Monte Carlo (MCMC) but its approximation error is often unknown. In this paper, we…
The vanishing ideal of a set of points $X = \{\mathbf{x}_1, \ldots, \mathbf{x}_m\}\subseteq \mathbb{R}^n$ is the set of polynomials that evaluate to $0$ over all points $\mathbf{x} \in X$ and admits an efficient representation by a finite…
Improving the robustness of neural nets in regression tasks is key to their application in multiple domains. Deep learning-based approaches aim to achieve this goal either by improving their prediction of specific values (i.e., point…
We introduce a class of algorithms, termed proximal interacting particle Langevin algorithms (PIPLA), for inference and learning in latent variable models whose joint probability density is non-differentiable. Leveraging proximal Markov…