Related papers: Understanding and Accelerating Particle-Based Vari…

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…

We study a mean-field spike and slab variational Bayes (VB) approximation to Bayesian model selection priors in sparse high-dimensional linear regression. Under compatibility conditions on the design matrix, oracle inequalities are derived…

Deep learning has revolutionized the last decade, being at the forefront of extraordinary advances in a wide range of tasks including computer vision, natural language processing, and reinforcement learning, to name but a few. However, it…

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…

In this paper we propose a wavelet-based methodology for estimation and variable selection in partially linear models. The inference is conducted in the wavelet domain, which provides a sparse and localized decomposition appropriate for…

This paper presents a novel algorithm, the particle-based, rapid incremental smoother (PaRIS), for efficient online approximation of smoothed expectations of additive state functionals in general hidden Markov models. The algorithm, which…

Semi-implicit variational inference (SIVI) has been introduced to expand the analytical variational families by defining expressive semi-implicit distributions in a hierarchical manner. However, the single-layer architecture commonly used…

Leveraging on recent advancements on adaptive methods for convex minimization problems, this paper provides a linesearch-free proximal gradient framework for globalizing the convergence of popular stepsize choices such as Barzilai-Borwein…

We present a Bayesian methodology for infinite as well as finite dimensional parameter identification for partial differential equation models. The Bayesian framework provides a rigorous mathematical framework for incorporating prior…

When the likelihood is analytically unavailable and computationally intractable, approximate Bayesian computation (ABC) has emerged as a widely used methodology for approximate posterior inference; however, it suffers from severe…

Hypervolume improvement (HVI) is commonly employed in multi-objective Bayesian optimization algorithms to define acquisition functions due to its Pareto-compliant property. Rather than focusing on specific statistical moments of HVI, this…

Traditional partial differential equations with constant coefficients often struggle to capture abrupt changes in real-world phenomena, leading to the development of variable coefficient PDEs and Markovian switching models. Recently,…

Capturing data from dynamic processes through cross-sectional measurements is seen in many fields, such as computational biology. Trajectory inference deals with the challenge of reconstructing continuous processes from such observations.…

In recent years, Full-Waveform Inversion (FWI) has been extensively used to derive high-resolution subsurface velocity models from seismic data. However, due to the nonlinearity and ill-posed nature of the problem, FWI requires a good…

Variational inference approximates the posterior distribution of a probabilistic model with a parameterized density by maximizing a lower bound for the model evidence. Modern solutions fit a flexible approximation with stochastic gradient…

Variational regression methods are an increasingly popular tool for their efficient estimation of complex. Given the mixed model representation of penalized effects, additive regression models with smoothed effects and scalar-on-function…

Recently, Stochastic Variational Inference (SVI) has been increasingly attractive thanks to its ability to find good posterior approximations of probabilistic models. It optimizes the variational objective with stochastic optimization,…

Bayesian inference can be embedded into an appropriately defined dynamics in the space of probability measures. In this paper, we take Brownian motion and its associated Fokker--Planck equation as a starting point for such embeddings and…

This paper studies the optimization of the KL functional on the Wasserstein space of probability measures, and develops a sampling framework based on Wasserstein gradient descent (WGD). We identify two important subclasses of the…

Variational methods are employed in situations where exact Bayesian inference becomes intractable due to the difficulty in performing certain integrals. Typically, variational methods postulate a tractable posterior and formulate a lower…