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Bayesian neural learning feature a rigorous approach to estimation and uncertainty quantification via the posterior distribution of weights that represent knowledge of the neural network. This not only provides point estimates of optimal…

We develop EigenVI, an eigenvalue-based approach for black-box variational inference (BBVI). EigenVI constructs its variational approximations from orthogonal function expansions. For distributions over $\mathbb{R}^D$, the lowest order term…

Inference tasks in signal processing are often characterized by the availability of reliable statistical modeling with some missing instance-specific parameters. One conventional approach uses data to estimate these missing parameters and…

Recent years have witnessed growing interest in semi-implicit variational inference (SIVI) methods due to their ability to rapidly generate samples from complex distributions. However, since the likelihood of these samples is non-trivial to…

Recent developments in generative modeling have utilized score-based methods coupled with stochastic differential equations to sample from complex probability distributions. However, these and other performant sampling methods generally…

Recent work shows that inference for Gaussian processes can be performed efficiently using iterative methods that rely only on matrix-vector multiplications (MVMs). Structured Kernel Interpolation (SKI) exploits these techniques by deriving…

Most of the fundamental, emergent, and phenomenological parameters of particle and nuclear physics are determined through parametric template fits. Simulations are used to populate histograms which are then matched to data. This approach is…

Variational methods are widely used for approximate posterior inference. However, their use is typically limited to families of distributions that enjoy particular conjugacy properties. To circumvent this limitation, we propose a family of…

We propose stepwise variational inference (VI) with vine copulas: a universal VI procedure that combines vine copulas with a novel stepwise estimation procedure of the variational parameters. Vine copulas consist of a nested sequence of…

We consider Bayesian inference problems with computationally intensive likelihood functions. We propose a Gaussian process (GP) based method to approximate the joint distribution of the unknown parameters and the data. In particular, we…

In this project, we propose a Variational Inference algorithm to approximate posterior distributions. Building on prior methods, we develop the Gradient-Steered Stein Variational Gradient Descent (G-SVGD) approach. This method introduces a…

Bayesian computational strategies for inference can be inefficient in approximating the posterior distribution in models that exhibit some form of periodicity. This is because the probability mass of the marginal posterior distribution of…

Variational inference consists in finding the best approximation of a target distribution within a certain family, where `best' means (typically) smallest Kullback-Leiber divergence. We show that, when the approximation family is…

While generative models have proved successful in many domains, they may pose a privacy leakage risk in practical deployment. To address this issue, differentially private generative model learning has emerged as a solution to train private…

Inferring parameters and testing hypotheses from gravitational wave signals is a computationally intensive task central to modern astrophysics. Nested sampling, a Bayesian inference technique, has become an established standard for this in…

Gaussian Processes (\textbf{GPs}) are flexible non-parametric models with strong probabilistic interpretation. While being a standard choice for performing inference on time series, GPs have few techniques to work in a streaming setting.…

Deep Generative Networks (DGNs) with probabilistic modeling of their output and latent space are currently trained via Variational Autoencoders (VAEs). In the absence of a known analytical form for the posterior and likelihood expectation,…

Gaussian processes (GPs) provide a probabilistic nonparametric representation of functions in regression, classification, and other problems. Unfortunately, exact learning with GPs is intractable for large datasets. A variety of approximate…

Gaussian process (GP) models form a core part of probabilistic machine learning. Considerable research effort has been made into attacking three issues with GP models: how to compute efficiently when the number of data is large; how to…

Diffusion models optimized via variational inference (VI) have emerged as a promising tool for generating samples from unnormalized target densities. These models create samples by simulating a stochastic differential equation, starting…