Related papers: An Explicit Surrogate for Gaussian Mixture Flow Ma…

Generative modeling typically concerns transporting a single source distribution to a target distribution via simple probability flows. However, in fields like computer graphics and single-cell genomics, samples themselves can be viewed as…

The mean-field theory for two-layer neural networks considers infinitely wide networks that are linearly parameterized by a probability measure over the parameter space. This nonparametric perspective has significantly advanced both the…

Flow matching has recently emerged as a promising alternative to diffusion-based generative models, offering faster sampling and simpler training by learning continuous flows governed by ordinary differential equations. Despite growing…

Existing model validation studies in geoscience often disregard or partly account for uncertainties in observations, model choices, and input parameters. In this work, we develop a statistical framework that incorporates a probabilistic…

We present an adaptive approach to the construction of Gaussian process surrogates for Bayesian inference with expensive-to-evaluate forward models. Our method relies on the fully Bayesian approach to training Gaussian process models and…

Distance measures between graphs are important primitives for a variety of learning tasks. In this work, we describe an unsupervised, optimal transport based approach to define a distance between graphs. Our idea is to derive…

The ubiquity of fluids in the physical world explains the need to accurately simulate their dynamics for many scientific and engineering applications. Traditionally, well established but resource intensive CFD solvers provide such…

The Gromov-Wasserstein distance is a notable extension of optimal transport. In contrast to the classic Wasserstein distance, it solves a quadratic assignment problem that minimizes the pair-wise distance distortion under the transportation…

Variational inference, such as the mean-field (MF) approximation, requires certain conjugacy structures for efficient computation. These can impose unnecessary restrictions on the viable prior distribution family and further constraints on…

Gaussian process surrogates are a popular alternative to directly using computationally expensive simulation models. When the simulation output consists of many responses, dimension-reduction techniques are often employed to construct these…

Engineers widely use Gaussian process regression framework to construct surrogate models aimed to replace computationally expensive physical models while exploring design space. Thanks to Gaussian process properties we can use both samples…

This paper proposes novel noise-free Bayesian optimization strategies that rely on a random exploration step to enhance the accuracy of Gaussian process surrogate models. The new algorithms retain the ease of implementation of the classical…

Slurry transportation via pipelines is essential for global industries, offering efficiency and environmental benefits. Specifically, the precise calibration of physical parameters for transporting raw phosphate material to fertilizer…

Exploring ensemble simulations is increasingly important across many scientific domains. However, supporting flexible post-hoc exploration remains challenging due to the trade-off between storing the expensive raw data and flexibly…

Gromov-Wasserstein (GW) is a powerful tool to compare probability measures whose supports are in different metric spaces. GW suffers however from a computational drawback since it requires to solve a complex non-convex quadratic program. We…

Existing methods to summarize posterior inference for mixture models focus on identifying a point estimate of the implied random partition for clustering, with density estimation as a secondary goal (Wade and Ghahramani, 2018; Dahl et al.,…

Bayesian inverse design provides a principled framework for inferring aerodynamic geometries from sparse flow observations while quantifying uncertainty. However, its practical use in computational fluid dynamics (CFD) is severely limited…

We propose a framework, named Aggregated Wasserstein, for computing a dissimilarity measure or distance between two Hidden Markov Models with state conditional distributions being Gaussian. For such HMMs, the marginal distribution at any…

We establish non-asymptotic bounds on the finite-sample behavior of generalized first-order iterative algorithms -- including gradient-based optimization methods and approximate message passing (AMP) -- with Gaussian data matrices and…

Gaussian mixture models find their place as a powerful tool, mostly in the clustering problem, but with proper preparation also in feature extraction, pattern recognition, image segmentation and in general machine learning. When faced with…