Related papers: Statistical Inference for Bures-Wasserstein Flows
Bayesian posterior inference is prevalent in various machine learning problems. Variational inference provides one way to approximate the posterior distribution, however its expressive power is limited and so is the accuracy of resulting…
Time warping function provides a mathematical representation to measure phase variability in functional data. Recent studies have developed various approaches to estimate optimal warping between functions and provide non-Euclidean models.…
Many studies have been conducted on flows of probability measures, often in terms of gradient flows. We utilize a generalized notion of derivatives with respect to time to model the instantaneous evolution of empirically observed…
We address the challenge of conducting inference for a categorical treatment effect related to a binary outcome variable while taking into account high-dimensional baseline covariates. The conventional technique used to establish…
A method for sequential Bayesian inference of the static parameters of a dynamic state space model is proposed. The method is based on the observation that many dynamic state space models have a relatively small number of static parameters…
The geometry of dynamical systems estimated from trajectory data is a major challenge for machine learning applications. Koopman and transfer operators provide a linear representation of nonlinear dynamics through their spectral…
The Riemannian geometry of covariance matrices has been essential to several successful applications, in computer vision, biomedical signal and image processing, and radar data processing. For these applications, an important ongoing…
This paper develops a rigorous probabilistic framework that extends denoising diffusion models to the setting of noncommutative random variables. Building on Voiculescu's theory of free entropy and free Fisher information, we formulate…
We observe two sequences of curve which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during…
I shortly describe the main results on elastically driven instabilities and elastic turbulence in viscoelastic inertia-less flows with curved streamlines. Then I describe a theory of elastic turbulence and prediction of elastic waves at…
The Bayesian approach to inverse problems is widely used in practice to infer unknown parameters from noisy observations. In this framework, the ensemble Kalman inversion has been successfully applied for the quantification of uncertainties…
Linear regression on network-linked observations has been an essential tool in modeling the relationship between response and covariates with additional network structures. Previous methods either lack inference tools or rely on restrictive…
We propose inferential tools for functional linear quantile regression where the conditional quantile of a scalar response is assumed to be a linear functional of a functional covariate. In contrast to conventional approaches, we employ…
Motivated by recent work involving the analysis of leveraging spatial correlations in sparsified mean estimation, we present a novel procedure for constructing covariance estimator. The proposed Random-knots (Random-knots-Spatial) and…
We study how sampling geometry contributes to uncertainty in modeling spatial geophysical observations as sampled random fields characterized by stationary, isotropic, parametric covariance functions. We incorporate the signature of…
We consider estimation of mean and covariance functions of functional snippets, which are short segments of functions possibly observed irregularly on an individual specific subinterval that is much shorter than the entire study interval.…
We introduce a class of stochastic advection problems amenable to analysis of turbulent transport. The statistics of the flow field are represented as a continuous time Markov process, a choice that captures the intuitive notion of…
For continuous-time linear stochastic dynamical systems driven by Wiener processes, we consider the problem of designing ensemble filters when the observation process is randomly time-sampled. We propose a continuous-discrete McKean--Vlasov…
Statistical models are an essential tool to model, forecast and understand the hydrological processes in watersheds. In particular, the understanding of time lags associated with the delay between rainfall occurrence and subsequent changes…
We consider a class of time-homogeneous diffusion processes on $\mathbb{R}^{n}$ with common invariant measure but varying volatility matrices. In Euclidean space, we show via stochastic control of the diffusion coefficient that the…