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The current quantum resource theory for Gaussian steering for continuous-variable systems is flawed and incomplete. Its primary shortcoming stems from an inadequate comprehension of the architecture of Gaussian channels transforming…
We suggest that the tools of contraction analysis for deterministic systems can be applied towards studying the convergence behavior of stochastic dynamical systems in the Wasserstein metric. In particular, we consider the case of Ito…
This paper introduces Wasserstein variational inference, a new form of approximate Bayesian inference based on optimal transport theory. Wasserstein variational inference uses a new family of divergences that includes both f-divergences and…
We study data-driven decision problems where historical observations are generated by a time-evolving distribution whose consecutive shifts are bounded in Wasserstein distance. We address this nonstationarity using a distributionally robust…
In this paper, we consider queueing systems where the dynamics are non-stationary and state-dependent. For performance analysis of these systems, fluid and diffusion models have been typically used. Although they are proven to be…
The problem of measuring the best linear approximation of a nonlinear system by means of multilevel excitation sequences is analyzed. A comparison between different types of sequences applied at the input of Wiener systems is provided by…
High-precision measurements require optimal setups and analysis tools to achieve continuous improvements. Systematic corrections need to be modeled with high accuracy and known uncertainty to reconstruct underlying physical phenomena. To…
We study the Wasserstein natural gradient in parametric statistical models with continuous sample spaces. Our approach is to pull back the $L^2$-Wasserstein metric tensor in the probability density space to a parameter space, equipping the…
We investigate barycenters of Gaussian process laws in adapted Wasserstein space. The adapted Wasserstein distance refines classical optimal transport by enforcing compatibility of transport plans with the temporal flow of information, and…
Distribution data refers to a data set where each sample is represented as a probability distribution, a subject area receiving burgeoning interest in the field of statistics. Although several studies have developed…
Bayesian optimization is a class of global optimization techniques. In Bayesian optimization, the underlying objective function is modeled as a realization of a Gaussian process. Although the Gaussian process assumption implies a random…
In this paper, a risk-aware motion control scheme is considered for mobile robots to avoid randomly moving obstacles when the true probability distribution of uncertainty is unknown. We propose a novel model predictive control (MPC) method…
Advances in experimental techniques allow the collection of high-resolution spatio-temporal data that track individual motile entities. These tracking data can be used to calibrate mathematical models describing the motility of individual…
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 present a novel approach to approximate Gaussian and mixture-of-Gaussians filtering. Our method relies on a variational approximation via a gradient-flow representation. The gradient flow is derived from a Kullback--Leibler discrepancy…
We study sparse optimal control of a non-local continuity equation, where the goal is to steer a distribution via finitely many controllable agents or actuators. This model arises naturally in mean-field multi-agent systems and takes the…
In this work, a versatile mathematical framework for multi-state probabilistic modeling of Resistive Switching (RS) devices is proposed for the first time. The mathematical formulation of memristor and Markov jump processes are combined…
Conditional distribution is a fundamental quantity for describing the relationship between a response and a predictor. We propose a Wasserstein generative approach to learning a conditional distribution. The proposed approach uses a…
Many time series can be modeled as a sequence of segments representing high-level discrete states, such as running and walking in a human activity application. Flexible models should describe the system state and observations in stationary…
We propose a Gaussian variational inference framework for the motion planning problem. In this framework, motion planning is formulated as an optimization over the distribution of the trajectories to approximate the desired trajectory…