相关论文: Optimal Switching Synthesis for Jump Linear System…
Dynamic scene rendering has taken a leap forward with the rise of 4D Gaussian Splatting, but there's still one elusive challenge: how to make 3D Gaussians move through time as naturally as they would in the real world, all while keeping the…
The theory of optimal transport of probability measures has wide-ranging applications across a number of different fields, including concentration of measure, machine learning, Markov chains, and economics. The generalisation of optimal…
As a natural approach to modeling system safety conditions, chance constraint (CC) seeks to satisfy a set of uncertain inequalities individually or jointly with high probability. Although a joint CC offers stronger reliability certificate,…
Change point detection for time series analysis is a difficult and important problem in applied statistics, for which a variety of approaches have been developed in the past several decades. Here, the Wasserstein metric is employed as a…
Statistical inference for time series such as curve estimation for time-varying models or testing for existence of change-point have garnered significant attention. However, these works are generally restricted to the assumption of…
We present a framework for obtaining explicit bounds on the rate of convergence to equilibrium of a Markov chain on a general state space, with respect to both total variation and Wasserstein distances. For Wasserstein bounds, our main tool…
We propose a machine learning framework for parameter estimation of single mode Gaussian quantum states. Under a Bayesian framework, our approach estimates parameters of suitable prior distributions from measured data. For phase-space…
We consider the problem of detecting jumps in an otherwise smoothly evolving trend whilst the covariance and higher-order structures of the system can experience both smooth and abrupt changes over time. The number of jump points is allowed…
We investigate the problem of synthesizing distributionally robust control policies for stochastic systems under safety and reach-avoid specifications. Using a game-theoretical framework, we consider the setting where the probability…
Stochastic optimal control usually requires an explicit dynamical model with probability distributions, which are difficult to obtain in practice. In this work, we consider the linear quadratic regulator (LQR) problem of unknown linear…
Model Updating is frequently used in Structural Health Monitoring to determine structures' operating conditions and whether maintenance is required. Data collected by sensors are used to update the values of some initially unknown…
Non-Gaussian noise influences many complex out-of-equilibrium systems on a wide range of scales such as quantum devices, active and living matter, and financial markets. Despite the ubiquitous nature of non-Gaussian noise, its effect on…
Switching dynamical systems provide a powerful, interpretable modeling framework for inference in time-series data in, e.g., the natural sciences or engineering applications. Since many areas, such as biology or discrete-event systems, are…
This paper presents the jump law of co-states in optimal control for state-dependent switched systems. The number of switches and the switching modes are assumed to be known a priori. A proposed jump law is rigorously derived by theoretical…
We study nonparametric density estimation problems where error is measured in the Wasserstein distance, a metric on probability distributions popular in many areas of statistics and machine learning. We give the first minimax-optimal rates…
We propose an open loop methodology based on sample statistics to solve chance constrained stochastic optimal control problems with probabilistic safety guarantees for linear systems where the additive Gaussian noise has unknown mean and…
A linear Gaussian state-space smoothing algorithm is presented for estimation of derivatives from a sequence of noisy measurements. The algorithm uses numerically stable square-root formulas, can handle simultaneous independent measurements…
State estimation allows to monitor power networks, exploiting field measurements to derive the most likely grid state. In the literature, measurement errors are usually assumed to follow zero-mean Gaussian distributions; however, it has…
Gaussian mixture models form a flexible and expressive parametric family of distributions that has found applications in a wide variety of applications. Unfortunately, fitting these models to data is a notoriously hard problem from a…
In this paper, we consider discrete-time non-linear stochastic dynamical systems with additive process noise in which both the initial state and noise distributions are uncertain. Our goal is to quantify how the uncertainty in these…