Related papers: Global Stationary Phase and the Sign Problem
This paper deals with the resolution of inverse problems in a periodic setting or, in other terms, the reconstruction of periodic continuous-domain signals from their noisy measurements. We focus on two reconstruction paradigms: variational…
The problems of optimally estimating a phase, a direction, and the orientation of a Cartesian frame (or trihedron) with general pure states are addressed. Special emphasis is put on estimation schemes that allow for inconclusive answers or…
The paper provides global optimization algorithms for two particularly difficult nonconvex problems raised by hybrid system identification: switching linear regression and bounded-error estimation. While most works focus on local…
This paper presents a numerical approach to the stochastic obstacle problem using the stochastic Galerkin (SG) method. Due to the low regularity of the solution, linear finite elements are employed in both the physical and random variable…
This paper presents an algorithmic framework for solving unconstrained stochastic optimization problems using only stochastic function evaluations. We employ central finite-difference based gradient estimation methods to approximate the…
Phase retrieval arises in various fields of science and engineering and it is well studied in a finite-dimensional setting. In this paper, we consider an infinite-dimensional phase retrieval problem to reconstruct real-valued signals living…
In this paper we consider the following real-valued and finite dimensional specific instance of the 1-D classical phase retrieval problem. Let ${\bf F}\in\mathbb{R}^N$ be an $N$-dimensional vector, whose discrete Fourier transform has a…
Distribution Regression on path-space refers to the task of learning functions mapping the law of a stochastic process to a scalar target. The learning procedure based on the notion of path-signature, i.e. a classical transform from rough…
Phase-space representations based on coherent states (P, Q, Wigner) have been successful in the creation of stochastic differential equations (SDEs) for the efficient stochastic simulation of high dimensional quantum systems. However many…
Generalized additive index models (GAIMs) offer a flexible semiparametric framework for capturing complex data relationships, balancing the interpretability of parametric models with the flexibility of nonparametric approaches. However,…
Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a…
We propose a simple, statistically principled, and theoretically justified method to improve supervised learning when the training set is not representative, a situation known as covariate shift. We build upon a well-established methodology…
In this article a new algorithm for the design of stationary input sequences for system identification is presented. The stationary input signal is generated by optimizing an approximation of a scalar function of the information matrix,…
In this paper, a local-global model reduction method is presented to solve stochastic optimal control problems governed by partial differential equations (PDEs). If the optimal control problems involve uncertainty, we need to use a few…
We develop a provably efficient importance sampling scheme that estimates exit probabilities of solutions to small-noise stochastic reaction-diffusion equations from scaled neighborhoods of a stable equilibrium. The moderate deviation…
This paper proposes a symbolic-numeric Bayesian filtering method for a class of discrete-time nonlinear stochastic systems to achieve high accuracy with a relatively small online computational cost. The proposed method is based on the…
Formulating the intended behavior of a dynamic system can be challenging. Signal temporal logic (STL) is frequently used for this purpose due to its suitability in formalizing comprehensible, modular, and versatile spatiotemporal…
A wider selection of step sizes is explored for the distributed subgradient algorithm for multi-agent optimization problems, for both time-invariant and time-varying communication topologies. The square summable requirement of the step…
The increased use of low-cost gyroscopes within inertial sensors for navigation purposes, among others, has brought to the development of a considerable amount of research in improving their measurement precision. Aside from developing…
Given a functional for a one-dimensional physical system, a classical problem is to minimize it by finding stationary solutions and then checking the positive definiteness of the second variation. Establishing the positive definiteness is,…