Related papers: Stochastic Optimal Prediction for the Kuramoto-Siv…
We propose a principal components regression method based on maximizing a joint pseudo-likelihood for responses and predictors. Our method uses both responses and predictors to select linear combinations of the predictors relevant for the…
The problem of estimating the constant parameters of the Kuramoto-Sivashinsky (KS) equation from observed data has received attention from researchers in physics, applied mathematics and statistics. This is motivated by the various physical…
We propose an adaptive randomized truncation estimator for Krylov subspace methods that optimizes the trade-off between the solution variance and the computational cost, while remaining unbiased. The estimator solves a constrained…
We report numerical simulations of one-dimensional cellular solutions of the stabilized Kuramoto-Sivashinsky equation. This equation offers a range of generic behavior in pattern-forming instabilities of moving interfaces, such as a host of…
Key to structured prediction is exploiting the problem structure to simplify the learning process. A major challenge arises when data exhibit a local structure (e.g., are made by "parts") that can be leveraged to better approximate the…
This paper is concerned with a class of stochastic optimization problems defined on a Banach space with almost sure conic-type constraints. For this class of problems, we investigate the consistency of optimal values and solutions…
This paper studies the sparse identification problem of unknown sparse parameter vectors in stochastic dynamic systems. Firstly, a novel sparse identification algorithm is proposed, which can generate sparse estimates based on least squares…
Nonlinear models for pattern evolution by ion beam sputtering on a material surface present an ongoing opportunity for new numerical simulations. A numerical analysis of the evolution of preexisting patterns is proposed to investigate…
We study in this paper boundary stabilization, in the L2 sense, of the perturbed Kuramoto-Sivashinsky (KS) equation subject to intermittent sensing. We assume that we measure the state on a given spatial subdomain during certain time…
Algorithm designers typically assume that the input data is correct, and then proceed to find "optimal" or "sub-optimal" solutions using this input data. However this assumption of correct data does not always hold in practice, especially…
This work establishes a general stochastic maximum principle for partially observed optimal control of semi-linear stochastic partial differential equations in a nonconvex control domain. The state evolves in a Hilbert space driven by a…
This paper develops online algorithms to track solutions of time-varying constrained optimization problems. Particularly, resembling workhorse Kalman filtering-based approaches for dynamical systems, the proposed methods involve…
This paper deals with the state prediction of nonlinear stochastic dynamic systems. The emphasis is laid on a solution to the integral Chapman-Kolmogorov equation by a deterministic-integration-rule-based point-mass method. A novel concept…
Missing value imputation is an important practical problem. There is a large body of work on it, but there does not exist any work that formulates the problem in a structured output setting. Also, most applications have constraints on the…
We address the interaction-time optimization for frequency estimation in a two-level system. The goal is to estimate with maximum precision a stochastic perturbation. Our approach is valid for any figure of merit used to define optimality,…
This paper considers an empirical likelihood inference for parameters defined by general estimating equations, when data are missing at random. The efficiency of existing estimators depends critically on correctly specifying the conditional…
We study the problem of designing optimal learning and decision-making formulations when only historical data is available. Prior work typically commits to a particular class of data-driven formulation and subsequently tries to establish…
We propose a method called ideal regression for approximating an arbitrary system of polynomial equations by a system of a particular type. Using techniques from approximate computational algebraic geometry, we show how we can solve ideal…
We study a high-dimensional regression setting under the assumption of known covariate distribution. We aim at estimating the amount of explained variation in the response by the best linear function of the covariates (the signal level). In…
In this work, we investigate an indirect approach for the numerical solution of optimal control problems via neural networks. A customized neural network is constructed, where optimal state, co-state and control trajectories are…