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We propose a recurrent neural network for a "model-free" simulation of a dynamical system with unknown parameters without prior knowledge. The deep learning model aims to jointly learn the nonlinear time marching operator and the effects of…
Recovery of the sparsity pattern (or support) of an unknown sparse vector from a small number of noisy linear measurements is an important problem in compressed sensing. In this paper, the high-dimensional setting is considered. It is shown…
Deep sequence models are receiving significant interest in current machine learning research. By representing probability distributions that are fit to data using maximum likelihood estimation, such models can model data on general…
This paper investigates gradient-based adaptive prediction and control for nonlinear stochastic dynamical systems under a weak convexity condition on the prediction-based loss. This condition accommodates a broad range of nonlinear models…
The problem of statistical learning is to construct an accurate predictor of a random variable as a function of a correlated random variable on the basis of an i.i.d. training sample from their joint distribution. Allowable predictors are…
This paper considers a simulation-based estimator for a general class of Markovian processes and explores some strong consistency properties of the estimator. The estimation problem is defined over a continuum of invariant distributions…
We consider the problem of parameter estimation in dynamic systems described by ordinary differential equations. A review of the existing literature emphasizes the need for deterministic global optimization methods due to the nonconvex…
Recurrent Neural networks (RNN) have shown promising potential for learning dynamics of sequential data. However, artificial neural networks are known to exhibit poor robustness in presence of input noise, where the sequential architecture…
We study detection methods for multivariable signals under dependent noise. The main focus is on three-dimensional signals, i.e. on signals in the space-time domain. Examples for such signals are multifaceted. They include geographic and…
Selecting the best regularization parameter in inverse problems is a classical and yet challenging problem. Recently, data-driven approaches have become popular to tackle this challenge. These approaches are appealing since they do require…
This paper considers the problem of multi-agent distributed linear regression in the presence of system noises. In this problem, the system comprises multiple agents wherein each agent locally observes a set of data points, and the agents'…
Both for the theoretical and practical treatment of Inverse Problems, the modeling of the noise is a crucial part. One either models the measurement via a deterministic worst-case error assumption or assumes a certain stochastic behavior of…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
We consider a setting, where the output of a linear dynamical system (LDS) is, with an unknown but fixed probability, replaced by noise. There, we present a robust method for the prediction of the outputs of the LDS and identification of…
This paper proposes a novel model inference procedure to identify system matrix from a single noisy trajectory over a finite-time interval. The proposed inference procedure comprises an observation data processor, a redundant data processor…
We study noise sensitivity of the consensus opinion of the voter model on finite graphs, with respect to noise affecting the initial opinions and noise affecting the dynamics. We prove that the final opinion is stable with respect to small…
Koopman operator theory has emerged as a leading data-driven approach that relies on a judicious choice of observable functions to realize global linear representations of nonlinear systems in the lifted observable space. However,…
High-dimensional time series data appear in many scientific areas in the current data-rich environment. Analysis of such data poses new challenges to data analysts because of not only the complicated dynamic dependence between the series,…
Predicting the response of nonlinear dynamical systems subject to random, broadband excitation is important across a range of scientific disciplines, such as structural dynamics and neuroscience. Building data-driven models requires…
Traditional statistical estimation, or statistical inference in general, is static, in the sense that the estimate of the quantity of interest does not change the future evolution of the quantity. In some sequential estimation problems…