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This paper considers learning the hidden causal network of a linear networked dynamical system (NDS) from the time series data at some of its nodes -- partial observability. The dynamics of the NDS are driven by colored noise that generates…
We consider signal source localization from range-difference measurements. First, we give some readily-checked conditions on measurement noises and sensor deployment to guarantee the asymptotic identifiability of the model and show the…
We use the general notion of set of indices to construct algebras of nonlinear generalized functions of Colombeau type. They are formally defined in the same way as the special Colombeau algebra, but based on more general growth condition…
This paper focuses on the problem of recursive nonlinear least squares parameter estimation in multi-agent networks, in which the individual agents observe sequentially over time an independent and identically distributed (i.i.d.)…
Ordinary differential equations (ODE) have been widely used for modeling dynamical complex systems. For high-dimensional ODE models where the number of differential equations is large, it remains challenging to estimate the ODE parameters…
This paper considers the problem of closed-loop identification of linear scalar systems with Gaussian process noise, where the system input is determined by a deterministic state feedback policy. The regularized least-square estimate (LSE)…
We study the asymptotic properties of the adaptive Lasso in cointegration regressions in the case where all covariates are weakly exogenous. We assume the number of candidate I(1) variables is sub-linear with respect to the sample size (but…
We consider the problem of asymptotic reconstruction of the state and parameter values in systems of ordinary differential equations. A solution to this problem is proposed for a class of systems of which the unknowns are allowed to be…
Consider a process satisfying a stochastic differential equation with unknown drift parameter, and suppose that discrete observations are given. It is known that a simple least squares estimator (LSE) can be consistent, but numerically…
Under distribution uncertainty, on the basis of discrete data we investigate the consistency of the least squares estimator (LSE) of the parameter for the stochastic differential equation (SDE) where the noise are characterized by…
Deep generative models offer a natural foundation for out-of-distribution (OOD) detection, yet prior work has shown that their assigned likelihoods are notoriously unreliable indicators for in- vs out-of-distribution data. In this paper, we…
Learning how complex dynamical systems evolve over time is a key challenge in system identification. For safety critical systems, it is often crucial that the learned model is guaranteed to converge to some equilibrium point. To this end,…
Two dynamical systems are topologically equivalent when their phase-portraits can be morphed into each other by a homeomorphic coordinate transformation on the state space. The induced equivalence classes capture qualitative properties such…
Neural networks are one of the most popularly used methods in machine learning and artificial intelligence nowadays. Due to the universal approximation theorem (Hornik et al. (1989)), a neural network with one hidden layer can approximate…
Differential equations are commonly used to model dynamical deterministic systems in applications. When statistical parameter estimation is required to calibrate theoretical models to data, classical statistical estimators are often…
We consider the problem of parameter estimation in a partially observed linear Gaussian system with small noises in the state and observation equations. We describe asymptotic properties of the MLE and Bayes estimators in the setting with…
We investigate the use of neural networks (NNs) for the estimation of hidden model parameters and uncertainty quantification from noisy observational data for inverse parameter estimation problems. We formulate the parameter estimation as a…
This paper addresses the data-driven identification of latent dynamical representations of partially-observed systems, i.e., dynamical systems for which some components are never observed, with an emphasis on forecasting applications,…
Ordinary Differential Equations (ODE) based models have become popular as foundation models for solving many time series problems. Combining neural ODEs with traditional RNN models has provided the best representation for irregular time…
In this article we perform an asymptotic analysis of parallel Bayesian logspline density estimators. Such estimators are useful for the analysis of datasets that are partitioned into subsets and stored in separate databases without the…