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Changes in the statistical properties of a stochastic process are typically assumed to occur via change-points, which demark instantaneous moments of complete and total change in process behavior. In cases where these transitions occur…
The linear fractional stable motion generalizes two prominent classes of stochastic processes, namely stable L\'evy processes, and fractional Brownian motion. For this reason it may be regarded as a basic building block for continuous time…
In this paper, we consider the data-driven discovery of stable dynamical models with a single equilibrium. The proposed approach uses a basis-function parameterization of the differential equations and the associated Lyapunov function. This…
This work proposes a detectability condition for linear time-varying systems based on the exponential dichotomy spectrum. The condition guarantees the existence of an observer, whose gain is determined only by the unstable modes of the…
Network models have been popular for modeling and representing complex relationships and dependencies between observed variables. When data comes from a dynamic stochastic process, a single static network model cannot adequately capture…
The question of how to incorporate curvature information in stochastic approximation methods is challenging. The direct application of classical quasi- Newton updating techniques for deterministic optimization leads to noisy curvature…
A wide variety of physical systems ranging from the firing of neurons to eutrophication of lakes to the presence of Arctic summer sea ice exhibit a phenomenon known as tipping. In mathematical models, tipping can be caused by bifurcations,…
In this paper we propose a new parameter estimator that ensures global exponential convergence of linear regression models requiring only the necessary assumption of identifiability of the regression equation,which we show is equivalent to…
The parameter convergence relies on a stringent persistent excitation (PE) condition in adaptive control. Several works have proposed a memory term in the last decade to translate the PE condition to a feasible finite excitation (FE)…
Nonlinear regression is a useful statistical tool, relating observed data and a nonlinear function of unknown parameters. When the parameter-dependent nonlinear function is computationally intensive, a straightforward regression analysis by…
Extracting the spectral representations of the neural processes that underlie spiking activity is key to understanding how the brain rhythms mediate cognitive functions. While spectral estimation of continuous time-series is well studied,…
In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially…
Discrete-state, continuous-time Markov models are widely used in the modeling of biochemical reaction networks. Their complexity often precludes analytic solution, and we rely on stochastic simulation algorithms to estimate system…
It is nontrivial to achieve exponential stability even for time-invariant nonlinear systems with matched uncertainties and persistent excitation (PE) condition. In this paper, without the need for PE condition, we address the problem of…
An adaptive observer is designed for online estimation of Hilbert-Schmidt operators from online measurement of the state for some class of nonlinear infinite-dimensional dynamical systems. Convergence is ensured under detectability and…
Four decades after their invention, quasi-Newton methods are still state of the art in unconstrained numerical optimization. Although not usually interpreted thus, these are learning algorithms that fit a local quadratic approximation to…
In this paper we investigate quasi-stationary distributions {\mu}_N of stochastic approximation algorithms with constant step size which can be viewed as random perturbations of a time-continuous dynamical system. Inspired by ecological…
We introduce a novel approach based on stochastic optimization to find the optimal sampling distribution for the data-driven stability analysis of switched linear systems. Our goal is to address limitations of existing approaches, in…
The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…
Surprise-based learning allows agents to rapidly adapt to non-stationary stochastic environments characterized by sudden changes. We show that exact Bayesian inference in a hierarchical model gives rise to a surprise-modulated trade-off…