Related papers: Time varying regression with hidden linear dynamic…
Nonlinear dynamic models are widely used for characterizing functional forms of processes that govern complex biological pathway systems. Over the past decade, validation and further development of these models became possible due to data…
We study filtering of multiscale dynamical systems with model error arising from unresolved smaller scale processes. The analysis assumes continuous-time noisy observations of all components of the slow variables alone. For a linear model…
Stochastic processes have found numerous applications in science, as they are broadly used to model a variety of natural phenomena. Due to their intrinsic randomness and uncertainty, they are, however, difficult to characterize. Here, we…
In this paper, a systematic approach is developed to embed the dynamical description of a nonlinear system into a linear parameter-varying (LPV) system representation. Initially, the nonlinear functions in the model representation are…
Classical optimization theory deals with fixed, time-invariant objective functions. However, time-varying optimization has emerged as an important subject for decision-making in dynamic environments. In this work, we study the problem of…
Identifying a linear system model from data has wide applications in control theory. The existing work on finite sample analysis for linear system identification typically uses data from a single system trajectory under i.i.d random inputs,…
The paper investigates the problem of estimating the state of a time-varying system with a linear measurement model; in particular, the paper considers the case where the number of measurements available can be smaller than the number of…
The Expectation-Maximization (EM) algorithm is a popular choice for learning latent variable models. Variants of the EM have been initially introduced, using incremental updates to scale to large datasets, and using Monte Carlo (MC)…
In the present work, a simple algorithm for stabilizing an unknown linear time-invariant system is proposed, assuming only that this system is stabilizable. The suggested algorithm is based on first performing a partial identification of…
Temporal non-stationarity, the phenomenon that time series distributions change over time, poses fundamental challenges to reliable time series forecasting. Intuitively, the complex time series can be decomposed into two factors, \ie…
For the last two decades, high-dimensional data and methods have proliferated throughout the literature. Yet, the classical technique of linear regression has not lost its usefulness in applications. In fact, many high-dimensional…
Data taken from observations of the natural world or laboratory measurements often depend on parameters which can vary in unexpected ways. In this paper we demonstrate how machine learning can be leveraged to detect changes in global…
Empirical modelling often aims for the simplest model consistent with the data. A new technique is presented which quantifies the consistency of the model dynamics as a function of location in state space. As is well-known, traditional…
We study a linear observation model with an unknown permutation called \textit{permuted/shuffled linear regression}, where responses and covariates are mismatched and the permutation forms a discrete, factorial-size parameter. The…
Time-varying parameter (TVP) models often assume that the TVPs evolve according to a random walk. This assumption, however, might be questionable since it implies that coefficients change smoothly and in an unbounded manner. In this paper,…
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…
In this work we introduce a new framework for performing temporal predictions in the presence of uncertainty. It is based on a simple idea of disentangling components of the future state which are predictable from those which are inherently…
This work proposes an algorithmic framework to learn time-varying graphs from online data. The generality offered by the framework renders it model-independent, i.e., it can be theoretically analyzed in its abstract formulation and then…
We introduce and study a variational framework for the analysis of empirical risk based inference for dynamical systems and ergodic processes. The analysis applies to a two-stage estimation procedure in which (i) the trajectory of an…
Dynamical modelling lies at the heart of our understanding of physical systems. Its role in science is deeper than mere operational forecasting, in that it allows us to evaluate the adequacy of the mathematical structure of our models.…