Related papers: A Widely Linear Complex Autoregressive Process of …

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the properties are (approximately) constant for some time and then slowly start…

We establish a general form of explicit, input-dependent, measure-valued warpings for learning nonstationary kernels. While stationary kernels are ubiquitous and simple to use, they struggle to adapt to functions that vary in smoothness…

This paper considers regression tasks involving high-dimensional multivariate processes whose structure is dependent on some {known} graph topology. We put forth a new definition of time-vertex wide-sense stationarity, or joint stationarity…

Stationary processes have been extensively studied in the literature. Their applications include modeling and forecasting numerous real life phenomena such as natural disasters, sales and market movements. When stationary processes are…

We introduce and explore a new class of stationary time series models for variance matrices based on a constructive definition exploiting inverse Wishart distribution theory. The main class of models explored is a novel class of stationary,…

The concept of a random process has been recently extended to graph signals, whereby random graph processes are a class of multivariate stochastic processes whose coefficients are matrices with a \textit{graph-topological} structure. The…

We introduce computational methods that allow for effective estimation of a flexible, parametric non-stationary spatial model when the field size is too large to compute the multivariate normal likelihood directly. In this method, the field…

It is by now established that, remarkably, the addition of noise to a nonlinear system may sometimes facilitate, rather than hamper the detection of weak signals. This phenomenon, usually referred to as stochastic resonance, was originally…

Nonlinear systems are capable of displaying complex behavior even if this is the result of a small number of interacting time scales. A widely studied case is when complex dynamics emerges out of a nonlinear system being forced by a simple…

In a wide range of applications, the stochastic properties of the observed time series change over time. The changes often occur gradually rather than abruptly: the prop- erties are (approximately) constant for some time and then slowly…

We study dynamical reversibility in stationary stochastic processes from an information theoretic perspective. Extending earlier work on the reversibility of Markov chains, we focus on finitary processes with arbitrarily long conditional…

An empirical algorithm is used here to study the stochastic and multifractal nature of nonlinear time series. A parameter can be defined to quantitatively measure the deviation of the time series from a Wiener process so that the…

The stochastic properties of a Langevin-type Markov process can be extracted from a given time series by a Markov analysis. Also processes that obey a stochastically forced second order differential equation can be analyzed this way by…

We propose a new structure for the complex-valued autoencoder by introducing additional degrees of freedom into its design through a widely linear (WL) transform. The corresponding widely linear backpropagation algorithm is also developed…

We develop an estimator for the high-dimensional covariance matrix of a locally stationary process with a smoothly varying trend and use this statistic to derive consistent predictors in non-stationary time series. In contrast to the…

Linear autoregressive models serve as basic representations of discrete time stochastic processes. Different attempts have been made to provide non-linear versions of the basic autoregressive process, including different versions based on…

Autoregressive models are widely used for tasks such as image and audio generation. The sampling process of these models, however, does not allow interruptions and cannot adapt to real-time computational resources. This challenge impedes…

We consider a stationary process (with either discrete or continuous time) and find an adaptive approximating stationary process combining approximation quality and supplementary good properties that can be interpreted as additional…

We derive a parallel sampling algorithm for computational inverse problems that present an unknown linear forcing term and a vector of nonlinear parameters to be recovered. It is assumed that the data is noisy and that the linear part of…

Nonsinusoidal oscillatory signals are everywhere. In practice, the nonsinusoidal oscillatory pattern, modeled as a 1-periodic wave-shape function (WSF), might vary from cycle to cycle. When there are finite different WSFs, $s_1,\ldots,s_K$,…