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The Gaussian process (GP) is a nonparametric prior distribution over functions indexed by time, space, or other high-dimensional index set. The GP is a flexible model yet its limitation is given by its very nature: it can only model…
A method based on wavelet transform and genetic programming is proposed for characterizing and modeling variations at multiple scales in non-stationary time series. The cyclic variations, extracted by wavelets and smoothened by cubic…
Stochastic process models for spatiotemporal data underlying random fields find substantial utility in a range of scientific disciplines. Subsequent to predictive inference on the values of the random field (or spatial surface indexed…
Theoretical studies of synchronization are usually based on models of coupled phase oscillators which, when isolated, have constant angular frequency. Stochastic discrete versions of these uniform oscillators have also appeared in the…
There are three equivalent ways of representing two jointly observed real-valued signals: as a bivariate vector signal, as a single complex-valued signal, or as two analytic signals known as the rotary components. Each representation has…
Sparse Subspace Clustering (SSC) has achieved state-of-the-art clustering quality by performing spectral clustering over a $\ell^{1}$-norm based similarity graph. However, SSC is a transductive method which does not handle with the data not…
The long time effect of nonlinear perturbation to oscillatory linear systems can be characterized by the averaging method, and we consider first-order averaging for its simplest applicability to high-dimensional problems. Instead of the…
We consider the problem of recovering of continuous multi-dimensional functions from the noisy observations over the regular grid. Our focus is at the adaptive estimation in the case when the function can be well recovered using a linear…
The decomposition of a signal is a fundamental tool in many fields of research, including signal processing, geophysics, astrophysics, engineering, medicine, and many more. By breaking down complex signals into simpler oscillatory…
We present and numerically implement a computational method to construct relativistic scattering amplitudes that obey analyticity, crossing, elastic and inelastic unitarity in three and four spacetime dimensions. The algorithm is based on…
The detection of continuous gravitational-wave signals requires to account for the motion of the detector with respect to the solar system barycenter in the data analysis. In order to search efficiently for such signals by means of the fast…
Irregularly sampled multivariate event streams remain a stubbornly difficult modality for generative modeling: tokenization-based approaches break down when inter-event intervals vary by orders of magnitude, and neural temporal point…
This paper addresses the problem of estimating the modes of an observed non-stationary mixture signal in the presence of an arbitrary distributed noise. A novel Bayesian model is introduced to estimate the model parameters from the…
In systems undergoing localization-delocalization quantum phase transitions due to disorder or monitoring, there is a crucial need for robust methods capable of distinguishing phases and uncovering their intrinsic properties. In this work,…
This paper develops a novel statistical approach to characterize temporally localised cross-oscillatory interactions between channels in a functional brain network. Brain signals are generally nonstationary and the proposed framework uses…
Time-series analysis is critical for a diversity of applications in science and engineering. By leveraging the strengths of modern gradient descent algorithms, the Fourier transform, multi-resolution analysis, and Bayesian spectral…
Neural time-series data contain a wide variety of prototypical signal waveforms (atoms) that are of significant importance in clinical and cognitive research. One of the goals for analyzing such data is hence to extract such…
We propose computationally efficient methods for estimating stationary multivariate spatial and spatial-temporal spectra from incomplete gridded data. The methods are iterative and rely on successive imputation of data and updating of model…
Change-point detection and locally stationary time series modeling are two major approaches for the analysis of non-stationary data. The former aims to identify stationary phases by detecting abrupt changes in the dynamics of a time series…
Functional data analysis deals with data recorded densely over time (or any other continuum) with one or more observed curves per subject. Conceptually, functional data are continuously defined, but in practice, they are usually observed at…