Related papers: Multiscale and multilevel technique for consistent…

The problem of change-point estimation is considered under a general framework where the data are generated by unknown stationary ergodic process distributions. In this context, the consistent estimation of the number of change-points is…

Most machine learning methods assume fixed probability distributions, limiting their applicability in nonstationary real-world scenarios. While continual learning methods address this issue, current approaches often rely on black-box models…

We introduce a segmentation algorithm to probe temporal organization of heterogeneities in human heartbeat interval time series. We find that the lengths of segments with different local values of heart rates follow a power-law…

Current algorithmic approaches for piecewise affine motion estimation are based on alternating motion segmentation and estimation. We propose a new method to estimate piecewise affine motion fields directly without intermediate…

In this paper, we study a fast and linearized finite difference method to solve the nonlinear time-fractional wave equation with multi fractional orders. We first propose a discretization to the multi-term Caputo derivative based on the…

We propose a high-order spacetime wavelet method for the solution of nonlinear partial differential equations with a user-prescribed accuracy. The technique utilizes wavelet theory with a priori error estimates to discretize the problem in…

We study nonlinear regression of real valued data in an individual sequence manner, where we provide results that are guaranteed to hold without any statistical assumptions. We address the convergence and undertraining issues of…

We assume a second-order source separation model where the observed multivariate time series is a linear mixture of latent, temporally uncorrelated time series with some components pure white noise. To avoid the modelling of noise, we…

Stationarity is a key assumption in many statistical models for random processes. With recent developments in the field of graph signal processing, the conventional notion of wide-sense stationarity has been extended to random processes…

We consider detecting the evolutionary oscillatory pattern of a signal when it is contaminated by non-stationary noises with complexly time-varying data generating mechanism. A high-dimensional dense progressive periodogram test is proposed…

Time-frequency analysis is an important and challenging task in many applications. Fourier and wavelet analysis are two classic methods that have achieved remarkable success in many fields. However, they also exhibit limitations when…

Testing for nonlinearity is one of the most important preprocessing steps in nonlinear time series analysis. Typically, this is done by means of the linear surrogate data methods. But it is a known fact that the validity of the results…

We present a method that models the evolution of an unbounded number of time series clusters by switching among an unknown number of regimes with linear dynamics. We develop a Bayesian non-parametric approach using a hierarchical Dirichlet…

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…

Modeling the temporal behavior of data is of primordial importance in many scientific and engineering fields. Baseline methods assume that both the dynamic and observation equations follow linear-Gaussian models. However, there are many…

In this paper, a class of high order numerical schemes is proposed to solve the nonlinear parabolic equations with variable coefficients. This method is based on our previous work [10] for convection-diffusion equations, which relies on a…

Linear, time-varying (LTV) systems composed of time shifts, frequency shifts, and complex amplitude scalings are operators that act on continuous finite-energy waveforms. This paper presents a novel, resource-efficient method for…

Many studies of biomedical time series signals aim to measure the association between frequency-domain properties of time series and clinical and behavioral covariates. However, the time-varying dynamics of these associations are largely…

The stationarity is assumed in vanilla Hawkes process, which reduces the model complexity but introduces a strong assumption. In this paper, we propose a fast multi-resolution segmentation algorithm to capture the time-varying…

Deploying off-the-shelf segmentation networks on biomedical data has become common practice, yet if structures of interest in an image sequence are visible only temporarily, existing frame-by-frame methods fail. In this paper, we provide a…