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Wavelets provide the flexibility to analyse stochastic processes at different scales. Here, we apply them to multivariate point processes as a means of detecting and analysing unknown non-stationarity, both within and across data streams.…
The TrendLSW R package has been developed to provide users with a suite of wavelet-based techniques to analyse the statistical properties of nonstationary time series. The key components of the package are (a) two approaches for the…
This paper describes the R package mvLSW. The package contains a suite of tools for the analysis of multivariate locally stationary wavelet (LSW) time series. Key elements include: (i) the simulation of multivariate LSW time series for a…
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…
Rhythmic data are ubiquitous in the life sciences. Biologists need reliable statistical tests to identify whether a particular experimental treatment has caused a significant change in a rhythmic signal. When these signals display…
Modeling non-stationary processes, where statistical properties vary across the input domain, is a critical challenge in machine learning; yet most scalable methods rely on a simplifying assumption of stationarity. This forces a difficult…
This article introduces the class of continuous time locally stationary wavelet processes. Continuous time models enable us to properly provide scale-based time series models for irregularly-spaced observations for the first time, while…
The real world is inherently non-stationary, with ever-changing factors, such as weather conditions and traffic flows, making it challenging for agents to adapt to varying environmental dynamics. Non-Stationary Reinforcement Learning (NSRL)…
This work introduces a wavelet neural network to learn a filter-bank specialized to fit non-stationary signals and improve interpretability and performance for digital signal processing. The network uses a wavelet transform as the first…
In this paper, we propose a fast, well-performing, and consistent method for segmenting a piecewise-stationary, linear time series with an unknown number of breakpoints. The time series model we use is the nonparametric Locally Stationary…
In this paper, an unsupervised Recurrent Wavelet Probabilistic Neural Network (RWPNN) is proposed, which aims at detecting anomalies in non-stationary environments by modelling the temporal features using a nonparametric density estimation…
A deep latent variable model is a powerful method for capturing complex distributions. These models assume that underlying structures, but unobserved, are present within the data. In this dissertation, we explore high-dimensional problems…
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…
We consider an approach to the analysis of nonstationary processes based on the application of wavelet basis sets constructed using segments of the analyzed time series. The proposed method is applied to the analysis of time series…
Abstract. Detecting anomalies in patterns of sensor data is important in many practical applications, including domestic activity monitoring for Active Assisted Living (AAL). How to represent and analyse these patterns, however, remains a…
Based on a novel dynamic Whittle likelihood approximation for locally stationary processes, a Bayesian nonparametric approach to estimating the time-varying spectral density is proposed. This dynamic frequency-domain based likelihood…
We consider a time series $X=\{X_k, k\in\mathbb{Z}\}$ with memory parameter $d\in\mathbb{R}$. This time series is either stationary or can be made stationary after differencing a finite number of times. We study the "Local Whittle Wavelet…
We propose an evolutionary state space model (E-SSM) for analyzing high dimensional brain signals whose statistical properties evolve over the course of a non-spatial memory experiment. Under E-SSM, brain signals are modeled as mixtures of…
We introduce a wavelet-based model of local stationarity. This model enlarges the class of locally stationary wavelet processes and contains processes whose spectral density function may change very suddenly in time. A notion of…
A new approach for the analysis of nonstationary signals is proposed, with a focus on audio applications. Following earlier contributions, nonstationarity is modeled via stationarity-breaking operators acting on Gaussian stationary random…