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This paper investigates unsupervised anomaly detection in multivariate time-series data using reinforcement learning (RL) in the latent space of an autoencoder. A significant challenge is the limited availability of anomalous data, often…
Understanding the evolving dependence between two clusters of multivariate signals is fundamental in neuroscience and other domains where sub-networks in a system interact dynamically over time. Despite the growing interest in multivariate…
We present USLR, a computational framework for longitudinal registration of brain MRI scans to estimate nonlinear image trajectories that are smooth across time, unbiased to any timepoint, and robust to imaging artefacts. It operates on the…
This article proposes an online bootstrap scheme for nonparametric level estimation in nonstationary time series. Our approach applies to a broad class of level estimators expressible as weighted sample averages over time windows, including…
Methods of estimation and forecasting for stationary models are well known in classical time series analysis. However, stationarity is an idealization which, in practice, can at best hold as an approximation, but for many time series may be…
Most real world phenomena such as sunlight distribution under a forest canopy, minerals concentration, stock valuation, exhibit nonstationary dynamics i.e. phenomenon variation changes depending on the locality. Nonstationary dynamics pose…
The article considers the problem of identifying the variable frequency of a sinusoidal signal. To obtain a regression model of the signal, an iterative differentiation of the original analytical expression is performed, and the swapping…
Neural recordings are nonstationary time series, i.e. their properties typically change over time. Identifying specific changes, e.g. those induced by a learning task, can shed light on the underlying neural processes. However, such changes…
This article introduces a nonparametric approach to multivariate time-varying power spectrum analysis. The procedure adaptively partitions a time series into an unknown number of approximately stationary segments, where some spectral…
Density estimation is a classical problem in statistics and has received considerable attention when both the data has been fully observed and in the case of partially observed (censored) samples. In survival analysis or clinical trials, a…
We propose a new class of univariate nonstationary time series models, using the framework of modulated time series, which is appropriate for the analysis of rapidly-evolving time series as well as time series observations with missing…
In this work, a novel approach for the construction and training of time series models is presented that deals with the problem of learning on large time series with non-equispaced observations, which at the same time may possess features…
We consider stochastic processes $Y(t)$ which can be represented as $Y(t)=(X(t))^s, s \in \mathbb{N},$ where $X(t)$ is a stationary strictly sub-Gaussian process and build a wavelet-based model that simulates $Y(t)$ with given accuracy and…
This paper illustrates novel methods for nonstationary time series modeling along with their applications to selected problems in neuroscience. These methods are semi-parametric in that inferences are derived by combining sequential…
Recurrent neural networks (RNNs) are nonlinear dynamical models commonly used in the machine learning and dynamical systems literature to represent complex dynamical or sequential relationships between variables. More recently, as deep…
We study the asymptotic behavior of wavelet coefficients of random processes with long memory. These processes may be stationary or not and are obtained as the output of non--linear filter with Gaussian input. The wavelet coefficients that…
Nonstationarity of the event rate is a persistent problem in modeling time series of events, such as neuronal spike trains. Motivated by a variety of patterns in neurophysiological spike train recordings, we define a general class of…
Machine learning (ML) has become a versatile tool for analyzing anomalous diffusion trajectories, yet most existing pipelines are trained on large collections of simulated data. In contrast, experimental trajectories, such as those from…
Spatial concurrent linear models, in which the model coefficients are spatial processes varying at a local level, are flexible and useful tools for analyzing spatial data. One approach places stationary Gaussian process priors on the…
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…