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A major tenet in theoretical neuroscience is that cognitive and behavioral processes are ultimately implemented in terms of the neural system dynamics. Accordingly, a major aim for the analysis of neurophysiological measurements should lie…

Effective connectivity analysis provides an understanding of the functional organization of the brain by studying how activated regions influence one other. We propose a nonparametric Bayesian approach to model effective connectivity…

Physiological signals are often corrupted by motion artifacts, baseline drift, and other low-SNR disturbances, which pose significant challenges for analysis. Additionally, these signals exhibit strong non-stationarity, with sharp peaks and…

How does soil pollution affect a plant's circadian clock? Are there any differences between how the clock reacts when exposed to different concentrations of elements of the periodic table? If so, can we characterise these differences? We…

Motivated with the concept of transform learning and the utility of rational wavelet transform in audio and speech processing, this paper proposes Rational Wavelet Transform Learning in Statistical sense (RWLS) for natural images. The…

Gaussian processes have become a popular tool for nonparametric regression because of their flexibility and uncertainty quantification. However, they often use stationary kernels, which limit the expressiveness of the model and may be…

We propose a novel approach for change-point detection and parameter learning in multivariate non-stationary time series exhibiting oscillatory behaviour. We approximate the process through a piecewise function defined by a sum of…

We present a new framework for the robust estimation of latent time series models which is fairly general and, for example, covers models going from ARMA to state-space models. This approach provides estimators which are (i) consistent and…

Deep learning utilizing transformers has recently achieved a lot of success in many vital areas such as natural language processing, computer vision, anomaly detection, and recommendation systems, among many others. Among several merits of…

Continuous collection of physiological data from wearable sensors enables temporal characterization of individual behaviors. Understanding the relation between an individual's behavioral patterns and psychological states can help identify…

The robust estimation of dynamically changing features, such as the position of prey, is one of the hallmarks of perception. On an abstract, algorithmic level, nonlinear Bayesian filtering, i.e. the estimation of temporally changing signals…

To capture the slowly time-varying spectral content of real-world time-series, a common paradigm is to partition the data into approximately stationary intervals and perform inference in the time-frequency domain. However, this approach…

In this paper, we study nonparametric models allowing for locally stationary regressors and a regression function that changes smoothly over time. These models are a natural extension of time series models with time-varying coefficients. We…

This paper addresses nonparametric estimation of nonlinear multivariate Hawkes processes, where the interaction functions are assumed to lie in a reproducing kernel Hilbert space (RKHS). Motivated by applications in neuroscience, the model…

We propose a nonlinear, wavelet based signal representation that is translation invariant and robust to both additive noise and random dilations. Motivated by the multi-reference alignment problem and generalizations thereof, we analyze the…

We propose a new class of waveform foundation models that departs from conventional sequence based representations by modeling physiological time series as realizations of latent event processes. Rather than treating signals as collections…

Time-varying linear state-space models are powerful tools for obtaining mathematically interpretable representations of neural signals. For example, switching and decomposed models describe complex systems using latent variables that evolve…

Neural activity patterns related to behavior occur at many scales in time and space from the atomic and molecular to the whole brain. Here we explore the feasibility of interpreting neurophysiological data in the context of many-body…

A common problem in neuroscience is to elucidate the collective neural representations of behaviorally important variables such as head direction, spatial location, upcoming movements, or mental spatial transformations. Often, these latent…

Most environmental phenomena, such as wind profiles, ozone concentration and sunlight distribution under a forest canopy, exhibit nonstationary dynamics i.e. phenomenon variation change depending on the location and time of occurrence.…