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Synthetic Data Generation has become essential for scalable, privacy-preserving statistical analysis. While standard approaches based on generative models, such as Normalizing Flows, have been widely used, they often suffer from slow…

We propose SymDiff, a method for constructing equivariant diffusion models using the framework of stochastic symmetrisation. SymDiff resembles a learned data augmentation that is deployed at sampling time, and is lightweight,…

Recent advances in self-supervised learning for EEG representation have largely relied on masked reconstruction, where models are trained to recover randomly masked signal segments. While effective at modeling local dependencies, such…

Classification of sleep stages plays an essential role in diagnosing sleep-related diseases including Sleep Disorder Breathing (SDB) disease. In this study, we propose an end-to-end deep learning architecture, named SSNet, which comprises…

This article proposes an active learning method for high dimensional data, based on intrinsic data geometries learned through diffusion processes on graphs. Diffusion distances are used to parametrize low-dimensional structures on the…

We designed a new artificial neural network by modifying the neural ordinary differential equation (NODE) framework to successfully predict the time evolution of the 2D mode profile in both the linear growth and nonlinear saturated stages.…

In clinical neuroscience, epileptic seizures have been associated with the sudden emergence of coupled activity across the brain. The resulting functional networks - in which edges indicate strong enough coupling between brain regions - are…

Unsupervised learning aims at the discovery of hidden structure that drives the observations in the real world. It is essential for success in modern machine learning. Latent variable models are versatile in unsupervised learning and have…

Diffusion models (DMs) have emerged as powerful foundation models for a variety of tasks, with a large focus in synthetic image generation. However, their requirement of large annotated datasets for training limits their applicability in…

Decomposing multivariate time series with certain basic dynamics is crucial for understanding, predicting and controlling nonlinear spatiotemporally dynamic systems such as the brain. Dynamic mode decomposition (DMD) is a method for…

Diffusion geometry is a manifold learning framework that uses random walks defined by Markov transition matrices to characterize the geometry of a dataset at multiple scales. We use diffusion geometry for neural representations,…

Diffusion models (DMs) have shown promising results on single-image super-resolution and other image-to-image translation tasks. Benefiting from more computational resources and longer inference times, they are able to yield more realistic…

A novel single-lead f-wave extraction algorithm based on the modern diffusion geometry data analysis framework is proposed. The algorithm is essentially an averaged beat subtraction algorithm, where the ventricular activity template is…

Sleep plays an important role in incremental learning and consolidation of memories in biological systems. Motivated by the processes that are known to be involved in sleep generation in biological networks, we developed an algorithm that…

Deep neural networks (DNN) have shown remarkable success in the classification of physiological signals. In this study we propose a method for examining to what extent does a DNN's performance rely on rediscovering existing features of the…

Learning nonlinear dynamics from diffusion data is a challenging problem since the individuals observed may be different at different time points, generally following an aggregate behaviour. Existing work cannot handle the tasks well since…

Diffusive dynamics abound in nature and have been especially studied in physical, biological, and financial systems. These dynamics are characterised by a linear growth of the mean squared displacement (MSD) with time. Often, the conditions…

Recently, physiological data such as electroencephalography (EEG) signals have attracted significant attention in affective computing. In this context, the main goal is to design an automated model that can assess emotional states. Lately,…

The goal of this thesis is to improve our understanding of the internal mechanisms by which deep artificial neural networks create meaningful representations and are able to generalize. We focus on the challenge of characterizing the…

Manifold learning techniques for dynamical systems and time series have shown their utility for a broad spectrum of applications in recent years. While these methods are effective at learning a low-dimensional representation, they are often…