Related papers: Manifold-regression to predict from MEG/EEG brain …

We develop Riemannian Stein Variational Gradient Descent (RSVGD), a Bayesian inference method that generalizes Stein Variational Gradient Descent (SVGD) to Riemann manifold. The benefits are two-folds: (i) for inference tasks in Euclidean…

Functional brain imaging through electroencephalography (EEG) relies upon the analysis and interpretation of high-dimensional, spatially organized time series. We propose to represent time-localized frequency domain characterizations of EEG…

Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the…

This paper is motivated by a regression analysis of electroencephalography (EEG) neuroimaging data with high-dimensional correlated responses with multi-level nested correlations. We develop a divide-and-conquer procedure implemented in a…

Despite signi cant progress in semi-supervised medical image segmentation, most existing segmentation networks overlook e ective methodological guidance for feature extraction and important prior information from datasets. In this paper, we…

This paper is focused on the statistical analysis of data consisting of a collection of multiple series of probability measures that are indexed by distinct time instants and supported over a bounded interval of the real line. By modeling…

In this work, we investigate Riemannian geometry based dimensionality reduction methods that respect the underlying manifold structure of the data. In particular, we focus on Principal Geodesic Analysis (PGA) as a nonlinear generalization…

Electroencephalography (EEG) is a critical, non-invasive method to monitor electrical brain activity. EEGs can span anywhere from a couple seconds to multiple hours, posing a major hurdle for existing deep learning methods due to two major…

We propose a novel quantile function-based approach for neuroimaging classification using Wasserstein-Fr\'echet regression, specifically applied to the detection of mild traumatic brain injury (mTBI) based on the MEG and MRI data.…

Synthesizing geometrical shapes from human brain activities is an interesting and meaningful but very challenging topic. Recently, the advancements of deep generative models like Generative Adversarial Networks (GANs) have supported the…

In recent years there has been increased interest in understanding the interplay between deep generative models (DGMs) and the manifold hypothesis. Research in this area focuses on understanding the reasons why commonly-used DGMs succeed or…

Overcomplete representations and dictionary learning algorithms kept attracting a growing interest in the machine learning community. This paper addresses the emerging problem of comparing multivariate overcomplete representations. Despite…

Steering a language model - intervening on its internal activations to change downstream behaviour - has recently expanded beyond linear interpolation to nonlinear methods such as angular and kernelized steering, which define intervention…

We study the tensor-on-tensor regression, where the goal is to connect tensor responses to tensor covariates with a low Tucker rank parameter tensor/matrix without the prior knowledge of its intrinsic rank. We propose the Riemannian…

Diffusion and flow models have become the dominant paradigm for generative modeling on Riemannian manifolds, with successful applications in protein backbone generation and DNA sequence design. However, these methods require tens to…

Deep Riemannian networks provide a powerful framework for Electroencephalography (EEG) decoding, but their practical applications are severely constrained. Accurately decoding EEG signals requires modeling complex temporal dynamics across…

We study the problem of network regression, where one is interested in how the topology of a network changes as a function of Euclidean covariates. We build upon recent developments in generalized regression models on metric spaces based on…

It has long been thought that high-dimensional data encountered in many practical machine learning tasks have low-dimensional structure, i.e., the manifold hypothesis holds. A natural question, thus, is to estimate the intrinsic dimension…

Low-dimensional structure in real-world data plays an important role in the success of generative models, which motivates diffusion models defined on intrinsic data manifolds. Such models are driven by stochastic differential equations…

In this paper, we propose a novel space-time geometric representation of human landmark configurations and derive tools for comparison and classification. We model the temporal evolution of landmarks as parametrized trajectories on the…