Related papers: A Novel Testing Approach for Differences Among Bra…

A fundamental question in data analysis, machine learning and signal processing is how to compare between data points. The choice of the distance metric is specifically challenging for high-dimensional data sets, where the problem of…

The ability to represent and compare machine learning models is crucial in order to quantify subtle model changes, evaluate generative models, and gather insights on neural network architectures. Existing techniques for comparing data…

Manifold hypothesis states that data points in high-dimensional space actually lie in close vicinity of a manifold of much lower dimension. In many cases this hypothesis was empirically verified and used to enhance unsupervised and…

We propose a novel semiparametric classifier based on Mahalanobis distances of an observation from the competing classes. Our tool is a generalized additive model with the logistic link function that uses these distances as features to…

In a number of disciplines, the data (e.g., graphs, manifolds) to be analyzed are non-Euclidean in nature. Geometric deep learning corresponds to techniques that generalize deep neural network models to such non-Euclidean spaces. Several…

Recent advances in semi-supervised learning methods rely on estimating the categories of unlabeled data using a model trained on the labeled data (pseudo-labeling) and using the unlabeled data for various consistency-based regularization.…

In many real-world applications data exhibits non-stationarity, i.e., its distribution changes over time. One approach to handling non-stationarity is to remove or minimize it before attempting to analyze the data. In the context of brain…

Deep learning models have become a popular choice for medical image analysis. However, the poor generalization performance of deep learning models limits them from being deployed in the real world as robustness is critical for medical…

Classification is a core topic in functional data analysis. A large number of functional classifiers have been proposed in the literature, most of which are based on functional principal component analysis or functional regression. In…

Brain connectivity analysis is now at the foreground of neuroscience research. A connectivity network is characterized by a graph, where nodes represent neural elements such as neurons and brain regions, and links represent statistical…

In increasingly many settings, data sets consist of multiple samples from a population of networks, with vertices aligned across these networks. For example, brain connectivity networks in neuroscience consist of measures of interaction…

Converging evidence shows that disease-relevant brain alterations do not appear in random brain locations, instead, its spatial pattern follows large scale brain networks. In this context, a powerful network analysis approach with a…

Symmetric positive definite (SPD) matrices arising from functional connectivity analysis of neuroimaging data can be endowed with a Riemannian geometric structure that standard methods fail to respect. While existing R packages provide some…

The need for efficiently comparing and representing datasets with unknown alignment spans various fields, from model analysis and comparison in machine learning to trend discovery in collections of medical datasets. We use manifold learning…

Network data are increasingly collected along with other variables of interest. Our motivation is drawn from neurophysiology studies measuring brain connectivity networks for a sample of individuals along with their membership to a low or…

Neural networks used for image classification tasks in critical applications must be tested with sufficient realistic data to assure their correctness. To effectively test an image classification neural network, one must obtain realistic…

Recent developments in experimental neuroscience make it possible to simultaneously record the activity of thousands of neurons. However, the development of analysis approaches for such large-scale neural recordings have been slower than…

Manifold learning using deep neural networks been shown to be an effective tool for building sophisticated prior image models that can be applied to noise reduction in low-dose CT. We propose a new iterative CT reconstruction algorithm,…

Efforts are underway to study ways via which the power of deep neural networks can be extended to non-standard data types such as structured data (e.g., graphs) or manifold-valued data (e.g., unit vectors or special matrices). Often,…

We introduce a multifidelity estimator of covariance matrices formulated as the solution to a regression problem on the manifold of symmetric positive definite matrices. The estimator is positive definite by construction, and the…