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In many biomedical problems, data are often heterogeneous, with samples spanning multiple patient subgroups, where different subgroups may have different disease subtypes, stages, or other medical contexts. These subgroups may be related,…
We introduce a generalized formulation of mutual information (MI) based on the extended Bregman divergence, a framework that subsumes the generalized S-Bregman (GSB) divergence family. The GSB divergence unifies two important classes of…
Data subset selection aims to find a smaller yet informative subset of a large dataset that can approximate the full-dataset training, addressing challenges associated with training neural networks on large-scale datasets. However, existing…
This paper analyzes the statistical performance of a robust spectral clustering method for latent structure recovery in noisy data matrices. We consider eigenvector-based clustering applied to a matrix of nonparametric rank statistics that…
As in other estimation scenarios, likelihood based estimation in the normal mixture set-up is highly non-robust against model misspecification and presence of outliers (apart from being an ill-posed optimization problem). A robust…
Gaussian graphical models are widely utilized to infer and visualize networks of dependencies between continuous variables. However, inferring the graph is difficult when the sample size is small compared to the number of variables. To…
Standard clinical assessments of upper-extremity motor function after stroke either rely on ordinal scoring, which lacks sensitivity, or time-based task metrics, which do not capture movement quality. In this work, we present a computer…
We present a Bayesian formulation of weighted stochastic block models that can be used to infer the large-scale modular structure of weighted networks, including their hierarchical organization. Our method is nonparametric, and thus does…
The Stratified Bootstrap Test (SBT) provides a nonparametric, resampling-based framework for assessing the stability of group-specific ranking patterns in multivariate survey or rating data. By repeatedly resampling observations and…
There are two notoriously hard problems in cluster analysis, estimating the number of clusters, and checking whether the population to be clustered is not actually homogeneous. Given a dataset, a clustering method and a cluster validation…
We consider the community detection problem in sparse random hypergraphs under the non-uniform hypergraph stochastic block model (HSBM), a general model of random networks with community structure and higher-order interactions. When the…
With the rapid growth of modern technology, many large-scale biomedical studies have been/are being/will be conducted to collect massive datasets with large volumes of multi-modality imaging, genetic, neurocognitive, and clinical…
Statistical analysis of magnetic resonance imaging (MRI) can help radiologists to detect pathologies that are otherwise likely to be missed. Deep learning (DL) has shown promise in modeling complex spatial data for brain anomaly detection.…
The existing barely-supervised medical image segmentation (BSS) methods, adopting a registration-segmentation paradigm, aim to learn from data with very few annotations to mitigate the extreme label scarcity problem. However, this paradigm…
This paper investigates an extremely challenging problem: barely-supervised volumetric medical image segmentation (BSS). A BSS training dataset consists of two parts: 1) a barely-annotated labeled set, where each labeled image contains only…
Robust optimization (RO) is a common approach to tractably obtain safeguarding solutions for optimization problems with uncertain constraints. In this paper, we study a statistical framework to integrate data into RO, based on learning a…
This thesis is dedicated to the statistical analysis of multi-sub ject fMRI data, with the purpose of identifying bain structures involved in certain cognitive or sensori-motor tasks, in a reproducible way across sub jects. To overcome…
Clustering is essential in data analysis and machine learning, but traditional algorithms like $k$-means and Gaussian Mixture Models (GMM) often fail with nonconvex clusters. To address the challenge, we introduce the Flexible Bivariate…
Clustering procedures typically estimate which data points are clustered together, a quantity of primary importance in many analyses. Often used as a preliminary step for dimensionality reduction or to facilitate interpretation, finding…
Structured data in the form of networks are increasingly common in a number of fields, including the social sciences, biology, physics, computer science, and many others. A key task in network analysis is community detection, which…