13 citations · 72 across the 18 of their papers we have counts for
18 papers
Contrastive inverse regression for dimension reduction
Sam Hawke, Hengrui Luo, Didong Li
Supervised dimension reduction (SDR) has been a topic of growing interest in data science, as it enables the reduction of high-dimensional covariates while preserving the functiona…
Tree Representations of Brain Structural Connectivity via Persistent Homology
Didong Li, Phuc Nguyen, Zhengwu Zhang +1
The brain structural connectome is generated by a collection of white matter fiber bundles constructed from diffusion weighted MRI (dMRI), acting as highways for neural activity. T…
Spherical Rotation Dimension Reduction with Geometric Loss Functions
Hengrui Luo, Jeremy E. Purvis, Didong Li
Modern datasets often exhibit high dimensionality, yet the data reside in low-dimensional manifolds that can reveal underlying geometric structures critical for data analysis. A pr…
Multi-group Gaussian Processes
Didong Li, Andrew Jones, Sudipto Banerjee +1
Gaussian processes (GPs) are pervasive in functional data analysis, machine learning, and spatial statistics for modeling complex dependencies. Modern scientific data sets are typi…
From the Greene--Wu Convolution to Gradient Estimation over Riemannian Manifolds
Tianyu Wang, Yifeng Huang, Didong Li
Over a complete Riemannian manifold of finite dimension, Greene and Wu introduced a convolution, known as Greene-Wu (GW) convolution. In this paper, we study properties of the GW c…
Inference for Gaussian Processes with Matérn Covariogram on Compact Riemannian Manifolds
Didong Li, Wenpin Tang, Sudipto Banerjee
Gaussian processes are widely employed as versatile modelling and predictive tools in spatial statistics, functional data analysis, computer modelling and diverse applications of m…
Contrastive latent variable modeling with application to case-control sequencing experiments
Andrew Jones, F. William Townes, Didong Li +1
High-throughput RNA-sequencing (RNA-seq) technologies are powerful tools for understanding cellular state. Often it is of interest to quantify and summarize changes in cell state t…
Probabilistic Contrastive Principal Component Analysis
Didong Li, Andrew Jones, Barbara Engelhardt
Dimension reduction is useful for exploratory data analysis. In many applications, it is of interest to discover variation that is enriched in a "foreground" dataset relative to a…
Principal Ellipsoid Analysis (PEA): Efficient non-linear dimension reduction & clustering
Debolina Paul, Saptarshi Chakraborty, Didong Li +1
Even with the rise in popularity of over-parameterized models, simple dimensionality reduction and clustering methods, such as PCA and k-means, are still routinely used in an amazi…
Exponential-wrapped distributions on symmetric spaces
Emmanuel Chevallier, Didong Li, Yulong Lu +1
In many applications, the curvature of the space supporting the data makes the statistical modelling challenging. In this paper we discuss the construction and use of probability d…
Random Lie Brackets that Induce Torsion: A Model for Noisy Vector Fields
Didong Li, Sayan Mukherjee
We define and study a random Lie bracket that induces torsion in expectation. Almost all stochastic analysis on manifolds have assumed parallel transport. Mathematically this assum…
Estimating densities with nonlinear support using Fisher-Gaussian kernels
Minerva Mukhopadhyay, Didong Li, David B Dunson
Current tools for multivariate density estimation struggle when the density is concentrated near a nonlinear subspace or manifold. Most approaches require choice of a kernel, with…
Geodesic Distance Estimation with Spherelets
Didong Li, David B Dunson
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these proc…
Efficient Weingarten Map and Curvature Estimation on Manifolds
Yueqi Cao, Didong Li, Huafei Sun +2
In this paper, we propose an efficient method to estimate the Weingarten map for point cloud data sampled from manifold embedded in Euclidean space. A statistical model is establis…
Classification via local manifold approximation
Didong Li, David B Dunson
Classifiers label data as belonging to one of a set of groups based on input features. It is challenging to obtain accurate classification performance when the feature distribution…
Efficient Manifold and Subspace Approximations with Spherelets
Didong Li, Minerva Mukhopadhyay, David B. Dunson
In statistical dimensionality reduction, it is common to rely on the assumption that high dimensional data tend to concentrate near a lower dimensional manifold. There is a rich li…
Principal bundles over statistical manifolds
Didong Li, Huafei Sun, Chen Tao +1
In this paper, we introduce the concept of principal bundles on statistical manifolds. After necessary preliminaries on information geometry and principal bundles on manifolds, we…
Riemannian Holonomy Groups of Statistical Manifolds
Didong Li, Huafei Sun, Chen Tao +1
Normal distribution manifolds play essential roles in the theory of information geometry, so do holonomy groups in classification of Riemannian manifolds. After some necessary prel…