5 papers
From Global to Local Correlation: Geometric Decomposition of Statistical Inference
Pawel Gajer, Jacques Ravel
Understanding feature-outcome associations in high-dimensional data remains challenging when relationships vary across subpopulations, yet standard methods assuming global associat…
Adaptive Geometric Regression for High-Dimensional Structured Data
Pawel Gajer, Jacques Ravel
We present a geometric framework for regression on structured high-dimensional data that shifts the analysis from the ambient space to a geometric object capturing the data's intri…
Intrinsic and Normal Mean Ricci Curvatures: A Bochner--Weitzenboeck Identity for Simple d-Vectors
Pawel Gajer, Jacques Ravel
We introduce two pointwise subspace averages of sectional curvature on a d-dimensional plane Pi in T_p M: (i) the intrinsic mean Ricci (the average of sectional curvatures of 2-pla…
The Geometry of Machine Learning Models
Pawel Gajer, Jacques Ravel
This paper presents a mathematical framework for analyzing machine learning models through the geometry of their induced partitions. By representing partitions as Riemannian simpli…
A New Approach to Compositional Data Analysis using \(L^{\infty}\)-normalization with Applications to Vaginal Microbiome
Pawel Gajer, Jacques Ravel
We introduce a novel approach to compositional data analysis based on -normalization, addressing challenges posed by zero-rich high-throughput data. Traditional methods…