85 citations · 85 across the 6 of their papers we have counts for
6 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…
Geometry of Deligne cohomology
Pawel Gajer
It is well known that degree two Deligne cohomology groups can be identified with groups of isomorphism classes of holomorphic line bundles with connections. There is also a geomet…