7 papers
Contextual Fraction on Permutation Gain Graphs: Exact Algorithms, Query Lower Bounds, and Dynamic Maintenance
Ronald Katende
For an explicitly represented finite empirical model, deciding whether the contextual fraction is strictly below one is NP-complete, while the standard exact linear program has one…
Counterfactual Operator Relevance for PDE Discovery: Screening, Pruning, and Identifiability
Ronald Katende
We study operator relevance in data-driven partial differential equation (PDE) discovery. Sparse residual methods can select terms that improve residual fit, but residual contribut…
Geometry as a Missing Axis of Representation Quality: The Variational Geometric Information Bottleneck under Data Scarcity
Ronald Katende
We study latent geometry as an explicit component of representation quality in data-scarce learning. For an encoder (Ï), we define (Q_{β,γ}(Ï)=I(Ï(X);Y)-β\mathcal C(Ï)-γd_{…
Core-Conditioned Regularized Matrix Tri-Factorization for High-Dimensional Structured Systems
Ronald Katende
This paper studies a regularized matrix tri-factorization \(A\approx PDQ\), where \(P\) and \(Q\) are side factors and \(D\) is a central core whose conditioning can be explicitly…
Interpretive Efficiency: Information-Geometric Foundations of Data Usefulness
Ronald Katende
Interpretability is central to trustworthy machine learning, yet existing metrics rarely quantify how effectively data support an interpretive representation. We propose Interpreti…
Structured Variational -Decomposition for Accurate and Stable Low-Rank Approximation
Ronald Katende
We introduce the -decomposition, a non-orthogonal matrix factorization of the form , where , , and…