Divergence Phase Index: A Riesz-Transform Framework for Multidimensional Phase Difference Analysis

2025-10-06 · Magaly Catanzariti, Hugo Aimar, Diego M. Mateos arxiv

We introduce the Divergence Phase Index (DPI), a novel framework for quantifying phase differences in one and multidimensional signals, grounded in harmonic analysis via the Riesz transform. Based on classical Hilbert Transform phase measures, the DPI extends these principles to higher dimensions, offering a geometry-aware metric that is invariant to intensity scaling and sensitive to structural changes. We applied this method on both synthetic and real-world datasets, including intracranial EEG (iEEG) recordings during epileptic seizures, high-resolution microscopy images, and paintings. In the 1D case, the DPI robustly detects hypersynchronization associated with generalized epilepsy, while in 2D, it reveals subtle, imperceptible changes in images and artworks. Additionally, it can detect rotational variations in highly isotropic microscopy images. The DPI's robustness to amplitude variations and its adaptability across domains enable its use in diverse applications from nonlinear dynamics, complex systems analysis, to multidimensional signal processing.

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A Unified Framework for Debiased Machine Learning: Riesz Representer Fitting under Bregman Divergence

2026-01-12 · Masahiro Kato arxiv

Estimating the Riesz representer is central to debiased machine learning for causal and structural parameter estimation. We propose generalized Riesz regression, a unified framework for estimating the Riesz representer b…

Direct Debiased Machine Learning via Bregman Divergence Minimization

2025-10-27 · Masahiro Kato arxiv

We develop a direct debiased machine learning framework comprising Neyman targeted estimation and generalized Riesz regression. Our framework unifies Riesz regression for automatic debiased machine learning, covariate ba…

genriesz: A Python Package for Automatic Debiased Machine Learning with Generalized Riesz Regression

2026-02-19 · Masahiro Kato arxiv

Efficient estimation of causal and structural parameters can be automated using the Riesz representation theorem and debiased machine learning (DML). We present genriesz, an open-source Python package that implements aut…

Isotropic and Steerable Wavelets in N Dimensions. A multiresolution analysis framework for ITK

2017-10-03 · Pablo Hernandez-Cerdan

This document describes the implementation of the external module ITKIsotropicWavelets, a multiresolution (MRA) analysis framework using isotropic and steerable wavelets in the frequency domain. This framework provides t…

Denoising

Learning density ratios in causal inference using Bregman-Riesz regression

2025-10-17 · Oliver J. Hines, Caleb H. Miles arxiv

The ratio of two probability density functions is a fundamental quantity that appears in many areas of statistics and machine learning, including causal inference, reinforcement learning, covariate shift, outlier detecti…

Reinforcement Learning Outlier Detection Data Augmentation Causal Inference