Gaussian Data

Gaussian data, characterized by its normal distribution, is central to numerous statistical and machine learning applications, with research focusing on efficiently handling high-dimensional datasets and addressing challenges posed by non-Gaussianity or corrupted data. Current efforts involve developing robust algorithms for tasks like classification, uncertainty quantification, and parameter estimation, often employing techniques such as debiased estimators, neural networks (including Gaussian radial basis function networks and their separable variants), and topological data analysis. These advancements improve the accuracy and efficiency of various applications, from medical image analysis and autonomous vehicle navigation to anomaly detection and robust principal component analysis.

Papers

March 31, 2023

Generalized Information Bottleneck for Gaussian Variables
Vudtiwat Ngampruetikorn, David J. Schwab
Representation Learning Meaningful Representation Mutual Information Information Bottleneck Gaussian Data

February 17, 2023

Are Gaussian data all you need? Extents and limits of universality in high-dimensional generalized linear estimation
Luca Pesce, Florent Krzakala, Bruno Loureiro, Ludovic Stephan
Continuum Limit RSD Difference of Gaussian Gaussian Mixture K$ Universality Generalized Linear Model Gaussian Data Mixture Signal Gaussian Universality

February 13, 2023

Online Arbitrary Shaped Clustering through Correlated Gaussian Functions
Ole Christian Eidheim
Back Propagation Unsupervised Manner Learning Method Gaussian Data Online Clustering Cluster Shape

November 21, 2022

High-Dimensional Undirected Graphical Models for Arbitrary Mixed Data
Konstantin Göbler, Anne Miloschewski, Mathias Drton, Sach Mukherjee
Graphical Model Gaussian Data Gaussian Copula Local Correlation High Dimensional Graphical Model

July 7, 2022

Learning and generalization of one-hidden-layer neural networks, going beyond standard Gaussian data
Hongkang Li, Shuai Zhang, Meng Wang
Neural Network LeArning Abstract Strong Generalization Generalization Error Gaussian Mixture Model Learning Problem Gaussian Data

May 26, 2022

Gaussian Universality of Perceptrons with Random Labels
Federica Gerace, Florent Krzakala, Bruno Loureiro, Ludovic Stephan, Lenka Zdeborová
Linear Classifier Gaussian Model Gaussian Data Random Label Elementary Perceptron Gaussian Universality

April 12, 2022

Unsupervised Anomaly and Change Detection with Multivariate Gaussianization
José A. Padrón-Hidalgo, Valero Laparra, Gustau Camps-Valls
Anomaly Detection Change Detection Unsupervised Method Gaussian Distribution Multivariate Gaussian Gaussian Data Multivariate Density Unsupervised Anomaly

January 14, 2021

Lecture notes on high-dimensional data
Sven-Ake Wegner
High Dimensional Data Data Science Gaussian Data Mathematical Text Lecture Note