Gaussian Approximation

Gaussian approximation is a widely used technique in various fields for simplifying complex probability distributions by approximating them with Gaussian distributions. Current research focuses on improving the accuracy and efficiency of these approximations, particularly for non-linear systems and high-dimensional data, employing methods like Taylor expansions, Riemannian geometry, and bootstrap techniques within models such as neural networks and generalized linear models. These advancements are crucial for enabling tractable inference in complex scenarios, improving the reliability of statistical estimations, and facilitating efficient algorithms in machine learning and other applications. The resulting improvements in accuracy and computational efficiency have significant implications for fields ranging from robotics and control systems to causal inference and Bayesian statistics.

Papers

November 12, 2024

Tukey g-and-h neural network regression for non-Gaussian data
Arthur P. Guillaumin, Natalia Efremova
Deep Regression Non Gaussian Gaussian Approximation Regression Framework Adaptive T Distribution

September 3, 2024

Planning to avoid ambiguous states through Gaussian approximations to non-linear sensors in active inference agents
Wouter M. Kouw
Task Planning Active Inference Human Sensing Gaussian Approximation Tractable Probabilistic Inference

May 26, 2024

Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning
Sergey Samsonov, Eric Moulines, Qi-Man Shao, Zhuo-Song Zhang, Alexey Naumov
Financial Application Parameter Estimation Stochastic Approximation Linear Function Approximation Non Asymptotic Analysis TD Learning Normal Distribution Gaussian Approximation Polyak Ruppert

February 23, 2024

Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities
Fengyi Li, Ayoub Belhadji, Youssef Marzouk
Mutual Information Combinatorial Optimization Problem Nonlinear Model Experimental Design Greedy Approach Random Selection Gaussian Approximation Log Sobolev

November 5, 2023

Riemannian Laplace Approximation with the Fisher Metric
Hanlin Yu, Marcelo Hartmann, Bernardo Williams, Mark Girolami, Arto Klami
Bayesian Inference Gaussian Distribution Laplace Approximation Fisher Information Metric Gaussian Approximation

April 8, 2023

Non-asymptotic approximations of Gaussian neural networks via second-order Poincar\'e inequalities
Alberto Bordino, Stefano Favaro, Sandra Fortini
Neural Network Gaussian Process Non Asymptotic Analysis Gaussian Approximation Gaussian Neural Network Poincar\'e Ball

March 24, 2023

GAPSLAM: Blending Gaussian Approximation and Particle Filters for Real-Time Non-Gaussian SLAM
Qiangqiang Huang, John J. Leonard
Simultaneous Localization and Mapping Particle Filter Real Time Inference Gaussian Approximation Gaussian Posterior Gaussian SLAM

February 21, 2023

Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression
Wenqi Cao, Gianluigi Pillonetto
Gaussian Process System Identification Impulse Response Bayesian Regularization Gaussian Approximation Independent Variable Collinearity

June 28, 2022

Supervised Training of Conditional Monge Maps
Charlotte Bunne, Andreas Krause, Marco Cuturi
Optimal Transport Input Convex Neural Network Supervised Training Monge Map Gaussian Approximation

June 15, 2022

Finite-Sample Guarantees for High-Dimensional DML
Victor Quintas-Martinez
Model Debiasing Finite Sample Guarantee Joint Inference Gaussian Approximation High Dimensional Causal

June 9, 2022

Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models
Pranjal Awasthi, Abhimanyu Das, Weihao Kong, Rajat Sen
Robust Learning Generalized Linear Model Adversarial Corruption Label Corruption Gaussian Approximation General Linear Corruption Process

March 14, 2022

Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks
Andrea Basteri, Dario Trevisan
Deep Neural Network Wasserstein Distance Hidden Layer Random Participation Gaussian Approximation

November 23, 2021

Critical Initialization of Wide and Deep Neural Networks through Partial Jacobians: General Theory and Applications
Darshil Doshi, Tianyu He, Andrey Gromov
Deep Neural Network Financial Application New Initialization Residual Connection Jacobian Matrix Criticality Ordered Spin Sequence Gaussian Approximation

Gaussian Approximation

Papers

Tukey g-and-h neural network regression for non-Gaussian data

Planning to avoid ambiguous states through Gaussian approximations to non-linear sensors in active inference agents

Gaussian Approximation and Multiplier Bootstrap for Polyak-Ruppert Averaged Linear Stochastic Approximation with Applications to TD Learning

Nonlinear Bayesian optimal experimental design using logarithmic Sobolev inequalities

Riemannian Laplace Approximation with the Fisher Metric

Non-asymptotic approximations of Gaussian neural networks via second-order Poincar\'e inequalities

GAPSLAM: Blending Gaussian Approximation and Particle Filters for Real-Time Non-Gaussian SLAM

Dealing with Collinearity in Large-Scale Linear System Identification Using Gaussian Regression

Supervised Training of Conditional Monge Maps

Finite-Sample Guarantees for High-Dimensional DML

Trimmed Maximum Likelihood Estimation for Robust Learning in Generalized Linear Models

Quantitative Gaussian Approximation of Randomly Initialized Deep Neural Networks

Critical Initialization of Wide and Deep Neural Networks through Partial Jacobians: General Theory and Applications