Link Function

Link functions model the relationship between a predictor variable and the expected value of a response variable in statistical models, particularly when the response is non-normal. Current research focuses on efficiently learning these functions within various model architectures, including single-index models, multi-index models, and neural networks, often employing gradient-based optimization methods like stochastic gradient descent on Riemannian manifolds. These advancements aim to improve the accuracy and efficiency of statistical inference and machine learning, particularly in high-dimensional settings and with non-Gaussian data. The ability to effectively learn link functions has broad implications across diverse fields, from causal inference and time series analysis to classification and regression problems.

Papers

July 14, 2024

Parameter Estimation for Generalized Low-Rank Matrix Sensing by Learning on Riemannian Manifolds
Osbert Bastani
Convergence Guarantee Parameter Estimation Riemannian Manifold Optimal Estimation Local Convergence Matrix Sensing Link Function

June 3, 2024

Neural network learns low-dimensional polynomials with SGD near the information-theoretic limit
Jason D. Lee, Kazusato Oko, Taiji Suzuki, Denny Wu
Neural Network Gradient Descent Stochastic Gradient Descent Information Theoretic Gradient Computation Statistical Complexity Single Index Model Link Function Dimensional Polynomial

October 30, 2023

On Learning Gaussian Multi-index Models with Gradient Flow
Alberto Bietti, Joan Bruna, Loucas Pillaud-Vivien
Gradient Flow Multi Index Model Gradient Flow Dynamic Link Function

July 28, 2023

On Single Index Models beyond Gaussian Data
Joan Bruna, Loucas Pillaud-Vivien, Aaron Zweig
High Dimensional Stochastic Gradient Descent Gaussian Data High Dimensional Regime Single Index Model Link Function

April 13, 2023

D-SVM over Networked Systems with Non-Ideal Linking Conditions
Mohammadreza Doostmohammadian, Alireza Aghasi, Houman Zarrabi
Optimization Algorithm Multi Agent Network Networked System Link Function

January 27, 2023

LegendreTron: Uprising Proper Multiclass Loss Learning
Kevin Lam, Christian Walder, Spiridon Penev, Richard Nock
Loss Function Supervised Baseline Class Loss Link Function

January 26, 2023

Causal Graph Discovery from Self and Mutually Exciting Time Series
Song Wei, Yao Xie, Christopher S. Josef, Rishikesan Kamaleswaran
Structural Causal Model Directed Acyclic Graph Self Information Causal Graph Discovery Link Function

April 22, 2022

A piece-wise constant approximation for non-conjugate Gaussian Process models
Sarem Seitz
Gaussian Process Sparse Variational Gaussian Process Link Function