Integral Regression

Integral regression is a technique used to estimate a continuous output variable from an input, often represented as a probability distribution (e.g., a heatmap). Current research focuses on improving the accuracy and efficiency of integral regression methods, particularly by addressing inherent biases and developing novel algorithms, such as bias-compensated integral regression and those leveraging Choquet integrals, to enhance performance and interpretability. These advancements are impacting diverse fields, including human pose estimation and policy modeling, where integral regression facilitates the integration of multiple models and data sources for improved decision-making. The development of integral representations for various activation functions in neural networks also contributes to a deeper understanding of function approximation capabilities.

Papers

February 9, 2024

Towards participatory multi-modeling for policy support across domains and scales: a systematic procedure for integral multi-model design
Vittorio Nespeca, Rick Quax, Marcel G. M. Olde Rikkert, Hubert P. L. M. Korzilius, Vincent A. W. J. Marchau, Sophie Hadijsotiriou, Tom Oreel, Jannie Coenen, Heiman Wertheim, Alexey Voinov, Etiënne A. J. A. Rouwette, Vítor V. Vasconcelos
Health Policy Recommendation Multiple Model Ghanaian Musical Scale Model Collaboration Medical Procedure Model Paradigm Integral Regression

March 28, 2023

Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Control
Tyler Lekang, Andrew Lamperski
Neural Network Activation Function Function Approximation Random Participation Neural Network Approximation Model Reference Adaptive Integral Regression

January 25, 2023

Bias-Compensated Integral Regression for Human Pose Estimation
Kerui Gu, Linlin Yang, Michael Bi Mi, Angela Yao
Human Pose Estimation Integral Regression

November 3, 2022

A $k$-additive Choquet integral-based approach to approximate the SHAP values for local interpretability in machine learning
Guilherme Dean Pelegrina, Leonardo Tomazeli Duarte, Michel Grabisch
Machine Learning Shapley Value Shapley Interaction Local Interpretability SHAP Value SHAP Clustering Integral Regression Choquet Integral

August 26, 2022

Large-N dynamics of the spiked tensor model with random initial conditions
Vasily Sazonov
Partial Differential Equation Saddle Point Initial Condition Spiked Tensor Integral Regression

December 20, 2021

Integral representations of shallow neural network with Rectified Power Unit activation function
Ahmed Abdeljawad, Philipp Grohs
Shallow Neural Network Shallow Network Integral Regression

Integral Regression

Papers

Towards participatory multi-modeling for policy support across domains and scales: a systematic procedure for integral multi-model design

Function Approximation with Randomly Initialized Neural Networks for Approximate Model Reference Adaptive Control

Bias-Compensated Integral Regression for Human Pose Estimation

A $k$-additive Choquet integral-based approach to approximate the SHAP values for local interpretability in machine learning

Large-N dynamics of the spiked tensor model with random initial conditions

Integral representations of shallow neural network with Rectified Power Unit activation function