Piecewise Polynomial

Piecewise polynomial functions, which approximate complex relationships by dividing the input space into segments and fitting a polynomial to each, are a powerful tool for modeling diverse data. Current research focuses on improving breakpoint identification algorithms for enhanced accuracy and efficiency, exploring the use of orthogonal polynomial bases and machine learning optimization techniques for better approximation and continuity, and developing efficient methods for piecewise polynomial regression, particularly for non-smooth functions. These advancements are impacting fields ranging from trajectory planning and electronic cam design to neural network verification and time series modeling, offering improved accuracy and interpretability in various applications.

Papers

October 14, 2024

A Counterexample in Image Registration
Serap A. Savari
Image Registration Piecewise Polynomial Counter Example

August 25, 2024

Improved identification of breakpoints in piecewise regression and its applications
Taehyeong Kim, Hyungu Lee, Hayoung Choi
Financial Application Novel Algorithm Greedy Algorithm Identification Accuracy Change Point Piecewise Polynomial

March 13, 2024

Machine Learning Optimized Orthogonal Basis Piecewise Polynomial Approximation
Hannes Waclawek, Stefan Huber
Gradient Descent Gradient Based Trajectory Planning Continuous Optimization Orthogonal Basis Piecewise Polynomial

March 4, 2024

Exponential Expressivity of ReLU$^k$ Neural Networks on Gevrey Classes with Point Singularities
Joost A. A. Opschoor, Christoph Schwab
Neural Network Singularity Free Expressivity Transfer Piecewise Polynomial Polygonal Domain Twenty Thousand Class

January 15, 2024

Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials
Ante Marić, Yiming Li, Sylvain Calinon
Online Learning Implicit Representation Shape Prior Gradient Information Piecewise Polynomial Polynomial Basis Smooth Representation

November 22, 2023

Piecewise Polynomial Regression of Tame Functions via Integer Programming
Gilles Bareilles, Johannes Aspman, Jiri Nemecek, Jakub Marecek
Integer Programming Polynomial System Nonconvex Function Piecewise Polynomial Tame Function

October 23, 2023

Mid-Long Term Daily Electricity Consumption Forecasting Based on Piecewise Linear Regression and Dilated Causal CNN
Zhou Lan, Ben Liu, Yi Feng, Danhuang Dong, Peng Zhang
Consumption Forecasting Electricity Demand Energy Prediction Piecewise Polynomial Mid Term Electricity

August 10, 2023

Optimizing Performance of Feedforward and Convolutional Neural Networks through Dynamic Activation Functions
Chinmay Rane, Kanishka Tyagi, Michael Manry
Convolutional Neural Network ReLU Activation Performance Optimization Transformer Feed Forward Layer Piecewise Polynomial

February 10, 2023

Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Making
Adam Block, Alexander Rakhlin, Max Simchowitz
Adversarial Learning Computational Complexity Online Prediction Piecewise Polynomial Smoothed Online Learning

November 27, 2022

Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions
Tu Anh-Nguyen, Joey Huchette
Neural Network Verification Compositional Ability New Formulation Piecewise Polynomial

October 19, 2022

Irregularly-Sampled Time Series Modeling with Spline Networks
Marin Biloš, Emanuel Ramneantu, Stephan Günnemann
Neural Network Time Series B Spline Random Sequence Free Counterpart Piecewise Polynomial Spline Based

May 25, 2022

Efficient and Near-Optimal Smoothed Online Learning for Generalized Linear Functions
Adam Block, Max Simchowitz
High Efficiency Optimal Regret Statistical Learning Piecewise Polynomial Sigma Lognormal Smoothed Online Learning Linear Function

November 11, 2021

Model-Based Reinforcement Learning via Stochastic Hybrid Models
Hany Abdulsamad, Jan Peters
Model Based Reinforcement Learning Nonlinear Dynamic Nonlinear Model Hybrid Modeling Piecewise Polynomial

Piecewise Polynomial

Papers

A Counterexample in Image Registration

Improved identification of breakpoints in piecewise regression and its applications

Machine Learning Optimized Orthogonal Basis Piecewise Polynomial Approximation

Exponential Expressivity of ReLU$^k$ Neural Networks on Gevrey Classes with Point Singularities

Online Learning of Continuous Signed Distance Fields Using Piecewise Polynomials

Piecewise Polynomial Regression of Tame Functions via Integer Programming

Mid-Long Term Daily Electricity Consumption Forecasting Based on Piecewise Linear Regression and Dilated Causal CNN

Optimizing Performance of Feedforward and Convolutional Neural Networks through Dynamic Activation Functions

Oracle-Efficient Smoothed Online Learning for Piecewise Continuous Decision Making

Neural Network Verification as Piecewise Linear Optimization: Formulations for the Composition of Staircase Functions

Irregularly-Sampled Time Series Modeling with Spline Networks

Efficient and Near-Optimal Smoothed Online Learning for Generalized Linear Functions

Model-Based Reinforcement Learning via Stochastic Hybrid Models