Characteristic Function

The characteristic function (CF), the Fourier transform of a probability distribution, offers a powerful alternative to directly modeling probability density functions, particularly for complex or high-dimensional data. Current research focuses on leveraging CFs in various applications, including generative modeling (using CF networks and graph optimizers for improved sample generation), causal inference (estimating interventional distributions in hybrid domains via characteristic interventional sum-product networks), and explainable AI (improving the accuracy and reliability of SHAP scores by refining the underlying CFs). This renewed interest in CFs is driven by their ability to handle diverse data types and circumvent limitations of traditional methods, leading to advancements in areas like time-series generation, stochastic system identification, and probabilistic neural network verification.

Papers

November 7, 2024

Interpretable Measurement of CNN Deep Feature Density using Copula and the Generalized Characteristic Function
David Chapman, Parniyan Farvardin
Deep Feature Deep Representation Dimensional Copula Characteristic Function Feature Density Interpretability Evaluation

October 23, 2024

Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform
Bastian Rieck
Machine Learning Gentle Introduction Topology Problem Topological Information Characteristic Function Topological Invariance Euler Characteristic

September 19, 2024

CF-GO-Net: A Universal Distribution Learner via Characteristic Function Networks with Graph Optimizers
Zeyang Yu, Shengxi Li, Danilo Mandic
Generative Model Generative Modeling Universal Learning Graph Optimization Characteristic Function

August 14, 2024

$\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains
Harsh Poonia, Moritz Willig, Zhongjie Yu, Matej Zečević, Kristian Kersting, Devendra Singh Dhami
Causal Inference Sum Product Network Characteristic Function Interventional Distribution

April 30, 2024

On Correcting SHAP Scores
Olivier Letoffe, Xuanxiang Huang, Joao Marques-Silva
Feature Attribution Characteristic Function SHAP Score

January 9, 2024

Generative neural networks for characteristic functions
Florian Brück
Loss Function Maximum Mean Discrepancy Generative Neural Network Characteristic Function

May 21, 2023

PCF-GAN: generating sequential data via the characteristic function of measures on the path space
Hang Lou, Siran Li, Hao Ni
Generative Adversarial Network Sequential Data New Measure Characteristic Function

December 6, 2022

Drift Identification for L\'{e}vy alpha-Stable Stochastic Systems
Harish S. Bhat
Data Drift Alpha Stable Characteristic Function

December 3, 2022

Probabilistic Verification of ReLU Neural Networks via Characteristic Functions
Joshua Pilipovsky, Vignesh Sivaramakrishnan, Meeko M. K. Oishi, Panagiotis Tsiotras
Neural Network ReLU Neural Network Characteristic Function Probabilistic Verification

August 16, 2022

Measuring Statistical Dependencies via Maximum Norm and Characteristic Functions
Povilas Daniušis, Shubham Juneja, Lukas Kuzma, Virginijus Marcinkevičius
P$ Norm Statistical Dependency Characteristic Function

June 18, 2022

Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach
Yuchen Zhu, Limor Gultchin, Arthur Gretton, Matt Kusner, Ricardo Silva
Causal Inference Causal Effect Novel Regression Kernel Method Measurement Error Characteristic Function Kernel Based Estimator Nonparametric Instrumental Variable

May 20, 2022

Learning Task-relevant Representations for Generalization via Characteristic Functions of Reward Sequence Distributions
Rui Yang, Jie Wang, Zijie Geng, Mingxuan Ye, Shuiwang Ji, Bin Li, Feng Wu
Strong Generalization Visual Reinforcement Learning DeepMind Control Suite Reward Prediction Characteristic Function Reward Distribution Task Induced Representation

Characteristic Function

Papers

Interpretable Measurement of CNN Deep Feature Density using Copula and the Generalized Characteristic Function

Topology meets Machine Learning: An Introduction using the Euler Characteristic Transform

CF-GO-Net: A Universal Distribution Learner via Characteristic Function Networks with Graph Optimizers

$\chi$SPN: Characteristic Interventional Sum-Product Networks for Causal Inference in Hybrid Domains

On Correcting SHAP Scores

Generative neural networks for characteristic functions

PCF-GAN: generating sequential data via the characteristic function of measures on the path space

Drift Identification for L\'{e}vy alpha-Stable Stochastic Systems

Probabilistic Verification of ReLU Neural Networks via Characteristic Functions

Measuring Statistical Dependencies via Maximum Norm and Characteristic Functions

Causal Inference with Treatment Measurement Error: A Nonparametric Instrumental Variable Approach

Learning Task-relevant Representations for Generalization via Characteristic Functions of Reward Sequence Distributions