Nonlinear Correlation

Nonlinear correlation analysis focuses on identifying and quantifying relationships between variables that are not linearly related, a crucial task in diverse fields hampered by the limitations of traditional linear methods. Current research emphasizes developing novel algorithms and model architectures, such as transformers and normalizing flows, to capture these complex relationships within high-dimensional data, including multivariate time series and multimodal representations. This work is significant for improving the accuracy and reliability of machine learning models across various applications, from forecasting to medical image analysis, by enabling more nuanced understanding of data dependencies. Furthermore, uncovering nonlinear correlations helps address issues like adversarial attacks and biases in machine learning systems.

Papers

June 22, 2024

Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations
Lorenzo Basile, Santiago Acevedo, Luca Bortolussi, Fabio Anselmi, Alex Rodriguez
Latent Representation Multimodal Representation Low Dimensional Manifold Latent Manifold Intrinsic Dimensionality Nonlinear Correlation

May 19, 2024

VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting
Yingnan Yang, Qingling Zhu, Jianyong Chen
Multivariate Time Series Multivariate Time Series Forecasting Cross Correlation Attention Based Correlation Module Correlation Transformer Nonlinear Correlation

May 24, 2023

Relating Implicit Bias and Adversarial Attacks through Intrinsic Dimension
Lorenzo Basile, Nikos Karantzas, Alberto D'Onofrio, Luca Bortolussi, Alex Rodriguez, Fabio Anselmi
Neural Network Adversarial Attack Implicit Bias Intrinsic Dimension Nonlinear Correlation

May 4, 2023

Accuracy on the Curve: On the Nonlinear Correlation of ML Performance Between Data Subpopulations
Weixin Liang, Yining Mao, Yongchan Kwon, Xinyu Yang, James Zou
Machine Learning Model Performance Spurious Correlation Aggregated Curve Semantically Meaningful Subpopulation Property Nonlinear Correlation

April 11, 2023

Prediction of brain tumor recurrence location based on multi-modal fusion and nonlinear correlation learning
Tongxue Zhou, Alexandra Noeuveglise, Romain Modzelewski, Fethi Ghazouani, Sébastien Thureau, Maxime Fontanilles, Su Ruan
Human Prediction Tumor Segmentation Multi Modal Fusion Nonlinear Correlation Brain Cancer

December 28, 2022

End-to-End Modeling Hierarchical Time Series Using Autoregressive Transformer and Conditional Normalizing Flow based Reconciliation
Shiyu Wang, Fan Zhou, Yinbo Sun, Lintao Ma, James Zhang, Yangfei Zheng, Bo Zheng, Lei Lei, Yun Hu
End to End Multivariate Time Series Forecasting Autoregressive Transformer Conditional Normalizing Flow Hierarchical Datasets Hierarchical Time Series Hierarchical Time Series Forecasting Nonlinear Correlation

December 20, 2022

A Pattern Discovery Approach to Multivariate Time Series Forecasting
Yunyao Cheng, Chenjuan Guo, Kaixuan Chen, Kai Zhao, Bin Yang, Jiandong Xie, Christian S. Jensen, Feiteng Huang, Kai Zheng
Multivariate Time Series Forecasting Complex Time Series Pattern Discovery Correlation Learning Nonlinear Correlation

Nonlinear Correlation

Papers

Intrinsic Dimension Correlation: uncovering nonlinear connections in multimodal representations

VCformer: Variable Correlation Transformer with Inherent Lagged Correlation for Multivariate Time Series Forecasting

Relating Implicit Bias and Adversarial Attacks through Intrinsic Dimension

Accuracy on the Curve: On the Nonlinear Correlation of ML Performance Between Data Subpopulations

Prediction of brain tumor recurrence location based on multi-modal fusion and nonlinear correlation learning

End-to-End Modeling Hierarchical Time Series Using Autoregressive Transformer and Conditional Normalizing Flow based Reconciliation

A Pattern Discovery Approach to Multivariate Time Series Forecasting