GCKAN extends Kolmogorov-Arnold Networks to analyze time series causality by extracting base weights and using sparsity penalties, enabling automatic time lag selection and improved inference accuracy.
https://arxiv.org/abs/2501.08958
🤔 Original Problem :
→ Existing neural network models for Granger causality struggle with high-dimensional nonlinear time series and limited samples
→ RNN models can't select time lags automatically, while MLP models have low inference efficiency with noisy data
-----
🔧 Solution in this Paper :
→ Introduces GCKAN that uses learnable univariate functions at edges instead of weights, making computation more efficient
→ Extracts base weights from KAN layers and applies sparsity-inducing penalty with ridge regularization
→ Proposes time-reversed algorithm that compares original and reversed series to reduce spurious connections
→ Uses component-wise architecture where each time series component is modeled separately
-----
💡 Key Insights :
→ KAN's smaller computational graph enables better handling of high-dimensional data
→ Time-reversed causality helps validate true causal relationships
→ Automatic time lag selection improves accuracy significantly
-----
📊 Results :
→ Outperformed baselines on Lorenz-96 with AUROC of 0.995-1.0
→ Achieved highest performance in 22/28 fMRI simulations
→ Superior results on gene networks with limited samples (AUROC 0.747)
→ Perfect AUROC 1.0 on VAR dataset scenarios
Share this post