FreqLens: Interpretable Frequency Attribution for Time Series Forecasting

TL;DR

FreqLens is an interpretable time series forecasting framework that automatically discovers and attributes dominant frequency components with theoretical guarantees, achieving accurate and meaningful frequency identification.

Contribution

It introduces learnable frequency discovery and axiomatic frequency attribution, enabling automatic, interpretable, and theoretically grounded frequency analysis in forecasting models.

Findings

Discovered daily and half-daily cycles in Traffic data with high accuracy.

Identified weekly cycles in Weather data, significantly longer than input window.

Achieved competitive or superior forecasting performance.

Abstract

Time series forecasting models often lack interpretability, limiting their adoption in domains requiring explainable predictions. We propose \textsc{FreqLens}, an interpretable forecasting framework that discovers and attributes predictions to learnable frequency components. \textsc{FreqLens} introduces two key innovations: (1) \emph{learnable frequency discovery} -- frequency bases are parameterized via sigmoid mapping and learned from data with diversity regularization, enabling automatic discovery of dominant periodic patterns without domain knowledge; and (2) \emph{axiomatic frequency attribution} -- a theoretically grounded framework that provably satisfies Completeness, Faithfulness, Null-Frequency, and Symmetry axioms, with per-frequency attributions equivalent to Shapley values. On Traffic and Weather datasets, \textsc{FreqLens} achieves competitive or superior performance while discovering physically meaningful frequencies: all 5 independent runs discover the 24-hour daily cycle ($24.6 \pm 0.1$h, 2.5\% error) and 12-hour half-daily cycle ($11.8 \pm 0.1$h, 1.6\% error) on Traffic, and weekly cycles ($10\times$ longer than the input window) on Weather. These results demonstrate genuine frequency-level knowledge discovery with formal theoretical guarantees on attribution quality.