Filtered Conformal Ellipsoids for Graph-Native Time Series

2012-03-01 · Source: stat.ML updates on arXiv.org · Field: Technology & Digital — Artificial Intelligence & Machine Learning, Data Science & Analytics · Depth: Expert, extended

Summary

Filtered Conformal Ellipsoids for Graph-Native Time Series introduces a novel method for generating joint prediction sets for multivariate time series, particularly effective for graph-native data. This approach integrates a frozen state-space filter, such as a GCN-GRU, to emit a one-step predictive mean and covariance, which dictates the ellipsoid's shape. Concurrently, split-conformal calibration is applied to the resulting Mahalanobis scores to determine the scalar radius, ensuring coverage without relying on Gaussian tail probabilities. The theoretical framework addresses challenges posed by dependent filtered scores and non-contracting recurrent hidden states by analyzing contraction within an "observable predictive-law quotient." Empirically, the learned graph filter (gnf) demonstrates superior sharpness on moderate-size graph-native traffic benchmarks like metr-la-20 and pems-bay-50, achieving width reductions of 23.6% and 40.5% over Static-CGIF. However, its effectiveness is context-dependent, with factor and copula baselines outperforming it on full-graph scale or non-graph-native datasets.

Key takeaway

For Machine Learning Engineers deploying forecasters for correlated sensor streams, Filtered Conformal Ellipsoids offer a robust approach to generate sharper joint prediction sets. If your application involves moderate-size graph-native multivariate time series, consider implementing the GCN-GRU-based "gnf" filter, which demonstrated significant width improvements. However, for full-graph scale or non-graph-native datasets, evaluate factor or copula baselines, as their performance can be superior in those contexts.

Key insights

Filtered conformal ellipsoids use learned covariance for shape and calibration for radius, achieving sharper, valid joint prediction sets.

Principles

• Filter determines ellipsoid shape; conformal calibration determines radius.
• Conformal calibration ensures coverage without relying on Gaussian tail probabilities.
• Analyze recurrent filter stability in an observable predictive-law quotient.

Method

Fit a frozen filter (e.g., GCN-GRU) to emit mean/covariance, then apply split-conformal calibration to Mahalanobis scores from a chronological block to define ellipsoidal prediction sets.

In practice

• Use "gnf" for moderate-N graph-native traffic for sharper ellipsoids.
• Consider factor/copula baselines for full-graph or non-graph-native data.
• Audit contraction and score-dependence quantities for filter stability.

Topics

• Conformal Prediction
• Multivariate Time Series
• Graph Neural Networks
• Predictive Uncertainty
• Mahalanobis Distance
• Traffic Forecasting

Best for: Research Scientist, AI Scientist, Machine Learning Engineer, Data Scientist

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Editorial summary, takeaway, and curation by AIssential. Original article published by stat.ML updates on arXiv.org.