Modeling Information Blackouts in Missing Not-At-Random Time Series Data

TL;DR

This paper introduces a latent state-space model for traffic data with blackouts, explicitly modeling missing not at random (MNAR) sensor failures to improve imputation and forecasting accuracy.

Contribution

It proposes a novel joint modeling framework combining traffic dynamics and sensor dropout mechanisms under MNAR assumptions, with an inference method using Extended Kalman Filter and EM.

Findings

Significant reduction in imputation RMSE compared to naive baselines.

Explicit MNAR modeling yields additional improvements, especially when missingness depends on latent states.

Temporal dynamics are the primary factor in performance gains.

Abstract

Large-scale traffic forecasting relies on fixed sensor networks that often exhibit blackouts: contiguous intervals of missing measurements caused by detector or communication failures. These outages are typically handled under a Missing At Random (MAR) assumption, even though blackout events may correlate with unobserved traffic conditions (e.g., congestion or anomalous flow), motivating a Missing Not At Random (MNAR) treatment. We propose a latent state-space framework that jointly models (i) traffic dynamics via a linear dynamical system and (ii) sensor dropout via a Bernoulli observation channel whose probability depends on the latent traffic state. Inference uses an Extended Kalman Filter with Rauch-Tung-Striebel smoothing, and parameters are learned via an approximate EM procedure with a dedicated update for detector-specific missingness parameters. On the Seattle inductive loop detector data, introducing latent dynamics yields large gains over naive baselines, reducing blackout imputation RMSE from 7.02 (LOCF) and 5.02 (linear interpolation + seasonal naive) to 4.23 (MAR LDS), corresponding to about a 64% reduction in MSE relative to LOCF. Explicit MNAR modeling provides a consistent but smaller additional improvement on real data (imputation RMSE 4.20; 0.8% RMSE reduction relative to MAR), with similar modest gains for short-horizon post-blackout forecasts (evaluated at 1, 3, and 6 steps). In controlled synthetic experiments, the MNAR advantage increases as the true missingness dependence on latent state strengthens. Overall, temporal dynamics dominate performance, while MNAR modeling offers a principled refinement that becomes most valuable when missingness is genuinely informative.