Bellman Conformal Inference: Calibrating Prediction Intervals For Time Series
This provides a solution for time series forecasting applications needing reliable uncertainty quantification, though it is incremental as it builds on conformal inference with a novel optimization twist.
The paper tackles the problem of generating calibrated prediction intervals for time series forecasting by introducing Bellman Conformal Inference (BCI), which optimizes interval lengths using a stochastic control approach and achieves long-term coverage under distribution shifts, resulting in substantially shorter intervals compared to existing methods.
We introduce Bellman Conformal Inference (BCI), a framework that wraps around any time series forecasting models and provides approximately calibrated prediction intervals. Unlike existing methods, BCI is able to leverage multi-step ahead forecasts and explicitly optimize the average interval lengths by solving a one-dimensional stochastic control problem (SCP) at each time step. In particular, we use the dynamic programming algorithm to find the optimal policy for the SCP. We prove that BCI achieves long-term coverage under arbitrary distribution shifts and temporal dependence, even with poor multi-step ahead forecasts. We find empirically that BCI avoids uninformative intervals that have infinite lengths and generates substantially shorter prediction intervals in multiple applications when compared with existing methods.