Beyond Accuracy: Information-Theoretic Decoder Evaluation Under Latent Intent

Abstract

A central challenge in assistive brain-to-robot control is decoding a user's latent intent from complex and noisy brain signals. Prior approaches evaluate decoders as single-trial classifiers with accuracy-based metrics, but this neglects the inherently sequential nature of assistive control. Since a planner must integrate intermittent, noisy decoder outputs over time, single-step accuracy can only be a proxy when predicting downstream task performance. We formalize brain-to-robot control as a partially observable Markov decision process (POMDP), and prove that there is a sharp phase transition: regret is uniformly bounded across the horizon as long as pairs of goals are all decoder-distinguishable, but grows linearly otherwise. We show that a single channel statistic, the worst-pair Chernoff information ${\Gamma }_{\min }$ sets this boundary. Then, we derive a closed-form regret predictor $U_{\mathrm{id}}(C)$, that can be computed from any confusion matrix in $O(K^2)$ time. Across two domains spanning orthogonal information channels, we show that $U_{\mathrm{id}}$ predicts cumulative planning regret beyond what accuracy can explain. We then highlight a pathological accuracy trap, in which two decoders have identical validation accuracy 35.1% on real EEG data (BNCI2014001 subject 5) but result in a difference of $9.6\times$ in held-out regret, which $U_{\mathrm{id}}$ predicts. Same-signal control confirms $U_{\mathrm{id}}$'s advantage with decoders that span independent feature channels. Ultimately, our work provides a drop-in diagnostic to evaluate and select sensors and decoders in sequential assistive control.