A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding

TL;DR

This paper introduces the Discriminative Kalman Filter (DKF), a nonlinear Bayesian filtering method that uses Gaussian approximations for improved neural decoding in brain-computer interfaces, enabling real-time control for users with paralysis.

Contribution

The paper presents the DKF, a novel nonlinear filtering approach that maintains closed-form updates and improves neural decoding accuracy in high-dimensional measurement scenarios.

Findings

DKF enables real-time neural decoding in brain-computer interfaces.

Successfully controlled cursor movements using neural signals in clinical trials.

Outperformed traditional methods in accuracy and computational efficiency.

Abstract

Given a stationary state-space model that relates a sequence of hidden states and corresponding measurements or observations, Bayesian filtering provides a principled statistical framework for inferring the posterior distribution of the current state given all measurements up to the present time. For example, the Apollo lunar module implemented a Kalman filter to infer its location from a sequence of earth-based radar measurements and land safely on the moon. To perform Bayesian filtering, we require a measurement model that describes the conditional distribution of each observation given state. The Kalman filter takes this measurement model to be linear, Gaussian. Here we show how a nonlinear, Gaussian approximation to the distribution of state given observation can be used in conjunction with Bayes' rule to build a nonlinear, non-Gaussian measurement model. The resulting approach, called the Discriminative Kalman Filter (DKF), retains fast closed-form updates for the posterior. We argue there are many cases where the distribution of state given measurement is better-approximated as Gaussian, especially when the dimensionality of measurements far exceeds that of states and the Bernstein-von Mises theorem applies. Online neural decoding for brain-computer interfaces provides a motivating example, where filtering incorporates increasingly detailed measurements of neural activity to provide users control over external devices. Within the BrainGate2 clinical trial, the DKF successfully enabled three volunteers with quadriplegia to control an on-screen cursor in real-time using mental imagery alone. Participant "T9" used the DKF to type out messages on a tablet PC.