[Re] The Discriminative Kalman Filter for Bayesian Filtering with Nonlinear and Non-Gaussian Observation Models

TL;DR

The paper tackles neural decoding under nonlinear and non-Gaussian observation models by evaluating the Discriminative Kalman Filter (DKF) as a Bayesian filtering approach. It implements a Python reproduction of Burkhart et al.'s DKF framework and reproduces Experiment 4.5 on a center-out reaching dataset, comparing DKF against linear KF, NW, GP, NN, and LSTM regressions, as well as EKF/UKF variants. The findings show that DKF with NW regression (DKF-NW) frequently achieves the best MAEE and generally improves over the Kalman baseline, though nRMSE gains are more modest and some implementations (e.g., GP) suffer from translation to Python. The work demonstrates practical viability of DKF in neuroprosthetics and suggests integrating discriminative filtering with modern latent-state models for improved neural decoding.

Abstract

Kalman filters provide a straightforward and interpretable means to estimate hidden or latent variables, and have found numerous applications in control, robotics, signal processing, and machine learning. One such application is neural decoding for neuroprostheses. In 2020, Burkhart et al. thoroughly evaluated their new version of the Kalman filter that leverages Bayes' theorem to improve filter performance for highly non-linear or non-Gaussian observation models. This work provides an open-source Python alternative to the authors' MATLAB algorithm. Specifically, we reproduce their most salient results for neuroscientific contexts and further examine the efficacy of their filter using multiple random seeds and previously unused trials from the authors' dataset. All experiments were performed offline on a single computer.

Figures (1)

• Figure 1: Summary of how the observation and process models of various Bayesian filtering methods relax those of the Kalman filter.