{"about":{"site":"https://codewithpapers.app","non_affiliation":"Code with Papers and Syntology are not affiliated with, endorsed by, or sponsored by Papers with Code, Meta, or the pwc-archive mirror.","licence":"CC BY-SA 4.0","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","attribution":"https://codewithpapers.app/attribution","modified":"archive material modified by Syntology; see the attribution page"},"url":"/paper/a-discriminative-approach-to-bayesian","title":"A Discriminative Approach to Bayesian Filtering with Applications to Human Neural Decoding","arxiv_id":"1807.06173","date":"2018-07-17","proceeding":null,"authors":["Michael C. Burkhart"],"abstract":"Given a stationary state-space model that relates a sequence of hidden states\nand corresponding measurements or observations, Bayesian filtering provides a\nprincipled statistical framework for inferring the posterior distribution of\nthe current state given all measurements up to the present time. For example,\nthe Apollo lunar module implemented a Kalman filter to infer its location from\na sequence of earth-based radar measurements and land safely on the moon.\n  To perform Bayesian filtering, we require a measurement model that describes\nthe conditional distribution of each observation given state. The Kalman filter\ntakes this measurement model to be linear, Gaussian. Here we show how a\nnonlinear, Gaussian approximation to the distribution of state given\nobservation can be used in conjunction with Bayes' rule to build a nonlinear,\nnon-Gaussian measurement model. The resulting approach, called the\nDiscriminative Kalman Filter (DKF), retains fast closed-form updates for the\nposterior. We argue there are many cases where the distribution of state given\nmeasurement is better-approximated as Gaussian, especially when the\ndimensionality of measurements far exceeds that of states and the Bernstein-von\nMises theorem applies. Online neural decoding for brain-computer interfaces\nprovides a motivating example, where filtering incorporates increasingly\ndetailed measurements of neural activity to provide users control over external\ndevices. Within the BrainGate2 clinical trial, the DKF successfully enabled\nthree volunteers with quadriplegia to control an on-screen cursor in real-time\nusing mental imagery alone. Participant \"T9\" used the DKF to type out messages\non a tablet PC.","url_abs":"http://arxiv.org/abs/1807.06173v1","url_pdf":"http://arxiv.org/pdf/1807.06173v1.pdf","source":{"archive":"pwc-archive (Hugging Face), CC BY-SA 4.0","snapshot":"2025-07-28","licence_url":"https://creativecommons.org/licenses/by-sa/4.0/legalcode","row_kind":"abstracts"},"code_links":[{"paper_slug":"a-discriminative-approach-to-bayesian","repo_url":"https://github.com/burkh4rt/DKF-implementations","is_official":1,"mentioned_in_paper":0,"mentioned_in_github":0,"framework":"none","reach":null}],"tasks":[{"task_slug":"sequential-bayesian-inference","task_name":"Sequential Bayesian Inference"}],"methods":[],"datasets_introduced":[],"methods_introduced":[],"results":[],"syntology":{"atlas_url":null,"mcp":null,"developers":"https://syntology.ai/developers"},"arxiv_metadata":null,"syntology_extracted_results":null}