dorsal/arxiv
View SchemaA Bayesian approach to source separation
| Authors | Kevin H. Knuth |
|---|---|
| Categories | |
| ArXiv ID | physics/0205032 |
| URL | https://arxiv.org/abs/physics/0205032 |
| Journal | ICA99 Proceedings, Aussois, France, Jan. 1999, pp. 283-8 |
Abstract
The problem of source separation is by its very nature an inductive inference problem. There is not enough information to deduce the solution, so one must use any available information to infer the most probable solution. We demonstrate that source separation problems are well-suited for the Bayesian approach which provides a natural and logically consistent method by which one can incorporate prior knowledge to estimate the most probable solution given that knowledge. We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes' Theorem and demonstrate how the Bayesian methodology makes explicit the underlying assumptions. We then further demonstrate the power of the Bayesian approach by deriving two separation algorithms that incorporate additional prior information. One algorithm separates signals that are known a priori to be decorrelated and the other utilizes information about the signal propagation through the medium from the sources to the detectors.
{
"annotation_id": "509f4ac8-624b-404c-94b1-80b197c8e548",
"date_created": "2026-03-02T18:00:39.047000Z",
"date_modified": "2026-03-02T18:00:39.047000Z",
"file_hash": "034d94ab6f74ade514da59913d4fcdae70a03c4d67a710e4f996d23e82132ed2",
"private": false,
"record": {
"abstract": "The problem of source separation is by its very nature an inductive inference\nproblem. There is not enough information to deduce the solution, so one must\nuse any available information to infer the most probable solution. We\ndemonstrate that source separation problems are well-suited for the Bayesian\napproach which provides a natural and logically consistent method by which one\ncan incorporate prior knowledge to estimate the most probable solution given\nthat knowledge.\n We derive the Bell-Sejnowski ICA algorithm from first principles, i.e. Bayes\u0027\nTheorem and demonstrate how the Bayesian methodology makes explicit the\nunderlying assumptions. We then further demonstrate the power of the Bayesian\napproach by deriving two separation algorithms that incorporate additional\nprior information. One algorithm separates signals that are known a priori to\nbe decorrelated and the other utilizes information about the signal propagation\nthrough the medium from the sources to the detectors.",
"arxiv_id": "physics/0205032",
"authors": [
"Kevin H. Knuth"
],
"categories": [
"physics.data-an",
"math.PR",
"physics.bio-ph",
"physics.med-ph"
],
"journal_ref": "ICA99 Proceedings, Aussois, France, Jan. 1999, pp. 283-8",
"title": "A Bayesian approach to source separation",
"url": "https://arxiv.org/abs/physics/0205032"
},
"schema_id": "dorsal/arxiv",
"source": {
"execution_id": "b11ea712-7b10-45b3-80ae-92381dd92eec",
"id": "arXiv Dataset IDs",
"type": "Model",
"variant": "snapshot-2026-03-01",
"version": "0.1.0"
},
"user_id": 1000002
}