A recursive least-squares extension of the natural gradient algorithm for blind signal separation of audio mixtures
Bibliographic record
Abstract
this paper. 2. EXISTING MAXIMUM-LIKELIHOOD BASED ALGORITHMS Let N i n s i , , 2 , 1 ), ( K = be scalar inputs (or sources) to the blind signal separation model at a time n . For simplicity, it is assumed that the mixing is linear and that the mixing matrix is square, i.e. the number of inputs N is equal to the number of mixtures N i n x i , , 2 , 1 ), ( K = . Therefore, the mixing matrix A is a square matrix of size N N . The mixing model can be expressed as: ) ( ) ( n n s A x = (1). The mixture x is then applied to a whitening matrix V . The resulting whitened mixtures in z are expressed as: ) ( ) ( ) ( ) ( n n n n s B s A V x V z = = = (2), where B is the resulting mixing matrix after the whitening stage. The purpose of the blind signal separation algorithms is to estimate a matrix W such that N N = I B W , where I is an identity matrix. Then the outputs of the separation process referred to as ) (n y would be identical to the source inputs ) (n s . Maximum Likelihood targets a separation via increasing the likelihood between the outputs ) (n i y and the inputs ) (n i s [5]. In the case of pre-whitened inputs, the cost function of the log-likelihood ) (W L of the de-mixing matrix W can be expressed as: # # # # # # # # # = # i i i p E L ) ( log ) ( z w W (3), where {} E refers to the expected value, i w is the th i row of the matrix W and () i p is a probability density function. The above cost function has the gradient ) (W L # as: # # # # # # # # # = = # # i T E L ) ( g log ) ( z y W (4), where i p y g = ) ( and is usually set to ) tanh( 2 i y for supergaussian data, such as audio data. Pre-whitening also constrains the matrix W to be orthogonal, meaning that N N = I W W . This constraint places the optimization of the cost func...
Fetched live from OpenAlex and de-inverted. Abstracts are not stored in this database: the inverted indexes are 8.6 GB of the frame’s 9.3 GB of text, and the host has 13 GB free.
How this classification was reachedexpand
Full frame distilled prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. Learned from the 10,348 direct Codex labels and 10,348 direct Gemma labels. Candidate is the union of thresholded teacher heads; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels or direct frontier model labels.
Codex and Gemma teacher scores by category
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.000 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.000 |
| Scholarly communication | 0.000 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.000 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one teacher head, not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".