Blind Source Separation (ICA / cocktail-party problem) L1-388
Unclaimed Principle — open for contribution
This Principle is declared in the catalog but has no reference solver, no pinned dataset, and is not registered on-chain. There is no reward pool. Submitting a cert against this Principle today will record the cert for reproducibility but pay zero PWM.
To claim it as a Bounty #7 contribution: open a PR adding (1) a reference solver, (2) ≥1 dataset pinned to IPFS, (3) updates to the L3 manifest with dataset CIDs. After verifier-agent triple-review, the founders' 3-of-5 multisig signs PWMRegistry.register() and the Principle becomes mineable.
Forward model E
N independent sources s_k[t] are linearly mixed by an unknown channel matrix A in R^{M x N} producing M observed sensor signals y[t] = A*s[t]. The goal is to recover both A and s up to scale and permutation ambiguity using only statistical assumptions (non-Gaussianity, non-stationarity, sparsity, or temporal structure).
L-DAG
Well-posedness W
- Existence:
- true
- Uniqueness:
- up to permutation and scale
- Stability:
- conditional
- κ:
- 100
Identifiable when at most one source is Gaussian (Darmois-Skitovich theorem). Convolutive BSS requires additional constraint (temporal coloration or higher statistics). Underdetermined (N > M) requires sparsity prior.
Solvability C
- Solver class:
- FastICA (deflation, symmetric), Infomax, JADE, SOBI (second-order blind), AMUSE, non-negative (NMF), deep (Conv-TasNet, DPRNN for audio)
- Convergence rate q:
- 2
- Complexity:
- FastICA: O(T*N^2) per iteration; JADE: O(N^4); SOBI: O(N*L^2) for L time lags