New Method for Recovering Components from Unlabeled Finite Mixtures Using Marginal Independence
Researchers have proposed a theoretical framework and estimator for recovering latent components from unlabeled finite mixture distributions without requiring labels, clean samples, or known mixing weights. The key identifying signal is marginal independence — the assumption that each latent component is statistically independent on at least one coordinate pair. The work advances unsupervised learning by providing identifiability guarantees and a practical estimator with convergence proofs, validated on synthetic and flow-cytometry data.
A new preprint submitted to arXiv introduces a framework for component recovery and mixing-matrix estimation from unlabeled finite mixtures, where observable distributions share the same latent components but have unknown mixing weights. The central theoretical contribution is a structural result showing that, under linear independence of univariate marginals, any independent affine combination of components must coincide with a single component — a property that extends to observable mixtures under full-rank and no-cancellation conditions. When every component exhibits marginal independence on at least one coordinate pair, all components are identifiable and the mixing matrix is recoverable. The authors propose a Product-Marginal Maximum Mean Discrepancy (PM-MMD) estimator and prove uniform convergence and stability under approximate marginal independence. An important practical distinction is drawn between irreducibility, which is not directly testable from unlabeled mixtures alone, and marginal independence, which yields a candidate-level diagnostic via held-out PM-MMD. Experiments on controlled datasets and flow-cytometry data demonstrate that condition-aware representative selection stabilizes PM-MMD and outperforms clustering, factorization, and pairwise mixture-proportion baselines.
What's missing
The scope of the flow-cytometry experiments — including dataset size, number of components, and generalizability to other biological or real-world domains — is not detailed in the abstract.
What different sources said
- arXiv cs.LGCenter
Identifiability and Estimation for Unlabeled Finite Mixtures under Marginal Independence
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