Kinks vs. Smoothness: Identifiability of Real Analytic nICA for Laplace-like Sources
Many machine learning systems try to explain complex data - like images or financial time series - in terms of hidden, independent factors that generated them. Recovering the true underlying factors, rather than some scrambled version of them, is the central challenge of nonlinear Independent Component Analysis (nICA). We prove identifiability (exact recovery) up to trivial ambiguities for real analytic generating functions when source probability density functions have a finite number of discontinuities in the first derivative. The Laplace distribution is the most prominent example satisfying this assumption. Our proof relies on the contrast between kinks in the source distribution and t...
| Authors | Isaac Manring, Kejun Huang |
|---|---|
| Primary category | cs.LG |
| Published | 18 September 2026 |
| Last updated at source | 7 October 2026 |
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