Non-independent component analysis
The Annals of Statistics · 2024 · Volume 52 · Issue 6
Abstract
A seminal result in the ICA literature states that for AY=ε, if the components of ε are independent and at most one is Gaussian, then A is identified up to sign and permutation of its rows (Signal Process. 36 (1994)). In this paper we study to which extent the independence assumption can be relaxed by replacing it with restrictions on higher order moment or cumulant tensors of ε. We document new conditions that establish identification for several nonindependent component models, for example, common variance models, and propose efficient estimation methods based on the identification results. We show that in situations where independence cannot be assumed the efficiency gains can be significant relative to methods that rely on independence.
Keywords
15A69, 62H99, Cumulants, Identifiability, Independent component analysis, tensors
Enable JavaScript for citation tools and additional paper interactions.