Provable Subspace Identification Under Post-Nonlinear Mixtures

10/14/2022
by   Qi Lyu, et al.
0

Unsupervised mixture learning (UML) aims at identifying linearly or nonlinearly mixed latent components in a blind manner. UML is known to be challenging: Even learning linear mixtures requires highly nontrivial analytical tools, e.g., independent component analysis or nonnegative matrix factorization. In this work, the post-nonlinear (PNL) mixture model – where unknown element-wise nonlinear functions are imposed onto a linear mixture – is revisited. The PNL model is widely employed in different fields ranging from brain signal classification, speech separation, remote sensing, to causal discovery. To identify and remove the unknown nonlinear functions, existing works often assume different properties on the latent components (e.g., statistical independence or probability-simplex structures). This work shows that under a carefully designed UML criterion, the existence of a nontrivial null space associated with the underlying mixing system suffices to guarantee identification/removal of the unknown nonlinearity. Compared to prior works, our finding largely relaxes the conditions of attaining PNL identifiability, and thus may benefit applications where no strong structural information on the latent components is known. A finite-sample analysis is offered to characterize the performance of the proposed approach under realistic settings. To implement the proposed learning criterion, a block coordinate descent algorithm is proposed. A series of numerical experiments corroborate our theoretical claims.

READ FULL TEXT

page 1

page 2

page 3

page 4

research
06/16/2021

Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder

This work focuses on the problem of unraveling nonlinearly mixed latent ...
research
01/06/2019

Learning Nonlinear Mixtures: Identifiability and Algorithm

Linear mixture models have proven very useful in a plethora of applicati...
research
06/14/2022

On Finite-Sample Identifiability of Contrastive Learning-Based Nonlinear Independent Component Analysis

Nonlinear independent component analysis (nICA) aims at recovering stati...
research
09/19/2019

Neural Network-Assisted Nonlinear Multiview Component Analysis: Identifiability and Algorithm

Multiview analysis aims at extracting shared latent components from data...
research
02/22/2018

Learning Mixtures of Linear Regressions with Nearly Optimal Complexity

Mixtures of Linear Regressions (MLR) is an important mixture model with ...
research
02/04/2021

Nonlinear Independent Component Analysis for Continuous-Time Signals

We study the classical problem of recovering a multidimensional source p...
research
06/09/2021

Independent mechanism analysis, a new concept?

Independent component analysis provides a principled framework for unsup...

Please sign up or login with your details

Forgot password? Click here to reset