Timezone: »

 
Poster
Provable Subspace Identification Under Post-Nonlinear Mixtures
Qi Lyu · Xiao Fu

Thu Dec 01 02:00 PM -- 04:00 PM (PST) @ Hall J #603

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 {\it 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 {\it 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.

Author Information

Qi Lyu (Oregon State University)
Xiao Fu (Oregon State University)

Related Events (a corresponding poster, oral, or spotlight)

More from the Same Authors

  • 2022 : Under-Counted Tensor Completion with Neural Network-based Side Information Learner »
    Shahana Ibrahim · Xiao Fu · Rebecca Hutchinson · Eugene Seo
  • 2022 Spotlight: Lightning Talks 1A-3 »
    Kimia Noorbakhsh · Ronan Perry · Qi Lyu · Jiawei Jiang · Christian Toth · Olivier Jeunen · Xin Liu · Yuan Cheng · Lei Li · Manuel Rodriguez · Julius von Kügelgen · Lars Lorch · Nicolas Donati · Lukas Burkhalter · Xiao Fu · Zhongdao Wang · Songtao Feng · Ciarán Gilligan-Lee · Rishabh Mehrotra · Fangcheng Fu · Jing Yang · Bernhard Schölkopf · Ya-Li Li · Christian Knoll · Maks Ovsjanikov · Andreas Krause · Shengjin Wang · Hong Zhang · Mounia Lalmas · Bolin Ding · Bo Du · Yingbin Liang · Franz Pernkopf · Robert Peharz · Anwar Hithnawi · Julius von Kügelgen · Bo Li · Ce Zhang
  • 2019 Poster: Crowdsourcing via Pairwise Co-occurrences: Identifiability and Algorithms »
    Shahana Ibrahim · Xiao Fu · Nikolaos Kargas · Kejun Huang