Latent variable models with hidden binary units appear in various applications. Learning such models, in particular in the presence of noise, is a challenging computational problem. In this paper we propose a novel spectral approach to this problem, based on the eigenvectors of both the second order moment matrix and third order moment tensor of the observed data. We prove that under mild non-degeneracy conditions, our method consistently estimates the model parameters at the optimal parametric rate. Our tensor-based method generalizes previous orthogonal tensor decomposition approaches, where the hidden units were assumed to be either statistically independent or mutually exclusive. We illustrate the consistency of our method on simulated data and demonstrate its usefulness in learning a common model for population mixtures in genetics.
|Original language||American English|
|Title of host publication||35th International Conference on Machine Learning, ICML 2018|
|Editors||Jennifer Dy, Andreas Krause|
|Publisher||International Machine Learning Society (IMLS)|
|Number of pages||15|
|State||Published - 2018|
|Event||35th International Conference on Machine Learning, ICML 2018 - Stockholm, Sweden|
Duration: 10 Jul 2018 → 15 Jul 2018
|Name||35th International Conference on Machine Learning, ICML 2018|
|Conference||35th International Conference on Machine Learning, ICML 2018|
|Period||10/07/18 → 15/07/18|
Bibliographical noteFunding Information:
This research was funded in part by NIH Grant 1R01HG008383-01A1.
© 2018 by authors.All right reserved.