Learning Mixtures of Low-Rank Models

Yanxi Chen, Cong Ma, H. Vincent Poor, Yuxin Chena

Research output: Contribution to journalArticlepeer-review

Abstract

We study the problem of learning mixtures of low-rank models, i.e. reconstructing multiple low-rank matrices from unlabelled linear measurements of each. This problem enriches two widely studied settings—low-rank matrix sensing and mixed linear regression — by bringing latent variables (i.e. unknown labels) and structural priors (i.e. low-rank structures) into consideration. To cope with the non-convexity issues arising from unlabelled heterogeneous data and low-complexity structure, we develop a three-stage meta-algorithm that is guaranteed to recover the unknown matrices with near-optimal sample and computational complexities under Gaussian designs. In addition, the proposed algorithm is provably stable against random noise. We complement the theoretical studies with empirical evidence that confirms the efficacy of our algorithm.

Original languageEnglish (US)
JournalIEEE Transactions on Information Theory
DOIs
StateAccepted/In press - 2021

All Science Journal Classification (ASJC) codes

  • Information Systems
  • Computer Science Applications
  • Library and Information Sciences

Keywords

  • Estimation
  • Linear regression
  • Matrix decomposition
  • Optimization
  • Sensors
  • Symmetric matrices
  • Task analysis
  • heterogeneous data
  • latent variable models
  • matrix sensing
  • meta-learning
  • mixed linear regression
  • non-convex optimization

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