Detection and Recovery of Hidden Submatrices

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In this paper, we study the problems of detection and recovery of hidden submatrices with elevated means inside a large Gaussian random matrix. We consider two different structures for the planted submatrices. In the first model, the planted matrices are disjoint, and their row and column indices can be arbitrary. Inspired by scientific applications, the second model restricts the row and column indices to be consecutive. In the detection problem, under the null hypothesis, the observed matrix is a realization of independent and identically distributed standard normal entries. Under the alternative, there exists a set of hidden submatrices with elevated means inside the same standard normal matrix. Recovery refers to the task of locating the hidden submatrices. For both problems, and for both models, we characterize the statistical and computational barriers by deriving information-theoretic lower bounds, designing and analyzing algorithms matching those bounds, and proving computational lower bounds based on the low-degree polynomials conjecture. In particular, we show that the space of the model parameters (i.e.,

Original languageEnglish
Pages (from-to)1-13
Number of pages13
JournalIEEE Transactions on Signal and Information Processing over Networks
StatePublished - 2024


  • Computational modeling
  • Information processing
  • Partitioning algorithms
  • Random matrices
  • Random variables
  • Signal to noise ratio
  • Standards
  • Task analysis
  • hidden structures
  • statistical and computational limits
  • statistical inference

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Information Systems
  • Computer Networks and Communications


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