Sparse multivariate Bernoulli processes in high dimensions

Parthe Pandit, Mojtaba Sahraee, Arash A. Amini, Sundeep Rangan, Alyson K. Fletcher

Research output: Contribution to conferencePaper

Abstract

We consider the problem of estimating the parameters of a multivariate Bernoulli process with auto-regressive feedback in the high-dimensional setting where the number of samples available is much less than the number of parameters. This problem arises in learning interconnections of networks of dynamical systems with spiking or binary valued data. We also allow the process to depend on its past up to a lag p, for a general p ≥ 1, allowing for more realistic modeling in many applications. We propose and analyze an `1-regularized maximum likelihood (ML) estimator under the assumption that the parameter tensor is approximately sparse. Rigorous analysis of such estimators is made challenging by the dependent and non-Gaussian nature of the process as well as the presence of the nonlinearities and multi-level feedback. We derive precise upper bounds on the mean-squared estimation error in terms of the number of samples, dimensions of the process, the lag p and other key statistical properties of the model. The ideas presented can be used in the rigorous high-dimensional analysis of regularized M-estimators for other sparse nonlinear and non-Gaussian processes with long-range dependence.

Original languageEnglish (US)
StatePublished - Jan 1 2020
Event22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019 - Naha, Japan
Duration: Apr 16 2019Apr 18 2019

Conference

Conference22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019
CountryJapan
CityNaha
Period4/16/194/18/19

ASJC Scopus subject areas

  • Artificial Intelligence
  • Statistics and Probability

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    Pandit, P., Sahraee, M., Amini, A. A., Rangan, S., & Fletcher, A. K. (2020). Sparse multivariate Bernoulli processes in high dimensions. Paper presented at 22nd International Conference on Artificial Intelligence and Statistics, AISTATS 2019, Naha, Japan.