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Main Menu - Block
- Overview
- Anatomy and Histology
- Cryo-Electron Microscopy
- Electron Microscopy
- Flow Cytometry
- Gene Targeting and Transgenics
- Immortalized Cell Line Culture
- Integrative Imaging
- Invertebrate Shared Resource
- Janelia Experimental Technology
- Mass Spectrometry
- Media Prep
- Molecular Genomics
- Primary & iPS Cell Culture
- Project Pipeline Support
- Project Technical Resources
- Quantitative Genomics
- Scientific Computing Software
- Scientific Computing Systems
- Viral Tools
- Vivarium
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Abstract
We consider the problem of estimating the parameters of a linear autoregressive model with sub-Gaussian innovations from a limited sequence of consecutive observations. Assuming that the parameters are compressible, we analyze the performance of the ℓ1-regularized least squares as well as a greedy estimator of the parameters and characterize the sampling trade-offs required for stable recovery in the non-asymptotic regime. Our results extend those of compressed sensing for linear models where the covariates are i.i.d. and independent of the observation history to autoregressive processes with highly inter-dependent covariates. We also derive sufficient conditions on the sparsity level that guarantee the minimax optimality of the ℓ1-regularized least squares estimate. Applying these techniques to simulated data as well as real-world datasets from crude oil prices and traffic speed data confirm our predicted theoretical performance gains in terms of estimation accuracy and model selection.