Empirical Bayesian Models of L1/L2 Mixed-norm Constraints

Deirel Paz-Linares, Mayrim Vega-Hernández, Eduardo Martínez Montes

2014

Abstract

Inverse problems are common in neuroscience and neurotechnology, where usually a small amount of data is available with respect to the large number of parameters needed formodelling the brain activity. Classical examples are the EEG/MEG source localization and the estimation of effective brain connectivity. Many kinds of constraints or prior information have been proposed to regularize these inverse problems. Combination of smoothness (L2 norm-based penalties) and sparseness (L1 norm-based penalties) seem to be a promising approach due to its flexibility, but the estimation of optimal weights for balancing these constraints became a critical issue (Vega-Hernández et al., 2008). Two important examples of constraints that combine L1/L2 norms are the Elastic Net (Vega-Hernández et al., 2008) and the Mixed-Norm L12 (MxN, Gramfort et al., 2012). The latter imposes the properties along different dimensions of a matrix inverse problem. In this work, we formulate an empirical Bayesian model based onan MxN prior distribution. The objective is to pursuesparse learning along the first dimension (along rows) preserving smoothness in the second dimension (along columns), by estimating both parameter and hyperparameters (regularization weights).

References

  1. Vega-Hernández M, et al. (2008): Penalized leastsquares methods for solving the EEG inverse problem. Stat Sin18:1535-1551.
  2. Alexandre-Gramfort, et al. (2012): Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods. Physics in Medicine and Biology 57: 1937-1961.
  3. Qing Li and Nan Lin. (2010): The Bayesian Elastic Net. Bayesian Analysis 5, Number 1: 151-170.
  4. Michael E. Tipping. 2001: Sparse Bayesian Learning and the Relevance Vector Machine. Journal of Machine Learning Research 1: 211-244.
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Paper Citation


in Harvard Style

Paz-Linares D., Vega-Hernández M. and Martínez Montes E. (2014). Empirical Bayesian Models of L1/L2 Mixed-norm Constraints . In - NEUROTECHNIX, ISBN , pages 0-0


in Bibtex Style

@conference{neurotechnix14,
author={Deirel Paz-Linares and Mayrim Vega-Hernández and Eduardo Martínez Montes},
title={Empirical Bayesian Models of L1/L2 Mixed-norm Constraints},
booktitle={ - NEUROTECHNIX,},
year={2014},
pages={},
publisher={SciTePress},
organization={INSTICC},
doi={},
isbn={},
}


in EndNote Style

TY - CONF
JO - - NEUROTECHNIX,
TI - Empirical Bayesian Models of L1/L2 Mixed-norm Constraints
SN -
AU - Paz-Linares D.
AU - Vega-Hernández M.
AU - Martínez Montes E.
PY - 2014
SP - 0
EP - 0
DO -