Publicaciones

Artículos publicados en revistas internacionales ISI

• Alvarez, Felipe; Flores, Salvador.
  Existence and Approximation for Variational Problems Under Uniform Constraints on the Gradient by Power Penalty (preprint here)
  
  SIAM J. Math. Anal., 47(5), 3466--3487, 2015. [+ bibtex citation]

  @Article{ AlvarezFlores2015,
  author = {Alvarez, Felipe and Flores, Salvador},
  title = {Existence and Approximation for Variational Problems Under Uniform Constraints on the Gradient by Power Penalty},
  journal = {SIAM J. Math. Anal.},
  year = {2015},
  volume={47},
  number={5},
  pages={3466--3487},
  doi = {DOI:10.1137/140988619},
  }

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• Flores, Salvador.
  SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression
  
  European Journal of Operational Research 246 (2015) pp. 44-50, 2015
  [+ bibtex citation]

  @Article{ FloresEJOR2015,
  author = "Salvador Flores",
  title = "SOCP relaxation bounds for the optimal subset selection problem applied to robust linear regression",
  journal = "EJOR",
  year = "2015",
  volume="246",
  number="1",
  pages="44--50" doi = "DOI: 10.1016/j.ejor.2015.04.024", }

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• Flores, Salvador.
  Sharp non-asymptotic performance bounds for $\ell_1$ and Huber robust regression estimators
  
  TEST 24(4), pp. 796-812, 2015. [+ bibtex citation]

  @Article{ Flores2015,
  author = "Salvador Flores",
  title = "Sharp non-asymptotic performance bounds for $\ell_1$ and Huber robust regression estimators",
  journal = "Test",
  year = "2015",
  number = "4",
  volume = "24",
  pages = "796 -- 812",
  doi = "DOI: 10.1007/s11749-015-0435-5", }

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• Flores, Salvador.
  On the efficient computation of robust regression estimators.
  
  Computational Statistics & Data Analysis, 54 (12),pp. 3044--3056, 2010. [+ bibtex citation]

  @Article{ Flores2010, author = "Salvador Flores",
  title = "On the efficient computation of robust regression estimators",
  journal = "Computational Statistics \& Data Analysis",
  volume = "54",
  number = "12",
  pages = "3044--3056",
  year = "2010",
  doi = "DOI: 10.1016/j.csda.2010.03.020", }

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• Alvarez, Felipe; Flores, Salvador.
  Remarks on Lipschitz solutions to measurable differential inclusions and an existence result for some nonconvex variational problems.
  
  J. Convex Anal. 15 (2), pp. 349-363, 2008. [bibtex citation]

  @article {Alvarez-Flores2008,
  AUTHOR = {Alvarez, Felipe and Flores, Salvador},
  TITLE = {Remarks on {L}ipschitz solutions to measurable differential inclusions and an
  existence result for some nonconvex variational problems},
  JOURNAL = {J. Convex Anal.},
  VOLUME = {15},
  YEAR = {2008},
  NUMBER = {2},
  PAGES = {349--363}
  }

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Artículos en preparación

• Flores, Salvador.
  Does Compressed Sensing Have Applications in Robust Statistics?
  

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  The connections between robust linear regression and sparse reconstruction are brought to light. We show that in the context of fixed design, the notion of breakdown point coincides with exact recovery of sparse signals from highly incomplete information. The main consequence of this connection in robust regression is that there exists, for any dimension, ``many'' designs on which the $\ell_1$ estimator has a positive breakdown point. This result clarifies a common misunderstanding on the robustness of M-estimators. [-]

Tesis de Doctorado

Titulo : "Global optimization problems in robust statistics "
Supervisores : Anne Ruiz-Gazen, Université Toulouse 1 Capitole
     Marcel Mongeau, Université Paul Sabatier
Defendida : 25 febrero, 2011
Comité : Jean-Baptiste Hiriart-Urruty, Université Paul Sabatier
       Marcel Mongeau, Université Paul Sabatier
       Fabio Schoen, Università di Firenze, Italy
       Michael Schyns, Université de Liège, Belgium
       Roy Welsch, Massachusetts Institute of Technology, USA





ver resumen [+]

Robust statistics is a branch of statistics dealing with the analysis of data containing contaminated observations. The robustness of an estimator is measured notably by means of the breakdown point. High-breakdown point estimators are usually defined as global minima of a non-convex scale of the errors, hence their computation is a challenging global optimization problem. The objective of this dissertation is to investigate the potential contributions of modern global optimization methods to this class of problems.
The first part of this thesis is devoted to the $\tau$-estimator for linear regression, which is defined as a global minimum of a nonconvex differentiable function. We investigate the impact of incorporating clustering techniques and stopping conditions in existing stochastic algorithms. The consequences of some phenomena involving the nearest neighbor in high dimension on clustering global optimization algorithms is thoroughly discussed as well.
The second part is devoted to deterministic algorithms for computing the least trimmed squares regression estimator, which is defined through a nonlinear mixed-integer program. Due to the combinatorial nature of this problem, we concentrated on obtaining lower bounds to be used in a branch-and-bound algorithm. In particular, we propose a second-order cone relaxation that can be complemented with concavity cuts that we obtain explicitly. Global optimality conditions are also provided. [-]

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© 2013 Salvador Flores

Last update: 19/08/2011