Full CV

Publications

Publiées dans des Revues internationales avec comite de lecture

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

  @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", }

  voir le resumé [+]

  The problem of providing efficient and reliable robust regression algorithms is considered. The impact of global optimization methods, such as stopping conditions and clustering techniques, in the calculation of robust regression estimators is investigated. The use of stopping conditions permits us to devise new algorithms that perform as well as the existing algorithms in less time and with adaptive algorithm parameters. Clustering global optimization is shown to be a general framework encompassing many of the existing algorithms. [-]
• Alvarez, Felipe; Flores, Salvador.
  Remarks on Lipschitz solutions to measurable differential inclusions and an existence result for some nonconvex variational problems. (preprint ici)
  
  J. Convex Anal. 15 (2008), no. 2, 349-363. [+bibtex]

  @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}
  }

  voir le resumé [+]

  In this paper we examine the problem of finding a Lipschitz function on an open domain with prescribed boundary values and whose gradient is required to satisfy some nonhomogeneous pointwise constraints a.e. in the domain, $$\nabla u(x) \in C(x)\ \text{ a.e. in }\Omega,\quad u|_{\partial \Omega}=g \in {\rm Lip}(\partial \Omega).$$ These constraints are supposed to be given by a measurable set-valued mapping $C:\mathbb{R}^n\rightrightarrows \mathbb{R}^n$   with convex, uniformly compact and nonempty-interior values. We discuss existence and metric properties of maximal solutions of such a problem. We exploit some connections with weak solutions to discontinuous Hamilton-Jacobi equations, and we provide a variational principle that characterizes maximal solutions. We investigate the case where the original problem is supplemented with bilateral obstacle constraints on the function values. Finally, as an application of these results, we prove existence for a specific class of nonconvex problems from the calculus of variations, with and without obstacle constraints, under mild regularity hypotheses on the data. [-]

En préparation

• Flores, Salvador.
  An improved Branch and Bound algorithm for an optimal feature subset selection problem from robust statistics.
  

  voir le resumé [+]

  We present a Branch and Bound algorithm for computing the Least Trimmed Squares estimator for performing strongly robust linear regression. The main novelty of our approach is the use of lower bounds obtained from a second order cone programming relaxation of the mixed-integer nonlinear programming problem that defines the estimator, which allows pruning at top levels of the enumeration tree. Numerical results show the gains in computing time, notably when the number of explicative variables is close to the number of cases. [-]
• Briceño, Luis.; Flores, Salvador.
  A new error correction technique with strong theoretical properties.
  

  voir le resumé [+]

  Consider the problem of recovering a vector from corrupted measurements of linear combinations of its components. It is known that when only a relatively small fraction of the measurements is corrupted, and the rest is error-free, the vector can be exactly recovered by $\ell_1$-norm minimization. We introduce a new, robust, error correction mechanism that covers the case when a fraction of the measurements is corrupted by arbitrary, eventually adversarial, errors and additionally all the measurements carry some noise. We show that, by solving a nonsmooth convex minimization problem, it is possible to recover the least-squares estimate of the vector as if it was contaminated with noise only. Moreover, we show that the fraction of arbitrary errors that the estimator can manage is exactly the same as that the $\ell_1$-norm minimization can face in the noiseless case. Finally, we present a globally convergent forward-backward algorithm for computing our estimator. [-]
• Alvarez, Felipe; Flores, Salvador.
  Exponential penalty for variational problems under uniform quasiconvex constraints on the gradient.
  

  voir le resumé [+]

  We study the following class of problems from the calculus of variations $$\text{Inf}\ \{ F(v)\mid \|k(\cdot,v,\nabla v)\|_\infty \leq 1,\ v\in g+W_0^{1,p} \}$$ for vector-valued functions and nonconvex $F$. In particular, existence of solutions to such problems is proved as well as existence of measure-valued lagrange multipliers associated to the uniform constraint. They are shown to satisfy an Euler- Lagrange equation as well as a complementarity property. [-]

Thése

Sujet : "Global optimization problems in robust statistics "
Directeurs : Anne Ruiz-Gazen, Université Toulouse 1 Capitole
     Marcel Mongeau, Université Paul Sabatier
Soutenue : 25 Février 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





voir le resumé [+]

La statistique robuste est une branche de la statistique qui s'intéresse à l'analyse de données contenant une proportion significative d'observations contaminées avec des erreurs dont l'ampleur et la structure peuvent être arbitraires. Les estimateurs robustes au sens du point de rupture sont généralement définis comme le minimum global d'une certaine measure non-convexe des erreurs, leur calcul est donc un pro\-blème d'optimisation globale très coûteux. L'objectif de cette thèse est d'étudier les contributions possibles des méthodes d'optimisation globale modernes à l'étude de cette classe de problèmes.
La première partie de la thèse est consacrée au $\tau$-estimateur pour la régression linéaire robuste, qui est défini comme étant un minimum global d'une fonction non-convexe et dérivable. Nous étudions l'impact des techniques d'agglomération et des conditions d'arrêt sur l'efficacité des algorithmes existants. Les conséquences de certains phénomènes liés au voisin le plus proche en grande dimension sur ces algorithmes agglomératifs d'optimisation globale sont aussi mises en évidence.
Dans la deuxième partie de la thèse, nous étudions des algorithmes déterministes pour le calcul de l'estimateur de moindres carrés tronqués, qui est défini à l'aide d'un programme en nombres entiers non linéaire. En raison de sa nature combinatoire, nous avons dirigé nos efforts vers l'obtention des bornes inférieures pouvant être utilisées dans un algorithme du type \emph{branch-and-bound}. Plus précisément, nous proposons une relaxation par un programme sur le cône de deuxième ordre, qui peut être renforcée avec des coupes dont nous présentons l'expression explicite. Nous fournissons également des conditions d'optimalité globale. [-]

• Accueil
  
• Interets Scientifiques
  
• Projects
  
• Liens sur l'Optimization
  

© 2011 Salvador Flores

Last update: 19/08/2011