README.md

   1 # model SELECTion
   2
   3 This code is the applied part of the PhD thesis of [Emilie Devijver](http://www.math.u-psud.fr/~devijver/).
   4
   5 ## Description
   6
   7 The function selmix delivers a multivariate Gaussian mixture in regression model collection.
   8 According to the parameter estimation, we can compute classical model selection criterion, as BIC or AIC, or slope heuristic, using the CAPUSHE package.
   9 The methodology used is described in 'Model-Based Clustering for High-Dimensional Data. Application to Functional Data.',
  10 available at [this location](https://hal.archives-ouvertes.fr/hal-01060063)
  11
  12 ## Arguments
  13
  14 Regressors, denoted by X (of size n x p) and responses, denoted by Y (of size n x q) are must-have arguments.
  15
  16 Optionally, we could add
  17
  18 * gamma: weight power in the Lasso penalty (according to Stadler et al., $\gamma \in \{0,1/2,1\}$;
  19 * mini: the minimum number of iterations;
  20 * maxi: the maximum number of iterations;
  21 * tau: the threshold for stopping EM algorithm;
  22 * kmin and kmax: the bounds of interesting number of components,
  23 * rangmin and rangmax: the bounds of interesting rank values.
  24
  25 ## Usage
  26
  27     objet = selmix(X,Y)
  28     objet.run(index)
  29
  30 For index=1, it computes the Lasso-MLE procedure.
  31 For index=2, it computes the Lasso-Rank procedure.
  32
  33 /!\ Be careful to the current path /!\
  34
  35 ## Values
  36
  37 * phiInit, rhoInit, piInit, gamInit: the initialization of the matrices phi, rho, pi and gamma,
  38 * gridLambda: grid of regularization parameters used to select relevant variables (if kmax-kmin=0, it is, if not, it is the last grid of regularization parameters)
  39 * A1,A2: indices of variables selected or not selected (matrices of size (p+1) x q x size(gridLambda))
  40 * Phi,Rho,Pi: estimations of each parameter thanks to the procedure LassoMLE if compute index=1, and thanks to the procedure LassoRank if computed index=2.
  41
  42
  43 ## Example
  44
  45     n=10;
  46     p=10;
  47     q=5;
  48     X=randn(n,p);
  49     Y=randn(n,q);
  50
  51     objet=selmix(X,Y);
  52     objet.run(1);
  53     objet.run(2);