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26 novembre 2020

Stage M2/Ecole d'ingenieur -- Identification et sélection de groupes de variables à partir de l'algorithme des Forêts Aléatoires

Catégorie : Stagiaire

Institutions: Universite Bretagne Sud, LMBA CNRS 6205, IRISA CNRS 6074.
Lieu: Campus Tohannic, Vannes, France.
Duration: 6 months.
Supervisors: Audrey Poterie & Charlotte Pelletier.
Contacts: audrey.poterie@univ-ubs.fr, charlotte.pelletier@univ-ubs.fr.

Keywords: Random forests for grouped variables, group variable identi fication, reccursive
feature selection, C++.

Supervised learning consists in explaining and/or predicting an output variable by using some
inputs. Here, we consider the context in which the inputs have a known and/or obvious group
structure. In many supervised problems, inputs can have a group structure or groups of inputs
can be de fined to capture the underlying input associations. In these cases, the study of groups
of variables can make more sense than the study of inputs taken individually.

For example, in the analysis of gene expression data, datasets contain the expression levels of
thousands of genes in a much smaller number of observations. Thus it has become frequent to use
in the analysis only a small number of genes, which are clustered into several groups representing
putative biological processes [2, 3]. Another example is functional data, like spectrometry data,
where researchers are often more interested by identifying discriminatory parts
of the curve rather than individual wavelengths. Finally, in some supervised methods such as
the CART algorithm [4], categorical inputs are converted into a group of dummy variables.
Thus, it seems quite natural to treat the dummy variables related to a categorical variable as a
group. In all these situations, elaborating a prediction rule based on groups of variables rather
than on the individual variables can improve both interpretation and prediction accuracy [5].
Several methods have already been proposed to deal with this problem. For instance, the logistic
regression regularized by the Group Lasso penalty (GL) enables to elaborate classi fication rules
based on groups of input variables [6]. Recently, two decision tree approaches and one random
forests algorithm, called Random Forests for Grouped Variables, have been developped to deal
with groups of inputs [7, 8]. These methods build prediction rules based on groups of inputs.
Furthermore in addition to the prediction purpose, these three new methods can also be used to
perform group variable selection thanks to the introduction for each of them of some grouped
variable importance scores.

The internship will focus on the algorithm named Random Forests for Grouped Variables [8]
(RFGV). The project will consist of three objectives.
The fi rst objective will be to propose an eficient implementation of the RFGV algorithm (for
both the training phase and the prediction phase). An implementation in R has already been
proposed for binary classi fication problems. The aim is twofold: (1) to improve this implementation
by proposing a multi-threading version in C++/Java/Cython, and (2) to extend the
implementation so as to deal with multi-class classifi cation tasks and regression problems.
In supervised problems with grouped inputs, the group structure is often unknown.
Then, the second objective will consist in developping an original and data-driven method to perform group
variable identi fication. The proposed strategy will be based on the RFGV algorithm and its
grouped importance score [7]. A wrapper strategy, such as the feature elimination algorithm
proposed by [9] or the selection approach introduced by [5], could be tested. The method will be
thoroughly assessed through experimental studies on several synthetic data sets.
Finally, the third objective will be to apply the proposed method on real data.

Candidate profi le
We are looking for a motivated and talented student in Master 2 (or equivalent) who:

The 6-month internship will take place at the Universite Bretagne Sud in Vannes. The salary will be around 500e per month.
The student will be supervised by:

To apply for this position, the candidate is requested to send a CV, a motivation letter and
academic records to audrey.poterie@univ-ubs.fr. The application deadline is: 31th January 2021.



[1] A. Y. Luaibi, A. J. Al-Ghusain, A. Rahman, M. H. Al-Sayah, and H. A. Al-Nashash, Noninvasive
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8th GCC Conference & Exhibition, pp. 1-4, IEEE, 2015.
[2] P. Tamayo, D. Scanfeld, B. L. Ebert, M. A. Gillette, C. W. Roberts, and J. P. Mesirov,
Metagene projection for cross-platform, cross-species characterization of global transcriptional
states," Proceedings of the National Academy of Sciences, vol. 104, no. 14, pp. 5959-5964, 2007.
[3] S.-I. Lee and S. Batzoglou, Application of independent component analysis to microarrays,"
Genome Biology, vol. 4, no. 11, p. R76, 2003.
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CRC Press, 1984.
[5] B. Gregorutti, B. Michel, and P. Saint-Pierre, Grouped variable importance with random
forests and application to multiple functional data analysis," Computational Statistics & Data
Analysis, vol. 90, pp. 15-35, 2015.
[6] L. Meier, S. Van De Geer, and P. Buhlmann, The group lasso for logistic regression," Journal
of the Royal Statistical Society: Series B (Statistical Methodology), vol. 70, no. 1, pp. 53-71,2008.
[7] A. Poterie, J.-F. Dupuy, V. Monbet, and L. Rouvere, Classi fication tree algorithm for
grouped variables," Computational Statistics, vol. 34, no. 4, pp. 1613-1648, 2019.
[8] A. Poterie, Arbres de decision et forêts aléatoires pour variables groupées. PhD thesis, INSA de Rennes, 2018.
[9] I. Guyon, J. Weston, S. Barnhill, and V. Vapnik, \Gene selection for cancer classi fication
using support vector machines," Machine learning, vol. 46, no. 1-3, pp. 389-422, 2002.

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