Arbres de décision et forêts aléatoires pour variables groupées

In many problems in supervised learning, inputs have a known and/or obvious group structure. In this context, elaborating a prediction rule that takes into account the group structure can be more relevant than using an approach based only on the individual variables for both prediction accuracy and interpretation. The goal of this thesis is to develop some tree-based methods adapted to grouped variables. Here, we propose two new tree-based approaches which use the group structure to build decision trees. The first approach allows to build binary decision trees for classification problems. A split of a node is defined according to the choice of both a splitting group and a linear combination of the inputs belonging to the splitting group. The second method, which can be used for prediction problems in both regression and classification, builds a non-binary tree in which each split is a binary tree. These two approaches build a maximal tree which is next pruned. To this end, we propose two pruning strategies, one of which is a generalization of the minimal cost-complexity pruning algorithm. Since decisions trees are known to be unstable, we introduce a method of random forests that deals with groups of inputs. In addition to the prediction purpose, these new methods can be also use to perform group variable selection thanks to the introduction of some measures of group importance, This thesis work is supplemented by an independent part in which we consider the unsupervised framework. We introduce a new clustering algorithm. Under some classical regularity and sparsity assumptions, we obtain the rate of convergence of the clustering risk for the proposed alqorithm.Dans de nombreux problèmes en apprentissage supervisé, les entrées ont une structure de groupes connue et/ou clairement identifiable. Dans ce contexte, l'élaboration d'une règle de prédiction utilisant les groupes plutôt que les variables individuelles peut être plus pertinente tant au niveau des performances prédictives que de l'interprétation. L'objectif de la thèse est de développer des méthodes par arbres adaptées aux variables groupées. Nous proposons deux approches qui utilisent la structure groupée des variables pour construire des arbres de décisions. La première méthode permet de construire des arbres binaires en classification. Une coupure est définie par le choix d'un groupe et d'une combinaison linéaire des variables du dit groupe. La seconde approche, qui peut être utilisée en régression et en classification, construit un arbre non-binaire dans lequel chaque coupure est un arbre binaire. Ces deux approches construisent un arbre maximal qui est ensuite élagué. Nous proposons pour cela deux stratégies d'élagage dont une est une généralisation du minimal cost-complexity pruning. Les arbres de décision étant instables, nous introduisons une méthode de forêts aléatoires pour variables groupées. Outre l'aspect prédiction, ces méthodes peuvent aussi être utilisées pour faire de la sélection de groupes grâce à l'introduction d'indices d'importance des groupes. Ce travail est complété par une partie indépendante dans laquelle nous nous plaçons dans un cadre d'apprentissage non supervisé. Nous introduisons un nouvel algorithme de clustering. Sous des hypothèses classiques, nous obtenons des vitesses de convergence pour le risque de clustering de l'algorithme proposé

Decisions trees and random forests for grouped variables

Dans de nombreux problèmes en apprentissage supervisé, les entrées ont une structure de groupes connue et/ou clairement identifiable. Dans ce contexte, l'élaboration d'une règle de prédiction utilisant les groupes plutôt que les variables individuelles peut être plus pertinente tant au niveau des performances prédictives que de l'interprétation. L'objectif de la thèse est de développer des méthodes par arbres adaptées aux variables groupées. Nous proposons deux approches qui utilisent la structure groupée des variables pour construire des arbres de décisions. La première méthode permet de construire des arbres binaires en classification. Une coupure est définie par le choix d'un groupe et d'une combinaison linéaire des variables du dit groupe. La seconde approche, qui peut être utilisée en régression et en classification, construit un arbre non-binaire dans lequel chaque coupure est un arbre binaire. Ces deux approches construisent un arbre maximal qui est ensuite élagué. Nous proposons pour cela deux stratégies d'élagage dont une est une généralisation du minimal cost-complexity pruning. Les arbres de décision étant instables, nous introduisons une méthode de forêts aléatoires pour variables groupées. Outre l'aspect prédiction, ces méthodes peuvent aussi être utilisées pour faire de la sélection de groupes grâce à l'introduction d'indices d'importance des groupes. Ce travail est complété par une partie indépendante dans laquelle nous nous plaçons dans un cadre d'apprentissage non supervisé. Nous introduisons un nouvel algorithme de clustering. Sous des hypothèses classiques, nous obtenons des vitesses de convergence pour le risque de clustering de l'algorithme proposé.In many problems in supervised learning, inputs have a known and/or obvious group structure. In this context, elaborating a prediction rule that takes into account the group structure can be more relevant than using an approach based only on the individual variables for both prediction accuracy and interpretation. The goal of this thesis is to develop some tree-based methods adapted to grouped variables. Here, we propose two new tree-based approaches which use the group structure to build decision trees. The first approach allows to build binary decision trees for classification problems. A split of a node is defined according to the choice of both a splitting group and a linear combination of the inputs belonging to the splitting group. The second method, which can be used for prediction problems in both regression and classification, builds a non-binary tree in which each split is a binary tree. These two approaches build a maximal tree which is next pruned. To this end, we propose two pruning strategies, one of which is a generalization of the minimal cost-complexity pruning algorithm. Since decisions trees are known to be unstable, we introduce a method of random forests that deals with groups of inputs. In addition to the prediction purpose, these new methods can be also use to perform group variable selection thanks to the introduction of some measures of group importance, This thesis work is supplemented by an independent part in which we consider the unsupervised framework. We introduce a new clustering algorithm. Under some classical regularity and sparsity assumptions, we obtain the rate of convergence of the clustering risk for the proposed alqorithm

Statistical analysis of a hierarchical clustering algorithm with outliers

It is well known that the classical single linkage algorithm usually fails to identify clusters in the presence of outliers. In this paper, we propose a new version of this algorithm, and we study its mathematical performances. In particular, we establish an oracle type inequality which ensures that our procedure allows to recover the clusters with large probability under minimal assumptions on the distribution of the outliers. We deduce from this inequality the consistency and some rates of convergence of our algorithm for various situations. Performances of our approach is also assessed through simulation studies and a comparison with classical clustering algorithms on simulated data is also presented

Classification tree algorithm for grouped variables

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VS-LTGARCHX: A Flexible Subset Selection Approach for Estimation of log-TGARCHX Models and Its Application to BTC Markets

The log-TGARCHX model is less restrictive in terms of inclusion of exogenous variables and asymmetry lags compared to the GARCHX model. However, adding less (more) covariates than necessary may lead to underfitting (overfitting), respectively. In this context, we propose a new algorithm, called VS-LTGARCHX, which incorporates a variable selection procedure into the log-TGARCHX estimation process. Furthermore, the VS-LTGARCHX algorithm is applied to extremely volatile BTC markets using 42 conditioning variables. Interestingly, our results show that the VS-LTGARCHX models outperform the specified benchmark models in one-step-ahead forecasting

Standardized evaluation of tumor-infiltrating lymphocytes in breast cancer: results of the ring studies of the international immuno-oncology biomarker working group

Multiple independent studies have shown that tumor-infiltrating lymphocytes (TIL) are prognostic in breast cancer with potential relevance for response to immune-checkpoint inhibitor therapy. Although many groups are currently evaluating TIL, there is no standardized system for diagnostic applications. This study reports the results of two ring studies investigating TIL conducted by the International Working Group on Immuno-oncology Biomarkers. The study aim was to determine the intraclass correlation coefficient (ICC) for evaluation of TIL by different pathologists. A total of 120 slides were evaluated by a large group of pathologists with a web-based system in ring study 1 and a more advanced software-system in ring study 2 that included an integrated feedback with standardized reference images. The predefined aim for successful ring studies 1 and 2 was an ICC above 0.7 (lower limit of 95% confidence interval (CI)). In ring study 1 the prespecified endpoint was not reached (ICC: 0.70; 95% CI: 0.62-0.78). On the basis of an analysis of sources of variation, we developed a more advanced digital image evaluation system for ring study 2, which improved the ICC to 0.89 (95% CI: 0.85-0.92). The Fleiss' kappa value fo