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Publication# Tree in Tree: from Decision trees to Decision Graphs

Abstract

Decision trees have been widely used as classifiers in many machine learning applications thanks to their lightweight and interpretable decision process. This paper introduces Tree in Tree decision graph (TnT), a framework that extends the conventional decision tree to a more generic and powerful directed acyclic graph. TnT constructs decision graphs by recursively growing decision trees inside the internal or leaf nodes instead of greedy training. The time complexity of TnT is linear to the number of nodes in the graph, and it can construct decision graphs on large datasets. Compared to decision trees, we show that TnT achieves better classification performance with reduced model size, both as a stand-alone classifier and as a base estimator in bagging/AdaBoost ensembles. Our proposed model is a novel, more efficient, and accurate alternative to the widely-used decision trees.

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Analyse I

Le contenu de ce cours correspond à celui du cours d'Analyse I, comme il est enseigné pour les étudiantes et les étudiants de l'EPFL pendant leur premier semestre. Chaque chapitre du cours correspond

Analyse I (partie 1) : Prélude, notions de base, les nombres réels

Concepts de base de l'analyse réelle et introduction aux nombres réels.

Analyse I (partie 2) : Introduction aux nombres complexes

Introduction aux nombres complexes

Decision tree learning

Decision tree learning is a supervised learning approach used in statistics, data mining and machine learning. In this formalism, a classification or regression decision tree is used as a predictive model to draw conclusions about a set of observations. Tree models where the target variable can take a discrete set of values are called classification trees; in these tree structures, leaves represent class labels and branches represent conjunctions of features that lead to those class labels.

Decision tree

A decision tree is a decision support hierarchical model that uses a tree-like model of decisions and their possible consequences, including chance event outcomes, resource costs, and utility. It is one way to display an algorithm that only contains conditional control statements. Decision trees are commonly used in operations research, specifically in decision analysis, to help identify a strategy most likely to reach a goal, but are also a popular tool in machine learning.

Directed acyclic graph

In mathematics, particularly graph theory, and computer science, a directed acyclic graph (DAG) is a directed graph with no directed cycles. That is, it consists of vertices and edges (also called arcs), with each edge directed from one vertex to another, such that following those directions will never form a closed loop. A directed graph is a DAG if and only if it can be topologically ordered, by arranging the vertices as a linear ordering that is consistent with all edge directions.

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We examine the connection of two graph parameters, the size of a minimum feedback arcs set and the acyclic disconnection. A feedback arc set of a directed graph is a subset of arcs such that after deletion the graph becomes acyclic. The acyclic disconnecti ...