Univariate decision tree induction using maximum margin classification

In many pattern recognition applications, first decision trees are used due to their simplicity and easily interpretable nature. In this paper, we propose a new decision tree learning algorithm called univariate margin tree where, for each continuous attribute, the best split is found using convex optimization. Our simulation results on 47 data sets show that the novel margin tree classifier performs at least as good as C4.5 and linear discriminant tree (LDT) with a similar time complexity. For two-class data sets, it generates significantly smaller trees than C4.5 and LDT without sacrificing from accuracy, and generates significantly more accurate trees than C4.5 and LDT for multiclass data sets with one-vs-rest methodology.Publisher's VersionAuthor Pre-Prin

Omnivariate rule induction using a novel pairwise statistical test

Rule learning algorithms, for example, RIPPER, induces univariate rules, that is, a propositional condition in a rule uses only one feature. In this paper, we propose an omnivariate induction of rules where under each condition, both a univariate and a multivariate condition are trained, and the best is chosen according to a novel statistical test. This paper has three main contributions: First, we propose a novel statistical test, the combined 5 x 2 cv t test, to compare two classifiers, which is a variant of the 5 x 2 cv t test and give the connections to other tests as 5 x 2 cv F test and k-fold paired t test. Second, we propose a multivariate version of RIPPER, where support vector machine with linear kernel is used to find multivariate linear conditions. Third, we propose an omnivariate version of RIPPER, where the model selection is done via the combined 5 x 2 cv t test. Our results indicate that 1) the combined 5 x 2 cv t test has higher power (lower type II error), lower type I error, and higher replicability compared to the 5 x 2 cv t test, 2) omnivariate rules are better in that they choose whichever condition is more accurate, selecting the right model automatically and separately for each condition in a rule.Publisher's VersionAuthor Post Prin

A new approach of top-down induction of decision trees for knowledge discovery

Top-down induction of decision trees is the most popular technique for classification in the field of data mining and knowledge discovery. Quinlan developed the basic induction algorithm of decision trees, ID3 (1984), and extended to C4.5 (1993). There is a lot of research work for dealing with a single attribute decision-making node (so-called the first-order decision) of decision trees. Murphy and Pazzani (1991) addressed about multiple-attribute conditions at decision-making nodes. They show that higher order decision-making generates smaller decision trees and better accuracy. However, there always exist NP-complete combinations of multiple-attribute decision-makings.;We develop a new algorithm of second-order decision-tree inductions (SODI) for nominal attributes. The induction rules of first-order decision trees are combined by \u27AND\u27 logic only, but those of SODI consist of \u27AND\u27, \u27OR\u27, and \u27OTHERWISE\u27 logics. It generates more accurate results and smaller decision trees than any first-order decision tree inductions.;Quinlan used information gains via VC-dimension (Vapnik-Chevonenkis; Vapnik, 1995) for clustering the experimental values for each numerical attribute. However, many researchers have discovered the weakness of the use of VC-dim analysis. Bennett (1997) sophistically applies support vector machines (SVM) to decision tree induction. We suggest a heuristic algorithm (SVMM; SVM for Multi-category) that combines a TDIDT scheme with SVM. In this thesis it will be also addressed how to solve multiclass classification problems.;Our final goal for this thesis is IDSS (Induction of Decision Trees using SODI and SVMM). We will address how to combine SODI and SVMM for the construction of top-down induction of decision trees in order to minimize the generalized penalty cost

Margin Optimal Classification Trees

In recent years there has been growing attention to interpretable machine learning models which can give explanatory insights on their behavior. Thanks to their interpretability, decision trees have been intensively studied for classification tasks, and due to the remarkable advances in mixed-integer programming (MIP), various approaches have been proposed to formulate the problem of training an Optimal Classification Tree (OCT) as a MIP model. We present a novel mixed-integer quadratic formulation for the OCT problem, which exploits the generalization capabilities of Support Vector Machines for binary classification. Our model, denoted as Margin Optimal Classification Tree (MARGOT), encompasses the use of maximum margin multivariate hyperplanes nested in a binary tree structure. To enhance the interpretability of our approach, we analyse two alternative versions of MARGOT, which include feature selection constraints inducing local sparsity of the hyperplanes. First, MARGOT has been tested on non-linearly separable synthetic datasets in 2-dimensional feature space to provide a graphical representation of the maximum margin approach. Finally, the proposed models have been tested on benchmark datasets from the UCI repository. The MARGOT formulation turns out to be easier to solve than other OCT approaches, and the generated tree better generalizes on new observations. The two interpretable versions are effective in selecting the most relevant features and maintaining good prediction quality

Learning understandable classifier models.

The topic of this dissertation is the automation of the process of extracting understandable patterns and rules from data. An unprecedented amount of data is available to anyone with a computer connected to the Internet. The disciplines of Data Mining and Machine Learning have emerged over the last two decades to face this challenge. This has led to the development of many tools and methods. These tools often produce models that make very accurate predictions about previously unseen data. However, models built by the most accurate methods are usually hard to understand or interpret by humans. In consequence, they deliver only decisions, and are short of any explanations. Hence they do not directly lead to the acquisition of new knowledge. This dissertation contributes to bridging the gap between the accurate opaque models and those less accurate but more transparent for humans. This dissertation first defines the problem of learning from data. It surveys the state-of-the-art methods for supervised learning of both understandable and opaque models from data, as well as unsupervised methods that detect features present in the data. It describes popular methods of rule extraction from unintelligible models which rewrite them into an understandable form. Limitations of rule extraction are described. A novel definition of understandability which ties computational complexity and learning is provided to show that rule extraction is an NP-hard problem. Next, a discussion whether one can expect that even an accurate classifier has learned new knowledge. The survey ends with a presentation of two approaches to building of understandable classifiers. On the one hand, understandable models must be able to accurately describe relations in the data. On the other hand, often a description of the output of a system in terms of its input requires the introduction of intermediate concepts, called features. Therefore it is crucial to develop methods that describe the data with understandable features and are able to use those features to present the relation that describes the data. Novel contributions of this thesis follow the survey. Two families of rule extraction algorithms are considered. First, a method that can work with any opaque classifier is introduced. Artificial training patterns are generated in a mathematically sound way and used to train more accurate understandable models. Subsequently, two novel algorithms that require that the opaque model is a Neural Network are presented. They rely on access to the network\u27s weights and biases to induce rules encoded as Decision Diagrams. Finally, the topic of feature extraction is considered. The impact on imposing non-negativity constraints on the weights of a neural network is considered. It is proved that a three layer network with non-negative weights can shatter any given set of points and experiments are conducted to assess the accuracy and interpretability of such networks. Then, a novel path-following algorithm that finds robust sparse encodings of data is presented. In summary, this dissertation contributes to improved understandability of classifiers in several tangible and original ways. It introduces three distinct aspects of achieving this goal: infusion of additional patterns from the underlying pattern distribution into rule learners, the derivation of decision diagrams from neural networks, and achieving sparse coding with neural networks with non-negative weights

A survey of cost-sensitive decision tree induction algorithms

The past decade has seen a significant interest on the problem of inducing decision trees that take account of costs of misclassification and costs of acquiring the features used for decision making. This survey identifies over 50 algorithms including approaches that are direct adaptations of accuracy based methods, use genetic algorithms, use anytime methods and utilize boosting and bagging. The survey brings together these different studies and novel approaches to cost-sensitive decision tree learning, provides a useful taxonomy, a historical timeline of how the field has developed and should provide a useful reference point for future research in this field