Carmela Cappelli

A statistical approach to growing a reliable honest tree

The introduction of a third stage in tree growing approach is suggested. The aim is to find a honest tree, that is, a tree which is not only understandable and accurate, but also statistically reliable. Testing procedures for both classification and regression trees are introduced. These procedures guide the search for those parts in tree structures which are statistically significant.

Exponential distance-based fuzzy clustering for interval-valued data

In several real life and research situations data are collected in the form of intervals, the so called interval-valued data. In this paper a fuzzy clustering method to analyse interval-valued data is presented. In particular, we address the problem of interval-valued data corrupted by outliers and noise. In order to cope with the presence of outliers we propose to employ a robust metric based on the exponential distance in the framework of the Fuzzy C-medoids clustering mode, the Fuzzy C-medoids clustering model for interval-valued data with exponential distance. The exponential distance assigns small weights to outliers and larger weights to those points that are more compact in the data set, thus neutralizing the effect of the presence of anomalous interval-valued data. Simulation results pertaining to the behaviour of the proposed approach as well as two empirical applications are provided in order to illustrate the practical usefulness of the proposed method.

Change point analysis of imprecise time series

Abstract In this paper we describe how to conduct a change-point analysis when dealing with time series imprecisely or vaguely observed, i.e. time ordered observations whose values are not known exactly, such as interval or ordinal time series (imprecise time series). In order to treat such time series, we propose to employ a fuzzy approach i.e. data are parameterized in the form of fuzzy variables. Then, to detect the number and location of change points we employ a deviation measure for fuzzy variables in the framework of Atheoretical Regression Trees (ART). We present simulation results pertaining to the behavior of the proposed approach as well as two empirical applications to real imprecise time series.

An Alternative Pruning Method Based on the Impurity-Complexity Measure

This paper provides a new pruning method for classification trees based on the impurity-complexity measure. Advantages of the proposed approach compared to the error-complexity pruning method are outlined showing an example on a real data set.

Missing Data Incremental Imputation through Tree Based Methods

Conditional mean imputation is a common way to deal with missing data. Although very simple to implement, the method might suffer from model misspecification and it results unsatisfactory for non linear data. We propose the iterative use of tree based models for missing data imputation in large data bases. The proposed procedure uses lexicographic order to rank missing values that occur in different variables and deals with these incrementally, i.e, augmenting the data by the previously filled in records according to the defined order.

Canonical Variates for Recursive Partitioning in Data Mining

This paper deals with the problem of dimension reduction in the general context of supervised statistical learning, with particular attention to data mining applications. The main goal of the proposed methodology is to improve tree based methods as prediction tool by introducing an alternative approach to data partitioning which is meant to handle large numbers of (possibly correlated) covariates. The key idea is to use suitable combinations of covariates recursively identified.

A Third Stage in Regression Tree Growing: Searching for Statistical Reliability

This paper suggests the introduction of a third stage in regresssion tree growing approach. To this aim, a statistical testing procedure based on the F statistics, is proposed. In particular, the testing procedure is applied to the CART sequence of pruned subtrees, resulting in a single final tree structured prediction rule, which is statistically reliable and might not coincide with any tree in the sequence itself.

An MLE strategy for combining optimally pruned decision trees

This paper provides a maximum likelihood estimation strategy to identify a tree-based model which, being a function of a set of observed optimally pruned trees, represents the final classification model. The strategy is based on a probability distribution and it uses a metric based on structural differences among trees. An example on a real dataset is also presented to show how the procedure works.

Consumer behaviour and online advertising: A fuzzy approach to the market segmentation

This study aims at analysing consumer behaviour towards online advertising, focusing on the attitude defined in terms of cognitive, affective and behavioural aspects. Likert scale was employed to capture these three aspects. However, subjective attitude is often a nebulous and vague feature to deal with. To this end, adopting a fuzzy clustering procedure, first a fuzzy coding of the levels of the Likert scale is adopted. Second, the Fuzzy k-Means clustering model for fuzzy data has been employed to segment a sample of web users. Two clusters have been identified that require different marketing communication strategies.

Theoretical Regression Trees: A Tool for Multiple Structural-Change Models Analysis

The analysis of structural-change models is nowadays a popular subject of research both in econometric and statistical literature. The most challenging task is to identify multiple breaks occurring at unknown dates. In case of multiple shifts in mean Cappelli and Reale (Provasi, C. (eds.) S.Co. 2005: Modelli Complessi e Metodi Computazionali Intensivi per la Stima e la Previsione, pp. 479–484. Cleup, Padova, 2005) have proposed a method called ART that employs regression trees to estimate the number and location of breaks. In this paper we focus on regime changes due to breaks in the coefficients of a parametric model and we propose an extension of ART that addresses this topic in the general framework of the linear model with multiple structural changes. The proposed approach considers in the tree growing phase the residuals of parametric models fitted to contiguous subseries obtained by splitting the original series whereas tree pruning together with model selection criteria provides the number of breaks. We present simulation results well as two empirical applications pertaining to the behavior of the proposed approach.