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Label Ranking (LR) is a non-standard supervised classification method with the aim of ranking a finite collection of labels according to a set of predictor variables. Traditional LR models assume indifference among alternatives. However, misassigning the ranking position of a highly relevant label is frequently regarded as more severe than failing to predict a trivial label. Moreover, switching two similar alternatives should be considered less severe than switching two different ones. Therefore, efficient LR classifiers should be able to take into account the similarities and individual weights of the items to be ranked. The contribution of this paper is to formulate and compare flexible item-weighted Label Ranking algorithms using bagging, random forest, and boosting ensemble methods.

Probabilistic topic models have become one of the most widespread machine learning technique for textual analysis purpose. In this framework, Latent Dirichlet Allocation (LDA) gained more and more popularity as a text modelling technique. The idea is that documents are represented as random mixtures over latent topics, where a distribution over words characterizes each topic. Unfortunately, topic models do not guarantee the interpretability of their outputs. The topics learned from the model may be characterized by a set of irrelevant or unchained words, being useless for the interpretation. In the framework of topic quality evaluation, the pairwise semantic cohesion among the top-N most probable words (for a given topic) is calculated by measures based on words co-occurrences. Many topic-quality metrics were proposed defining different score measures such as: Pointwise Mutual Information (PMI), also called UCI; an asymmetrical measure called UMass; Normalized Pointwise Mutual Information (NPMI), a measure based on tf-idf scores , and a measure called CV proposed by Roder et al. Although these several measures in the literature have already considered cooccurrence between words as a measure of association, none has undertaken a statistical approach based on hypotheses testing to assess whether the co-occurrence obtained between two words can be attributed to the chance or if these links carry relevant information about the structure of topics. Thus, we propose a new coherence measure based on Statistically Validated Network to evaluate the interpretability of the top words of a topic.

Label Ranking (LR), an emerging non-standard supervised classification problem, aims at training preference models that order a finite set of labels based on a set of predictor features. Traditional LR models regard all labels as equally important. However, in many cases, failing to predict the ranking position of a highly relevant label can be considered more severe than failing to predict a trivial one. Moreover, an efficient LR classifier should be able to take into account the similarity between the items to be ranked. Indeed, swapping two similar elements should be less penalized than swapping two dissimilar ones. The contribution of the present paper is to formulate more flexible item-weighted label ranking models that make use of well-known decision tree ensemble models; respectively: bagging, random forest and boosting. The three proposed weighted LR classifiers encode the similarity structure and the individual label importance provided by a domain expert. The predictive performances of the three algorithms are compared, through simulations, to determine which ensemble procedure produces the best results for different noise levels and weight sets.

The task of combining preference rankings and approval voting is a relevant issue in social choice theory. The preference-approval voting (PAV) analyses the preferences of a group of individuals over a set of items. The main difference with the classical approaches for preference data consists in introducing, in addition to the ranking of candidates, a further distinction; candidates are subsetted in “acceptable” and “unacceptable”, or also in “good set” and “bad set” (a way to express the approval/disapproval). This work introduces the definition of a new measure to quantify disagreement between preference-approval profiles. For each pair of alternatives, we consider the two possible disagreements in approvals and rankings and merge them through a function h(·) increasing in each component. We show that our approach allows to emphasize particularly those cases in which both ranking and approval show simultaneously the maximum discordance.

Probabilistic topic models are machine learning tools for processing and understanding large text document collections. Among the different models in the literature, Latent Dirichlet Allocation (LDA) has turned out to be the benchmark of the topic modelling community. The key idea is to represent text documents as random mixtures over latent semantic structures called topics. Each topic follows a multinomial distribution over the vocabulary words. In order to understand the result of a topic model, researchers usually select the top-n (essential words) words with the highest probability given a topic and look for meaningful and interpretable semantic themes. This work proposes a new method for exploring topics in LDA models, using Statistically Validated Networks (SVNs). The main idea of the proposed method is to consider co-occurrence between essential words as a measure of association. Two different approaches, called undirected and directed are proposed. Firstly, the symmetrical asso- ciation between two words is taken into account, i.e. how many times two words are found in the same sentence. Conversely, in the directed approach, the order in which the words are in the sentence is also considered. We use hypothesis testing to assess whether the co-occurrence between two words can be attributed to the chance or if these links carry relevant information about the structure of topics. Specifically, textual data is represented as a bipartite network in which one set of nodes is made by sentences, and the other set of nodes is made by a list of essential words associated with a given topic. A link between a word and a sentence is set if the word belongs to that sentence. Therefore, the projection of the bipartite network on the set of words results in a word-co-occurrence network. Note that the directed approach produces a directed network while the undirected one an undirected network. Indeed, a directed link from one word to another may be val- idated, but not the other way around. The two methods are applied to a real dataset, highlighting the differences.

The outbreak of coronavirus disease 2019 (COVID-19) was highly stressful for people. In general, fear and anxiety about a disease can be overwhelming and cause strong emotions in adults and children. One way to cope with this stress consists in listening to music. Aim of this work is to understand if the music heard during the lock-down reflects the emotions generated by the pandemic on each of us. So, the primary goal of this work is to build two indices for measuring the anger and joy levels of the top streamed songs by Italian Spotify users (during the SARS-CoV-2 pandemic), and study their evolution over time. A Hierarchical Cluster Analysis has been applied in order to identify groups of weeks reflecting common musical sentiments, and a Beta regression model is used to validate the results of cluster analysis.

Decision tree learning is among the most popular and most traditional families of machine learning algorithms. While these techniques excel in being quite intuitive and interpretable, they also suffer from instability: small perturbations in the training data may result in big changes in the predictions. The so-called ensemble methods combine the output of multiple trees, which makes the decision more reliable and stable. They have been primarily applied to numeric prediction problems and to classification tasks. In the last years, some attempts to extend the ensemble methods to ordinal data can be found in the literature, but no concrete methodology has been provided for preference data. In this paper, we extend decision trees, and in the following also ensemble methods to ranking data. In particular, we propose a theoretical and computational definition of bagging and boosting, two of the best known ensemble methods. In an experimental study using simulated data and real-world datasets, our results confirm that known results from classification, such as that boosting outperforms bagging, could be successfully carried over to the ranking case.

Preference data are a particular type of ranking data that arise when several individuals express their preferences over a finite set of items. Within this framework, the main issue concerns the aggregation of the preferences to identify a compromise or a “consensus”, defined as the closest ranking (i.e. with the minimum distance or maximum correlation) to the whole set of preferences. Many approaches have been proposed, but they are not sensitive to the importance of items: i.e. changing the rank of a highly-relevant element should result in a higher penalty than changing the rank of a negligible one. The goal of this paper is to investigate the consensus between rankings taking into account the importance of items (element weights). For this purpose, we present: i) an element weighted rank correlation coefficient as an extension of the Emond and Mason’s one, and ii) an element weighted rank distance as an extension of the Kemeny distance. The one-to-one correspondence between the weighted distance and the rank correlation coefficient is analytically proved. Moreover, a procedure to obtain the consensus ranking among several individuals is described and its performance is studied both by simulation and by the application to real datasets.

Gli alberi decisionali sono una tecnica predittiva di machine learning particolarmente diffusa, utilizzata per prevedere delle variabili discrete (classificazione) o continue (regressione). Gli algoritmi alla base di queste tecniche sono intuitivi e interpretabili, ma anche instabili. Infatti, per rendere la classificazione più affidabile si `e soliti combinare l’output di più alberi. In letteratura, sono stati proposti diversi approcci per classificare ranking data attraverso gli alberi decisionali, ma nessuno di questi tiene conto ne dell’importanza, ne delle somiglianza dei singoli elementi di ogni ranking. L’obiettivo di questo articolo `e di proporre un’estensione ponderata del metodo boosting per ranking, che tenga conto della struttura di similarità e dell’importanza dei singoli elementi. I vantaggi di questa procedura sono mostrati con un esempio su un dataset reale. Decision tree learning is one of the most popular families of machine learning algorithms. These techniques are quite intuitive and interpretable but also unstable. It is necessary to use ensemble methods that combine the output of multiple trees, to make the procedure more reliable and stable. Many approaches have been proposed for ranking data, but they are not sensitive to the importance of items. For example, changing the rank of a highly-relevant element should result in a higher penalty than changing a negligible one. Likewise, swapping two similar elements should be less penalized than swapping two dissimilar ones. This paper extends the boosting ensemble method to weighted ranking data, proposing a theoretical and computational definition of item-weighted boosting. The advantages of this procedure are shown through an example on a real data set.

Linear mixed-effects models are a class of models widely used for analyzing different types of data: longitudinal, clustered and panel data. Many fields, in which a statistical methodology is required, involve the employment of linear mixed models, such as biology, chemistry, medicine, finance and so forth. One of the most important processes, in a statistical analysis, is given by model selection. Hence, since there are a large number of linear mixed model selection procedures available in the literature, a pressing issue is how to identify the best approach to adopt in a specific case. We outline mainly all approaches focusing on the part of the model subject to selection (fixed and/or random), the dimensionality of models and the structure of variance and covariance matrices, and also, wherever possible, the existence of an implemented application of the methodologies set out.

Environmental data usually have a spatio-temporal structure; pollutant concentrations, for example, are recorded along time and space. Generalized Additive Models (GAMs) represent a suitable tool to model spatial and/or temporal trends of this kind of data, that can be treated as functional, although they are collected as discrete observations. Frequently, the attention is focused on the prediction of a single pollutant at an unmonitored site and, at this aim, we extend kriging for functional data to a multivariate context by exploiting the correlation with the other pollutants. In particular, we propose two procedures: the first one (FKED) combines the regression of a variable (pollutant), of primary interest on the other variables, with functional kriging of the regression residuals; the second one (FCK) is based on linear unbiased prediction of spatially correlated multivariate random processes. The performance of the two proposed procedures is assessed by cross validation; data recorded during a year (2011) from the monitoring network of the state of California (USA) are considered.

In the framework of preference rankings, the interest can lie in finding which predictors and which interactions are able to explain the observed preference structures. The last years have seen a remarkable owering of works about the use of decision tree for clustering preference vectors. As a matter of fact, decision trees are useful and intuitive, but they are very unstable: small perturbations bring big changes. This is the reason why it could be necessary to use more stable procedures in order to clustering ranking data. In this work, following the idea of Bolton (2003), a Projection Pursuit (PP) clustering algorithm for preference data will be proposed in order to extract useful information in a low-dimensional subspace by starting from a high but most empty dimensional space. Projection pursuit clustering is a synthesis of projection pursuit and nonhierarchical clustering methods that simultaneously attempts to cluster the data and to find a low-dimensional representation of this cluster structure. As introduced by Huber (1985), a PP algorithm consists of two components: an index function I(α) that measures the "usefulness" of projection and a search algorithm that varies the projection direction so as to find the optimal projections, given the index function I(α) and the data set X. In this work a proper specified Projection index function for discrete data will be defined: several distances will be used to evaluate distances between the density of the projected data and the uninteresting uniform density. We also propose diagnostics for finding the optimum number of clusters in projection pursuit clustering. All the methodology is illustrated and evaluated on one simulated and one real dataset.

Within the framework of preference rankings, the interest can lie in finding which predictors and which interactions are able to explain the observed preference structures, because preference decisions will usually depend on the characteristics of both the judges and the objects being judged. This work proposes the use of a univariate decision tree for ranking data based on the weighted distances for complete and incomplete rankings, and considers the area under the ROC curve both for pruning and model assessment. Two real and well-known datasets, the SUSHI preference data and the University ranking data, are used to display the performance of the methodology.