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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.

In the framework of preference rankings, the interest can lie in clustering individuals or items in order to reduce the complexity of the preference space for an easier interpretation of collected data. The last years have seen a remarkable flowering 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, a Projection Clustering Unfolding (PCU) algorithm for preference data will be proposed in order to extract useful information in a low-dimensional subspace by starting from an high but mostly empty dimensional space. Comparison between unfolding configurations and PCU solutions will be carried out through Procrustes analysis.

Il volume raccoglie gli appunti delle lezioni del corso di Diritto civile e nella sostanza anticipa un contributo al volume di prossima uscita su Il Contratto in generale del Trattato del diritto privato curato da Salvatore Mazzamuto.

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.

Le tre grandi novità che hanno interessato la responsabilità contrattuale nell’ultimo ventennio, e cioè la “contrattualizzazione” della responsabilità medica (1999), l’inversione dell’onere di prova (dell’inadempimento e soprattutto) dell’inesatto adempimento (2001), e l’abbandono esplicito della categoria delle “obbligazioni di mezzi” (2008), restituiscono un sistema incoerente ed eccessivamente rigido. Il nuovo assetto conseguente allo spostamento della responsabilità medica verso la responsabilità contrattuale (1999) – in cui è comunque ancora il paziente, creditore di una prestazione di mezzi, a dover provare la colpa, tranne che nelle prestazioni routinarie – ha infatti retto sino al tempo in cui in quest’ultimo ambito, quello contrattuale, albergavano ancora le obbligazioni di mezzi e la relativa disciplina sostanzialmente aquiliana in punto di favor debitoris (è il creditore-danneggiato a dover provare la colpa). Quando, però, qualche anno più tardi, la giurisprudenza ha abbandonato quella distinzione – potrebbe dirsi, prima sul piano processuale (2001) e poi sostanziale (2008) – i nodi sono venuti al pettine: il medico, che aveva già indossato malvolentieri il “camice” contrattuale, non ha infatti retto la severità di un regime - in cui è sempre il debitore a dover provare l’assenza di colpa – tradizionalmente poco congeniale alle obbligazioni professionali, con la conseguenza che legislatore (2017) e giurisprudenza – come era forse prevedibile20 – hanno dovuto venirgli in soccorso, (ri)qualificando la fattispecie in senso extracontrattuale e sgravandolo dell’onere della prova del nesso di causalità.

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.

Probabilistic topic models have become one of the most widespread machine learning techniques in textual analysis. Topic discovering is an unsupervised process that does not guarantee the interpretability of its output. Hence, the automatic evaluation of topic coherence has attracted the interest of many researchers over the last decade, and it is an open research area. This article offers a new quality evaluation method based on statistically validated networks (SVNs). The proposed probabilistic approach consists of representing each topic as a weighted network of its most probable words. The presence of a link between each pair of words is assessed by statistically validating their co-occurrence in sentences against the null hypothesis of random co-occurrence. The proposed method allows one to distinguish between high-quality and low-quality topics, by making use of a battery of statistical tests. The statistically significant pairwise associations of words represented by the links in the SVN might reasonably be expected to be strictly related to the semantic coherence and interpretability of a topic. Therefore, the more connected the network, the more coherent the topic in question. We demonstrate the effectiveness of the method through an analysis of a real text corpus, which shows that the proposed measure is more correlated with human judgement than the state-of-the-art coherence measures.

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.