arXiv subjects

Laura Anderlucci

Publications and source records attributed to Laura Anderlucci.

10 recordsLinked to original sources

arXiv2026

A Poisson Factor Mixture Model for the Analysis of Linguistic Competence in Italian University Students' Writing

Public debate on the alleged decline of language skills among younger generations often focuses on university students, the most highly educated segment of the population. Rather than addressing the ill posed question of linguistic decline, this paper examines how formal written Italian is currently used by university students and whether systematic patterns of competence and heterogeneity can be identified. The analysis is based on data from the UniversITA project, which collected formal texts written by a large and nationally representative sample of Italian university students. Texts were annotated for linguistically motivated features covering orthography, lexicon, syntax, morphosyntax, coherence, register, and sentence structure, yielding low frequency multivariate count data. To analyse these data, we propose a novel model-based clustering approach based on a Poisson factor mixture model that accounts for dependence among linguistic features and unobserved population heterogeneity. The results identify two correlated dimensions of writing competence, interpretable as communicative competence and linguistic grammatical competence. When educational and socio demographic information is incorporated, distinct student profiles emerge that are associated with field of study and educational background. These findings provide quantitative evidence on contemporary writing and offer insights relevant for language education and higher education policy.

stat.ME↗

arXiv2025

Model-Based Clustering of Functional Data Via Random Projection Ensembles

Clustering functional data is a challenging task due to intrinsic infinite-dimensionality and the need for stable, data-adaptive partitioning. In this work, we propose a clustering framework based on Random Projections, which simultaneously performs dimensionality reduction and generates multiple stochastic representations of the original functions. Each projection is clustered independently, and the resulting partitions are then aggregated through an ensemble consensus procedure, enhancing robustness and mitigating the influence of any single projection. To focus on the most informative representations, projections are ranked according to clustering quality criteria, and only a selected subset is retained. In particular, we adopt Gaussian Mixture Models as base clusterers and employ the Kullback-Leibler divergence to order the random projections; these choices enable fast computation and eliminate the need to specify the number of clusters a priori. The performance of the proposed methodology is assessed through an extensive simulation study and two real-data applications, one from spectroscopy data for food authentication and one from log-periodograms of speech recording; the obtained results suggest that the proposal represents an effective tool for the clustering of functional data.

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arXiv2020

Deep Mixtures of Unigrams for uncovering Topics in Textual Data

Mixtures of Unigrams are one of the simplest and most efficient tools for clustering textual data, as they assume that documents related to the same topic have similar distributions of terms, naturally described by Multinomials. When the classification task is particularly challenging, such as when the document-term matrix is high-dimensional and extremely sparse, a more composite representation can provide better insight on the grouping structure. In this work, we developed a deep version of mixtures of Unigrams for the unsupervised classification of very short documents with a large number of terms, by allowing for models with further deeper latent layers; the proposal is derived in a Bayesian framework. The behaviour of the Deep Mixtures of Unigrams is empirically compared with that of other traditional and state-of-the-art methods, namely $k$-means with cosine distance, $k$-means with Euclidean distance on data transformed according to Semantic Analysis, Partition Around Medoids, Mixture of Gaussians on semantic-based transformed data, hierarchical clustering according to Ward's method with cosine dissimilarity, Latent Dirichlet Allocation, Mixtures of Unigrams estimated via the EM algorithm, Spectral Clustering and Affinity Propagation clustering. The performance is evaluated in terms of both correct classification rate and Adjusted Rand Index. Simulation studies and real data analysis prove that going deep in clustering such data highly improves the classification accuracy.

stat.ML↗

arXiv2020

High-dimensional clustering via Random Projections

In this work, we address the unsupervised classification issue by exploiting the general idea of Random Projection Ensemble. Specifically, we propose to generate a set of low dimensional independent random projections and to perform model-based clustering on each of them. The top $B^*$ projections, i.e. the projections which show the best grouping structure are then retained. The final partition is obtained by aggregating the clusters found in the projections via consensus. The performances of the method are assessed on both real and simulated datasets. The obtained results suggest that the proposal represents a promising tool for high-dimensional clustering.

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arXiv2019

Matrix sketching for supervised classification with imbalanced classes

Matrix sketching is a recently developed data compression technique. An input matrix A is efficiently approximated with a smaller matrix B, so that B preserves most of the properties of A up to some guaranteed approximation ratio. In so doing numerical operations on big data sets become faster. Sketching algorithms generally use random projections to compress the original dataset and this stochastic generation process makes them amenable to statistical analysis. The statistical properties of sketching algorithms have been widely studied in the context of multiple linear regression. In this paper we propose matrix sketching as a tool for rebalancing class sizes in supervised classification with imbalanced classes. It is well-known in fact that class imbalance may lead to poor classification performances especially as far as the minority class is concerned.

stat.ML↗

arXiv2019

Quantile-based clustering

A new cluster analysis method, $K$-quantiles clustering, is introduced. $K$-quantiles clustering can be computed by a simple greedy algorithm in the style of the classical Lloyd's algorithm for $K$-means. It can be applied to large and high-dimensional datasets. It allows for within-cluster skewness and internal variable scaling based on within-cluster variation. Different versions allow for different levels of parsimony and computational efficiency. Although $K$-quantiles clustering is conceived as nonparametric, it can be connected to a fixed partition model of generalized asymmetric Laplace-distributions. The consistency of $K$-quantiles clustering is proved, and it is shown that $K$-quantiles clusters correspond to well separated mixture components in a nonparametric mixture. In a simulation, $K$-quantiles clustering is compared with a number of popular clustering methods with good results. A high-dimensional microarray dataset is clustered by $K$-quantiles.

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arXiv2019

One-class classification with application to forensic analysis

The analysis of broken glass is forensically important to reconstruct the events of a criminal act. In particular, the comparison between the glass fragments found on a suspect (recovered cases) and those collected on the crime scene (control cases) may help the police to correctly identify the offender(s). The forensic issue can be framed as a one-class classification problem. One-class classification is a recently emerging and special classification task, where only one class is fully known (the so-called target class), while information on the others is completely missing. We propose to consider classic Gini's transvariation probability as a measure of typicality, i.e. a measure of resemblance between an observation and a set of well-known objects (the control cases). The aim of the proposed Transvariation-based One-Class Classifier (TOCC) is to identify the best boundary around the target class, that is, to recognise as many target objects as possible while rejecting all those deviating from this class.

stat.AP↗

arXiv2019

Classifying textual data: shallow, deep and ensemble methods

This paper focuses on a comparative evaluation of the most common and modern methods for text classification, including the recent deep learning strategies and ensemble methods. The study is motivated by a challenging real data problem, characterized by high-dimensional and extremely sparse data, deriving from incoming calls to the customer care of an Italian phone company. We will show that deep learning outperforms many classical (shallow) strategies but the combination of shallow and deep learning methods in a unique ensemble classifier may improve the robustness and the accuracy of "single" classification methods.

cs.CL↗

arXiv2017

The Importance of Being Clustered: Uncluttering the Trends of Statistics from 1970 to 2015

In this paper we retrace the recent history of statistics by analyzing all the papers published in five prestigious statistical journals since 1970, namely: Annals of Statistics, Biometrika, Journal of the American Statistical Association, Journal of the Royal Statistical Society, series B and Statistical Science. The aim is to construct a kind of "taxonomy" of the statistical papers by organizing and by clustering them in main themes. In this sense being identified in a cluster means being important enough to be uncluttered in the vast and interconnected world of the statistical research. Since the main statistical research topics naturally born, evolve or die during time, we will also develop a dynamic clustering strategy, where a group in a time period is allowed to migrate or to merge into different groups in the following one. Results show that statistics is a very dynamic and evolving science, stimulated by the rise of new research questions and types of data.

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arXiv2015

Covariance pattern mixture models for the analysis of multivariate heterogeneous longitudinal data

We propose a novel approach for modeling multivariate longitudinal data in the presence of unobserved heterogeneity for the analysis of the Health and Retirement Study (HRS) data. Our proposal can be cast within the framework of linear mixed models with discrete individual random intercepts; however, differently from the standard formulation, the proposed Covariance Pattern Mixture Model (CPMM) does not require the usual local independence assumption. The model is thus able to simultaneously model the heterogeneity, the association among the responses and the temporal dependence structure. We focus on the investigation of temporal patterns related to the cognitive functioning in retired American respondents. In particular, we aim to understand whether it can be affected by some individual socio-economical characteristics and whether it is possible to identify some homogenous groups of respondents that share a similar cognitive profile. An accurate description of the detected groups allows government policy interventions to be opportunely addressed. Results identify three homogenous clusters of individuals with specific cognitive functioning, consistent with the class conditional distribution of the covariates. The flexibility of CPMM allows for a different contribution of each regressor on the responses according to group membership. In so doing, the identified groups receive a global and accurate phenomenological characterization.

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