Persona: Martín Arevalillo, Jorge
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Martín Arevalillo
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Jorge
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Publicación Skewness-Kurtosis Model-Based Projection Pursuit with Application to Summarizing Gene Expression Data(MDPI, 2022-04-24) Martín Arevalillo, Jorge; Navarro Veguillas, HilarioNon-normality is a usual fact when dealing with gene expression data. Thus, flexible models are needed in order to account for the underlying asymmetry and heavy tails of multivariate gene expression measures. This paper addresses the issue by exploring the projection pursuit problem under a flexible framework where the underlying model is assumed to follow a multivariate skew-t distribution. Under this assumption, projection pursuit with skewness and kurtosis indices is addressed as a natural approach for data reduction. The work examines its properties giving some theoretical insights and delving into the computational side in regards to the application to real gene expression data. The results of the theory are illustrated by means of a simulation study; the outputs of the simulation are used in combination with the theoretical insights to shed light on the usefulness of skewness-kurtosis projection pursuit for summarizing multivariate gene expression data. The application to gene expression measures of patients diagnosed with triple-negative breast cancer gives promising findings that may contribute to explain the heterogeneity of this type of tumors.Publicación Skewness-Based Projection Pursuit as an Eigenvector Problem in Scale Mixtures of Skew-Normal Distributions(MDPI, 2021-06-03) Martín Arevalillo, Jorge; Navarro Veguillas, HilarioThis paper addresses the projection pursuit problem assuming that the distribution of the input vector belongs to the flexible and wide family of multivariate scale mixtures of skew normal distributions. Under this assumption, skewness-based projection pursuit is set out as an eigenvector problem, described in terms of the third order cumulant matrix, as well as an eigenvector problem that involves the simultaneous diagonalization of the scatter matrices of the model. Both approaches lead to dominant eigenvectors proportional to the shape parametric vector, which accounts for the multivariate asymmetry of the model; they also shed light on the parametric interpretability of the invariant coordinate selection method and point out some alternatives for estimating the projection pursuit direction. The theoretical findings are further investigated through a simulation study whose results provide insights about the usefulness of skewness model-based projection pursuit in the statistical practice.Publicación New Insights on the Multivariate Skew Exponential Power Distribution(De Gruyter, 2023) Martín Arevalillo, Jorge; Navarro Veguillas, HilarioThe multivariate exponential power is a useful distribution for modeling departures from normality in data by means of a tail weight scalar parameter that regulates the non-normality of the model. The incorporation of a shape asymmetry vector into the model serves to account for potential asymmetries and gives rise to the multivariate skew exponential power distribution. This work is aimed at revisiting the skew exponential power distribution taking as a starting point its formulation as a scale mixture of skew-normal distributions. The paper provides some highlights and theoretical insights on the role played by its parameters to assess two complementary aspects of the multivariate non-normality such as directional asymmetry and tail weight behavior regardless of the asymmetry. The intuition behind both issues relies on well-known mathematical ideas about skewness maximization and convex transform stochastic orderings.Publicación Data projections by skewness maximization under scale mixtures of skew-normal vectors(Springer, 2020-02-22) Martín Arevalillo, Jorge; Navarro Veguillas, HilarioMultivariate scale mixtures of skew-normal distributions are flexible models that account for the non-normality of data by means of a tail weight parameter and a shape vector representing the asymmetry of the model in a directional fashion. Its stochastic representation involves a skew-normal vector and a non negative mixing scalar variable, independent of the skew-normal vector, that injects tail weight behavior into the model. In this paper we look into the problem of finding the projection that maximizes skewness for vectors that follow a scale mixture of skew-normal distribution; when a simple condition on the moments of the mixing variable is fulfilled, it can be shown that the direction yielding the maximal skewness is proportional to the shape vector. This finding stresses the directional nature of the shape vector to regulate the asymmetry; it also provides the theoretical foundations motivating the skewness based projection pursuit problem in this class of distributions. Some examples that illustrate the application of our results are also given; they include a simulation experiment with artificial data, which sheds light on the usefulness and implications of our results, and the application to real data.Publicación Bayesian networks established functional differences between breast cancer subtypes(PLOS, 2020-06-11) Trilla Fuertes, Lucía; Gámez Pozo, Ángelo; López Vacas, Rocío; López Camacho, Elena; Prado Vázquez, Guillermo; Zapater Moros, Andrea; Díaz Almirón, Mariana; Ferrer Gómez, María; Nanni, Paolo; Zamora Auñón, Pilar; Espinosa, Enrique; Maín, Paloma; Fresno Vara, Juan Ángel; Martín Arevalillo, Jorge; Navarro Veguillas, HilarioBreast cancer is a heterogeneous disease. In clinical practice, tumors are classified as hormonal receptor positive, Her2 positive and triple negative tumors. In previous works, our group defined a new hormonal receptor positive subgroup, the TN-like subtype, which had a prognosis and a molecular profile more similar to triple negative tumors. In this study, proteomics and Bayesian networks were used to characterize protein relationships in 96 breast tumor samples. Components obtained by these methods had a clear functional structure. The analysis of these components suggested differences in processes such as mitochondrial function or extracellular matrix between breast cancer subtypes, including our new defined subtype TN-like. In addition, one of the components, mainly related with extracellular matrix processes, had prognostic value in this cohort. Functional approaches allow to build hypotheses about regulatory mechanisms and to establish new relationships among proteins in the breast cancer context.