arXiv subjects

José L. Torrecilla

Publications and source records attributed to José L. Torrecilla.

5 recordsLinked to original sources

arXiv2018

Data learning from big data

Technology is generating a huge and growing availability of observa tions of diverse nature. This big data is placing data learning as a central scientific discipline. It includes collection, storage, preprocessing, visualization and, essentially, statistical analysis of enormous batches of data. In this paper, we discuss the role of statistics regarding some of the issues raised by big data in this new paradigm and also propose the name of data learning to describe all the activities that allow to obtain relevant knowledge from this new source of information.

stat.OT↗

arXiv2018

Feature selection in functional data classification with recursive maxima hunting

Dimensionality reduction is one of the key issues in the design of effective machine learning methods for automatic induction. In this work, we introduce recursive maxima hunting (RMH) for variable selection in classification problems with functional data. In this context, variable selection techniques are especially attractive because they reduce the dimensionality, facilitate the interpretation and can improve the accuracy of the predictive models. The method, which is a recursive extension of maxima hunting (MH), performs variable selection by identifying the maxima of a relevance function, which measures the strength of the correlation of the predictor functional variable with the class label. At each stage, the information associated with the selected variable is removed by subtracting the conditional expectation of the process. The results of an extensive empirical evaluation are used to illustrate that, in the problems investigated, RMH has comparable or higher predictive accuracy than the standard dimensionality reduction techniques, such as PCA and PLS, and state-of-the-art feature selection methods for functional data, such as maxima hunting.

stat.ML↗

arXiv2016

On the use of reproducing kernel Hilbert spaces in functional classification

The Hájek-Feldman dichotomy establishes that two Gaussian measures are either mutually absolutely continuous with respect to each other (and hence there is a Radon-Nikodym density for each measure with respect to the other one) or mutually singular. Unlike the case of finite dimensional Gaussian measures, there are non-trivial examples of both situations when dealing with Gaussian stochastic processes. This paper provides: (a) Explicit expressions for the optimal (Bayes) rule and the minimal classification error probability in several relevant problems of supervised binary classification of mutually absolutely continuous Gaussian processes. The approach relies on some classical results in the theory of Reproducing Kernel Hilbert Spaces (RKHS). (b) An interpretation, in terms of mutual singularity, for the "near perfect classification" phenomenon described by Delaigle and Hall (2012). We show that the asymptotically optimal rule proposed by these authors can be identified with the sequence of optimal rules for an approximating sequence of classification problems in the absolutely continuous case. (c) A new model-based method for variable selection in binary classification problems, which arises in a very natural way from the explicit knowledge of the RN-derivatives and the underlying RKHS structure. Different classifiers might be used from the selected variables. In particular, the classical, linear finite-dimensional Fisher rule turns out to be consistent under some standard conditions on the underlying functional model.

stat.ME↗

arXiv2015

The mRMR variable selection method: a comparative study for functional data

The use of variable selection methods is particularly appealing in statistical problems with functional data. The obvious general criterion for variable selection is to choose the `most representative' or `most relevant' variables. However, it is also clear that a purely relevance-oriented criterion could lead to select many redundant variables. The mRMR (minimum Redundance Maximum Relevance) procedure, proposed by Ding and Peng (2005) and Peng et al. (2005) is an algorithm to systematically perform variable selection, achieving a reasonable trade-off between relevance and redundancy. In its original form, this procedure is based on the use of the so-called mutual information criterion to assess relevance and redundancy. Keeping the focus on functional data problems, we propose here a modified version of the mRMR method, obtained by replacing the mutual information by the new association measure (called distance correlation) suggested by Székely et al. (2007). We have also performed an extensive simulation study, including 1600 functional experiments (100 functional models $\times$ 4 sample sizes $\times$ 4 classifiers) and three real-data examples aimed at comparing the different versions of the mRMR methodology. The results are quite conclusive in favor of the new proposed alternative.

stat.ME↗

arXiv2015

Variable selection in functional data classification: a maxima-hunting proposal

Variable selection is considered in the setting of supervised binary classification with functional data $\{X(t),\ t\in[0,1]\}$. By "variable selection" we mean any dimension-reduction method which leads to replace the whole trajectory $\{X(t),\ t\in[0,1]\}$, with a low-dimensional vector $(X(t_1),\ldots,X(t_k))$ still keeping a similar classification error. Our proposal for variable selection is based on the idea of selecting the local maxima $(t_1,\ldots,t_k)$ of the function ${\mathcal V}_X^2(t)={\mathcal V}^2(X(t),Y)$, where ${\mathcal V}$ denotes the "distance covariance" association measure for random variables due to Székely, Rizzo and Bakirov (2007). This method provides a simple natural way to deal with the relevance vs. redundancy trade-off which typically appears in variable selection. This paper includes (a) Some theoretical motivation: a result of consistent estimation on the maxima of ${\mathcal V}_X^2$ is shown. We also show different theoretical models for the underlying process $X(t)$ under which the relevant information in concentrated in the maxima of ${\mathcal V}_X^2$. (b) An extensive empirical study, including about 400 simulated models and real data examples, aimed at comparing our variable selection method with other standard proposals for dimension reduction.

stat.ME↗