Application of regularization methods to high-dimensional data as tool for predicting the geographic origin of the saltwater clam Ruditapes philippinarum - Sampaio, Clara Yokochi de Sousa (2022)
As a consequence of science and technology evolution,data dimensionality has been growing and, along side, the need to solve problems containing these complex types of data. Generically, a data analysis problem is termed high-dimensional when the amount of variables used to explain a certain phenomeno is higher than the number of instances of this same event in a dataset. In the context ofLinear and Generalized Linear Models,high-dimensional datasets provoke the non invertibility of the Fisher Information Matrix, which interferes with the estimation of the model parameters. Most regression models resort to intricate numerical and iterative methods for the assessment of the model coefﬁcients,which often require the non-singularity oft he Fishe rInformation Matrix. Totackle the difﬁculties that emerge when the model’s Fisher Information Matrix is singular, a series of regularization methods have been used to analyze which predictor variables have signiﬁcant linkage to the outcome and estimate their coefﬁcients. Ridge,Least Absolute Shrink age and Selection Operator (LASSO) and Elastic Net methods were at the outset of regularization techniques and, because of this,they are seen as being eminently linked. The algorithms behind these three methods differ in few aspects, see mingly in such a way thatL ASSO overcomes Ridge’s and Elastic Net overcomes LASSO’s difﬁculties. To counter fraud connected to the mislabeling of product origin, regularization methods were applied to predict th elocation of origin of Ruditapes philippinarum,a species of saltwater clam that is commercially harvested for human consumption. The exploited dataset constitutes 30 clam samples, detailing information on 44 composition features,with the purpose of identifying which features distinguish between three geographic origins: Ria de Vigo, Ria de Aveiro, Estuário do Tejo, i.e, a classical Multinomial Logistic Regression problem. However, given the high-dimensionality of the dataset (number of variables higher than the number of observations),theestimationofthemodelcoefﬁcientsposses,asexplainedabove,furtherdifﬁculties. To overcome this problem, the three touched upon regularization methods were applied to model the origin of the clams. Additionally, since datasets of only 30 samples challenge the process of model validation, the re-sampling technique of Monte Carlo Cross-Validation was also implemented. We ﬁnalize comparing the results between the three methods.