Sparse semi-supervised heterogeneous interbattery bayesian analysis

The Bayesian approach to feature extraction, known as factor analysis (FA), has been widely studied in machine learning to obtain a latent representation of the data. An adequate selection of the probabilities and priors of these bayesian models allows the model to better adapt to the data nature (i.e. heterogeneity, sparsity), obtaining a more representative latent space. The objective of this article is to propose a general FA framework capable of modelling any problem. To do so, we start from the Bayesian Inter-Battery Factor Analysis (BIBFA) model, enhancing it with new functionalities to be able to work with heterogeneous data, to include feature selection, and to handle missing values as well as semi-supervised problems. The performance of the proposed model, Sparse Semi-supervised Heterogeneous Interbattery Bayesian Analysis (SSHIBA), has been tested on different scenarios to evaluate each one of its novelties, showing not only a great versatility and an interpretability gain, but also outperforming most of the state-of-the-art algorithms.The authors wish to thank Irene Santos, for fruitful discussions and help during the earlier stages of our work. The work of Pablo M. Olmos was partly supported by the Spanish government (Ministerio de Ciencia e Innovación) under grants TEC2017-92552-EXP and RTI2018-099655-B-100; the Comunidad de Madrid under grants IND2017/TIC-7618, IND2018/TIC-9649, IND2020/TIC-17372, and Y2018/TCS-4705; the BBVA Foundation under the Domain Alignment and Data Wrangling with Deep Generative Models (Deep-DARWiN) project; and the European Union (European Regional Development Fund and the European Research Council) through the European Union's Horizon 2020 Research and Innovation Program under grant 714161. C. Sevilla-Salcedo and V. Gómez-Verdejo's work has been partly funded by the Spanish MINECO grants TEC2017-83838-R and PID2020-115363RB-I00