Rafael Sojo

Rafael Sojo, Pedro Larrañaga, Concha Bielza

This paper introduces two transfer learning methodologies for estimating nonparametric Bayesian networks under scarce data. We propose two algorithms, a constraint-based structure learning method, called PC-stable-transfer learning (PCS-TL), and a score-based method, called hill climbing transfer learning (HC-TL). We also define particular metrics to tackle the negative transfer problem in each of them, a situation in which transfer learning has a negative impact on the model's performance. Then, for the parameters, we propose a log-linear pooling approach. For the evaluation, we learn kernel density estimation Bayesian networks, a type of nonparametric Bayesian network, and compare their transfer learning performance with the models alone. To do so, we sample data from small, medium and large-sized synthetic networks and datasets from the UCI Machine Learning repository. Then, we add noise and modifications to these datasets to test their ability to avoid negative transfer. To conclude, we perform a Friedman test with a Bergmann-Hommel post-hoc analysis to show statistical proof of the enhanced experimental behavior of our methods. Thus, PCS-TL and HC-TL demonstrate to be reliable algorithms for improving the learning performance of a nonparametric Bayesian network with scarce data, which in real industrial environments implies a reduction in the required time to deploy the network.

Rafael Sojo, Javier Díaz-Rozo, Concha Bielza et al.

This paper introduces a new type of probabilistic semiparametric model that takes advantage of data binning to reduce the computational cost of kernel density estimation in nonparametric distributions. Two new conditional probability distributions are developed for the new binned semiparametric Bayesian networks, the sparse binned kernel density estimation and the Fourier kernel density estimation. These two probability distributions address the curse of dimensionality, which typically impacts binned models, by using sparse tensors and restricting the number of parent nodes in conditional probability calculations. To evaluate the proposal, we perform a complexity analysis and conduct several comparative experiments using synthetic data and datasets from the UCI Machine Learning repository. The experiments include different binning rules, parent restrictions, grid sizes, and number of instances to get a holistic view of the model's behavior. As a result, our binned semiparametric Bayesian networks achieve structural learning and log-likelihood estimations with no statistically significant differences compared to the semiparametric Bayesian networks, but at a much higher speed. Thus, the new binned semiparametric Bayesian networks prove to be a reliable and more efficient alternative to their non-binned counterparts.