Rafael A. Moral

AntÔnia A. L. Dos Santos, Rafael A. Moral, Danilo A. Sarti et al.

In plant breeding the presence of a genotype by environment (GxE) interaction has a strong impact on cultivation decision making and the introduction of new crop cultivars. The combination of linear and bilinear terms has been shown to be very useful in modelling this type of data. A widely-used approach to identify GxE is the Additive Main Effects and Multiplicative Interaction Effects (AMMI) model. However, as data frequently can be high-dimensional, Markov chain Monte Carlo (MCMC) approaches can be computationally infeasible. In this article, we consider a variational inference approach for such a model. We derive variational approximations for estimating the parameters and we compare the approximations to MCMC using both simulated and real data. The new inferential framework we propose is on average two times faster whilst maintaining the same predictive performance as MCMC.

Antonia A. L. Dos Santos, Danilo A. Sarti, Rafael A. Moral et al.

We propose a Bayesian tensor regression model to accommodate the effect of multiple factors on phenotype prediction. We adopt a set of prior distributions that resolve identifiability issues that may arise between the parameters in the model. Further, we incorporate a spike-and-slab structure that identifies which interactions are relevant for inclusion in the linear predictor, even when they form a subset of the available variables. Simulation experiments show that our method outperforms previous related models and machine learning algorithms under different sample sizes and degrees of complexity. We further explore the applicability of our model by analysing real-world data related to wheat production across Ireland from 2010 to 2019. Our model performs competitively and overcomes key limitations found in other analogous approaches. Finally, we adapt a set of visualisations for the posterior distribution of the tensor effects that facilitate the identification of optimal interactions between the tensor variables, whilst accounting for the uncertainty in the posterior distribution.

Estevão B. Prado, Andrew C. Parnell, Keefe Murphy et al.

We propose some extensions to semi-parametric models based on Bayesian additive regression trees (BART). In the semi-parametric BART paradigm, the response variable is approximated by a linear predictor and a BART model, where the linear component is responsible for estimating the main effects and BART accounts for non-specified interactions and non-linearities. Previous semi-parametric models based on BART have assumed that the set of covariates in the linear predictor and the BART model are mutually exclusive in an attempt to avoid poor coverage properties and reduce bias in the estimates of the parameters in the linear predictor. The main novelty in our approach lies in the way we change the tree-generation moves in BART to deal with this bias and resolve non-identifiability issues between the parametric and non-parametric components, even when they have covariates in common. This allows us to model complex interactions involving the covariates of primary interest, both among themselves and with those in the BART component. Our novel method is developed with a view to analysing data from an international education assessment, where certain predictors of students' achievements in mathematics are of particular interpretational interest. Through additional simulation studies and another application to a well-known benchmark dataset, we also show competitive performance when compared to regression models, alternative formulations of semi-parametric BART, and other tree-based methods. The implementation of the proposed method is available at \url{https://github.com/ebprado/CSP-BART}.

Estevão B. Prado, Rafael A. Moral, Andrew C. Parnell

Bayesian Additive Regression Trees (BART) is a tree-based machine learning method that has been successfully applied to regression and classification problems. BART assumes regularisation priors on a set of trees that work as weak learners and is very flexible for predicting in the presence of non-linearity and high-order interactions. In this paper, we introduce an extension of BART, called Model Trees BART (MOTR-BART), that considers piecewise linear functions at node levels instead of piecewise constants. In MOTR-BART, rather than having a unique value at node level for the prediction, a linear predictor is estimated considering the covariates that have been used as the split variables in the corresponding tree. In our approach, local linearities are captured more efficiently and fewer trees are required to achieve equal or better performance than BART. Via simulation studies and real data applications, we compare MOTR-BART to its main competitors. R code for MOTR-BART implementation is available at https://github.com/ebprado/MOTR-BART.

Gabriel R. Palma, Sally McClean, Brahim Allan et al.

TV customers today face many choices from many live channels and on-demand services. Providing a personalised experience that saves customers time when discovering content is essential for TV providers. However, a reliable understanding of their behaviour and preferences is key. When creating personalised recommendations for TV, the biggest challenge is understanding viewing behaviour within households when multiple people are watching. The objective is to detect and combine individual profiles to make better-personalised recommendations for group viewing. Our challenge is that we have little explicit information about who is watching the devices at any time (individuals or groups). Also, we do not have a way to combine more than one individual profile to make better recommendations for group viewing. We propose a novel framework using a Gaussian mixture model averaging to obtain point estimates for the number of household TV profiles and a Bayesian random walk model to introduce uncertainty. We applied our approach using data from real customers whose TV-watching data totalled approximately half a million observations. Our results indicate that combining our framework with the selected features provides a means to estimate the number of household TV profiles and their characteristics, including shifts over time and quantification of uncertainty.