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We consider the prediction of weak effects in a multiple-output regressionsetup, when covariates are expected to explain a small amount, less than$\approx 1%$, of the variance of the target variables. To facilitate theprediction of the weak effects, we constrain our model structure by introducinga novel Bayesian approach of sharing information between the regression modeland the noise model. Further reduction of the effective number of parameters isachieved by introducing an infinite shrinkage prior and group sparsity in thecontext of the Bayesian reduced rank regression, and using the Bayesianinfinite factor model as a flexible low-rank noise model. In our experimentsthe model incorporating the novelties outperformed alternatives in genomicprediction of rich phenotype data. In particular, the information sharingbetween the noise and regression models led to significant improvement inprediction accuracy.

Bayesian Information Sharing Between Noise And Regression Models Improves Prediction of Weak Effects