Multi-task learning improves ancestral state reconstruction.

We consider the ancestral state reconstruction problem where we need to infer phenotypes of ancestors using observations from present-day species. For this problem, we propose a multi-task learning method that uses regularized maximum likelihood to estimate the ancestral states of various traits simultaneously. We then show both theoretically and by simulation that this method improves the estimates of the ancestral states compared to the maximum likelihood method. The result also indicates that for the problem of ancestral state reconstruction under the Brownian motion model, the maximum likelihood method can be improved.