Consensus collapsed tree

[annazhukova]

Find a way to create a consensus prediction based on several ACRs, i.e. if we reconstruct several trees from the same data (with different methods or even different runs of the same stochastic tree inference tool, or with resampling, etc.)

Useful links: Kendall et al. for metrics for tree comparison, and Kendall et al. for comparisons of 'collapsed' trees.

[saishikawa]

I'm thinking about that. Metric from Kendall et al. can be straightforwardly applied to the PastML prediction (i.e. approximated tree) as we introduce the averaged depth of the compressed node to Kendall's formula. Finding a consensus prediction can be archived by finding a centroid of prediction space which are derived by different trees.

One point of discussion is that we have ancestral state for each node. That is, we need to consider not only 'topological changes' of prediction (which are taken into account by Kendall et al.), but also 'state changes' of it: if two predictions have same topology but different ancestral states for several nodes, this should be counted in the metric.