Mina Karzand (UW-Madison) - Focused Learning in Tree-Structured Graphical Models

Focused Learning in Tree-Structured Graphical Models

This talk is about the predictive power of learned graphical models where we show that an incorrect or incomplete combinatorial structure (graph) can nevertheless yield accurate predictions. 

In particular, in the first half of the talk, I look into learning tree structured Ising models in which the learned model is used subsequently for prediction based on partial observations (given the realization of a subset of variables, predict the value of the remaining ones). The vast majority of previous work on learning graphical models aims to correctly recover the underlying graph structure.  In the data-constrained regime, learning the entire graph structure correctly is usually impossible. I show that it is possible to efficiently learn a tree model that gives accurate predictions even when there is insufficient data to learn the correct structure.

The second half of the talk is about speciation rate estimation in phylogenetic trees. This problem is essentially one of inferring features of sequences at the leaves of the tree) of a latent tree model (phylogeny). I show that to estimate the speciation rate efficiently, it is not necessary to follow the popular approach of reconstructing the complete tree structure as an intermediate step, which requires long DNA sequences. Instead, one can extract precisely the right type of information about the rates by zooming into carefully chosen local structures. My results show that an incomplete and partially incorrect summary of the tree structure is enough to estimate the speciation rate with the minimax optimal dependence on the length of observed DNA sequences.

Joint work with Guy Bresler, Sebastien Roch and Robert Nowak.

Host: Eric Jonas