סמינר המחלקה להנדסת תעשייה

Recovering tree models via spectral graph theory
 

Ariel Jaffe is a Gibbs assistant professor in the program of applied mathematics, Yale University
The lecture will be heldon
Tuesday, December 29, 2020, at 14:00 Via Zoom
https://us02web.zoom.us/j/81941109328?pwd=Z04rVGltdmI1Qm5jQjZEZWtwNDgvUT09
 

Abstract:
Modeling high dimensional data by latent tree graphical models is a common approach in multiple machine learning
applications. In these models, the key task is to infer the structure of the tree, given only observations on its terminal
nodes. A canonical example of this setting is the tree of life, where the evolutionary history of a set of organisms is
inferred by their nucleotide or protein sequences.
In our work, we show that the tree structure is strongly related to the spectral properties of a fully connected graph,
defined over the terminal nodes of the tree. This relation forms the theoretical basis of two new methods to recover
latent tree models: (i) spectral neighbor joining, where subsets of nodes are iteratively merged to form the full tree,
and (ii) spectral top down recovery, where the terminal nodes are iteratively partitioned into smaller subsets.
Comparing our approach to several competing methods, we show that in many settings, spectral methods have
stronger theoretical guarantees and work better in practice.
 

Bio:
Ariel Jaffe is a Gibbs assistant professor in the program of applied mathematics, Yale University.
Previously, he completed his Ph.D. in the Weizmann Institute of Science under the guidance of Prof. Boaz Nadler.
His research interests include statistical machine learning and high dimensional data analysis, with a focus on
applications in the fields of computational biology and signal processing.