Robustifying Algorithms of Learning Latent Trees with Vector Variables

by   Fengzhuo Zhang, et al.

We consider learning the structures of Gaussian latent tree models with vector observations when a subset of them are arbitrarily corrupted. First, we present the sample complexities of Recursive Grouping (RG) and Chow-Liu Recursive Grouping (CLRG) without the assumption that the effective depth is bounded in the number of observed nodes, significantly generalizing the results in Choi et al. (2011). We show that Chow-Liu initialization in CLRG greatly reduces the sample complexity of RG from being exponential in the diameter of the tree to only logarithmic in the diameter for the hidden Markov model (HMM). Second, we robustify RG, CLRG, Neighbor Joining (NJ) and Spectral NJ (SNJ) by using the truncated inner product. These robustified algorithms can tolerate a number of corruptions up to the square root of the number of clean samples. Finally, we derive the first known instance-dependent impossibility result for structure learning of latent trees. The optimalities of the robust version of CLRG and NJ are verified by comparing their sample complexities and the impossibility result.


Learning Latent Tree Graphical Models

We study the problem of learning a latent tree graphical model where sam...

Spectral Methods for Learning Multivariate Latent Tree Structure

This work considers the problem of learning the structure of multivariat...

SGA: A Robust Algorithm for Partial Recovery of Tree-Structured Graphical Models with Noisy Samples

We consider learning Ising tree models when the observations from the no...

Breadth-First Depth-Next: Optimal Collaborative Exploration of Trees with Low Diameter

We consider the problem of collaborative tree exploration posed by Fraig...

Latent tree models

Latent tree models are graphical models defined on trees, in which only ...

Predictive Learning on Sign-Valued Hidden Markov Trees

We provide high-probability sample complexity guarantees for exact struc...

Please sign up or login with your details

Forgot password? Click here to reset