Model Approximation Using Cascade of Tree Decompositions

by   Navid Tafaghodi Khajavi, et al.

In this paper, we present a general, multistage framework for graphical model approximation using a cascade of models such as trees. In particular, we look at the problem of covariance matrix approximation for Gaussian distributions as linear transformations of tree models. This is a new way to decompose the covariance matrix. Here, we propose an algorithm which incorporates the Cholesky factorization method to compute the decomposition matrix and thus can approximate a simple graphical model using a cascade of the Cholesky factorization of the tree approximation transformations. The Cholesky decomposition enables us to achieve a tree structure factor graph at each cascade stage of the algorithm which facilitates the use of the message passing algorithm since the approximated graph has less loops compared to the original graph. The overall graph is a cascade of factor graphs with each factor graph being a tree. This is a different perspective on the approximation model, and algorithms such as Gaussian belief propagation can be used on this overall graph. Here, we present theoretical result that guarantees the convergence of the proposed model approximation using the cascade of tree decompositions. In the simulations, we look at synthetic and real data and measure the performance of the proposed framework by comparing the KL divergences.


page 10

page 16

page 19


Robust estimation of tree structured Gaussian Graphical Model

Consider jointly Gaussian random variables whose conditional independenc...

The Inverse G-Wishart Distribution and Variational Message Passing

Message passing on a factor graph is a powerful paradigm for the coding ...

The Quality of the Covariance Selection Through Detection Problem and AUC Bounds

We consider the problem of quantifying the quality of a model selection ...

Optimal Tree Decompositions Revisited: A Simpler Linear-Time FPT Algorithm

In 1996, Bodlaender showed the celebrated result that an optimal tree de...

Convergent Propagation Algorithms via Oriented Trees

Inference problems in graphical models are often approximated by casting...

Cascade Size Distributions and Why They Matter

How likely is it that a few initial node activations are amplified to pr...

Linear approximation to the statistical significance autocovariance matrix in the asymptotic regime

Approximating significance scans of searches for new particles in high-e...

Please sign up or login with your details

Forgot password? Click here to reset