Efficient Evolutionary Models with Digraphons

04/26/2021
by   Abhinav Tamaskar, et al.
0

We present two main contributions which help us in leveraging the theory of graphons for modeling evolutionary processes. We show a generative model for digraphons using a finite basis of subgraphs, which is representative of biological networks with evolution by duplication. We show a simple MAP estimate on the Bayesian non parametric model using the Dirichlet Chinese restaurant process representation, with the help of a Gibbs sampling algorithm to infer the prior. Next we show an efficient implementation to do simulations on finite basis segmentations of digraphons. This implementation is used for developing fast evolutionary simulations with the help of an efficient 2-D representation of the digraphon using dynamic segment-trees with the square-root decomposition representation. We further show how this representation is flexible enough to handle changing graph nodes and can be used to also model dynamic digraphons with the help of an amortized update representation to achieve an efficient time complexity of the update at O(√(|V|)log|V|).

READ FULL TEXT
POST COMMENT

Comments

There are no comments yet.

Authors

page 1

page 2

page 3

page 4

05/31/2020

A Fast Algorithm for Online k-servers Problem on Trees

We consider online algorithms for the k-servers problem on trees. There ...
11/03/2018

Efficient Projection onto the Perfect Phylogeny Model

Several algorithms build on the perfect phylogeny model to infer evoluti...
08/18/2018

Bayesian Hidden Markov Tree Models for Clustering Genes with Shared Evolutionary History

Determination of functions for poorly characterized genes is crucial for...
11/27/2012

A simple non-parametric Topic Mixture for Authors and Documents

This article reviews the Author-Topic Model and presents a new non-param...
01/13/2019

A Fully Bayesian Infinite Generative Model for Dynamic Texture Segmentation

Generative dynamic texture models (GDTMs) are widely used for dynamic te...
10/15/2018

A simple proof of Pitman-Yor's Chinese restaurant process from its stick-breaking representation

For a long time, the Dirichlet process has been the gold standard discre...
This week in AI

Get the week's most popular data science and artificial intelligence research sent straight to your inbox every Saturday.