Optimal Estimation of Gaussian (Poly)trees

This is an implementation of the following paper: "Optimal Estimation of Gaussian (Poly)trees".

Introduction

We develop optimal algorithms for learning undirected Gaussian trees and directed Gaussian polytrees from data. We consider both problems of distribution learning (i.e. in KL distance) and structure learning (i.e. exact recovery).

1. [Chow-Liu algorithm] The first approach is based on the Chow-Liu algorithm, and learns an optimal tree-structured distribution efficiently.
2. [PC-tree] The second approach is a modification of the PC algorithm for polytrees that uses partial correlation as a conditional independence tester for constraint-based structure learning. We derive explicit finite-sample guarantees for both approaches, and show that both approaches are optimal by deriving matching lower bounds.

Prerequisites

• Python 3.6+
  • argpase
  • numpy
  • pandas
  • scipy
  • sklearn
  • networkx
  • tqdm
  • causallearn
  • Tetrad

Contents

• data.py - generate synthetic data.
• config.py - simulation parameters.
• evaluate.py - performance evauation
• main.py - main algorihtm.
• method.py- including mutual information tester, chow-liu tree algorithm, and pc-tree algorithm

Parameters

Parameter	Type	Description	Options
n	int	number of samples	-
d	int	number of variables	-
tg	str	type of graph (default: random tree)	-

Running a simple demo

The simplest way to try out Polytree is to run a simple example:

$ git clone https://github.com/YohannaWANG/Polytree.git
$ cd Polytree/
$ python $ cd Polytree/main.py

Runing as a command

Alternatively, you can install the package and run the algorithm as a command:

$ pip install git+git://github.com/YohannaWANG/Polytree
$ cd Polytree
$ python main.py --d 100 --n 1000 

Performance comparison

SHD	PRR