# Efficient comparison of independence structures of log-linear models

## TL;DR

This paper introduces a novel, efficient metric for directly comparing the independence structures of log-linear models, facilitating better evaluation of structure learning algorithms without requiring full distribution learning.

## Contribution

It presents the first direct, efficient measure for comparing log-linear model structures, avoiding distortions from parameter learning.

## Key findings

- The measure is proven to be a metric.
- The computation method is efficient relative to the number of variables.
- Applicable for evaluating structure learning algorithms.

## Abstract

Log-linear models are a family of probability distributions which capture relationships between variables. They have been proven useful in a wide variety of fields such as epidemiology, economics and sociology. The interest in using these models is that they are able to capture context-specific independencies, relationships that provide richer structure to the model. Many approaches exist for automatic learning of the independence structure of log-linear models from data. The methods for evaluating these approaches, however, are limited, and are mostly based on indirect measures of the complete density of the probability distribution. Such computation requires additional learning of the numerical parameters of the distribution, which introduces distortions when used for comparing structures. This work addresses this issue by presenting the first measure for the direct and efficient comparison of independence structures of log-linear models. Our method relies only on the independence structure of the models, which is useful when the interest lies in obtaining knowledge from said structure, or when comparing the performance of structure learning algorithms, among other possible uses. We present proof that the measure is a metric, and a method for its computation that is efficient in the number of variables of the domain.