The IBMAP approach for Markov networks structure learning

TL;DR

The paper introduces IBMAP, a probabilistic approach for learning Markov network structures that mitigates errors from independence tests, demonstrating improved accuracy and efficiency over existing methods through extensive experiments.

Contribution

It presents IBMAP, a novel probabilistic framework for structure learning in Markov networks, and the IBMAP-HC algorithm, which outperforms existing algorithms in data efficiency and structure quality.

Findings

IBMAP-HC outperforms existing algorithms in synthetic and real data.

IBMAP improves structure learning accuracy and data efficiency.

Using IBMAP-HC in EDAs enhances convergence to optimal solutions.

Abstract

In this work we consider the problem of learning the structure of Markov networks from data. We present an approach for tackling this problem called IBMAP, together with an efficient instantiation of the approach: the IBMAP-HC algorithm, designed for avoiding important limitations of existing independence-based algorithms. These algorithms proceed by performing statistical independence tests on data, trusting completely the outcome of each test. In practice tests may be incorrect, resulting in potential cascading errors and the consequent reduction in the quality of the structures learned. IBMAP contemplates this uncertainty in the outcome of the tests through a probabilistic maximum-a-posteriori approach. The approach is instantiated in the IBMAP-HC algorithm, a structure selection strategy that performs a polynomial heuristic local search in the space of possible structures. We present an extensive empirical evaluation on synthetic and real data, showing that our algorithm outperforms significantly the current independence-based algorithms, in terms of data efficiency and quality of learned structures, with equivalent computational complexities. We also show the performance of IBMAP-HC in a real-world application of knowledge discovery: EDAs, which are evolutionary algorithms that use structure learning on each generation for modeling the distribution of populations. The experiments show that when IBMAP-HC is used to learn the structure, EDAs improve the convergence to the optimum.