DeepAI

# Algorithms and Complexity Results for Exact Bayesian Structure Learning

Bayesian structure learning is the NP-hard problem of discovering a Bayesian network that optimally represents a given set of training data. In this paper we study the computational worst-case complexity of exact Bayesian structure learning under graph theoretic restrictions on the super-structure. The super-structure (a concept introduced by Perrier, Imoto, and Miyano, JMLR 2008) is an undirected graph that contains as subgraphs the skeletons of solution networks. Our results apply to several variants of score-based Bayesian structure learning where the score of a network decomposes into local scores of its nodes. Results: We show that exact Bayesian structure learning can be carried out in non-uniform polynomial time if the super-structure has bounded treewidth and in linear time if in addition the super-structure has bounded maximum degree. We complement this with a number of hardness results. We show that both restrictions (treewidth and degree) are essential and cannot be dropped without loosing uniform polynomial time tractability (subject to a complexity-theoretic assumption). Furthermore, we show that the restrictions remain essential if we do not search for a globally optimal network but we aim to improve a given network by means of at most k arc additions, arc deletions, or arc reversals (k-neighborhood local search).

• 28 publications
• 36 publications
02/04/2014

### Parameterized Complexity Results for Exact Bayesian Network Structure Learning

Bayesian network structure learning is the notoriously difficult problem...
06/24/2020

### Turbocharging Treewidth-Bounded Bayesian Network Structure Learning

We present a new approach for learning the structure of a treewidth-boun...
11/06/2017

### On Structural Parameterizations of the Edge Disjoint Paths Problem

In this paper we revisit the classical Edge Disjoint Paths (EDP) problem...
01/14/2022

### Reliable Causal Discovery with Improved Exact Search and Weaker Assumptions

Many of the causal discovery methods rely on the faithfulness assumption...
11/28/2020

### On Parameterized Complexity of Liquid Democracy

In liquid democracy, each voter either votes herself or delegates her vo...
06/05/2014

### Advances in Learning Bayesian Networks of Bounded Treewidth

This work presents novel algorithms for learning Bayesian network struct...
05/12/2022

### Viable Algorithmic Options for Creating and Adapting Emergent Software Systems

Given the complexity of modern software systems, it is of great importan...