Summary of Structural Perspective on Constraint-based Learning Of Markov Networks, by Tuukka Korhonen et al.
Structural perspective on constraint-based learning of Markov networks
by Tuukka Korhonen, Fedor V. Fomin, Pekka Parviainen
First submitted to arxiv on: 13 Mar 2024
Categories
- Main: Machine Learning (cs.LG)
- Secondary: Artificial Intelligence (cs.AI); Discrete Mathematics (cs.DM)
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| Summary difficulty | Written by | Summary |
|---|---|---|
| High | Paper authors | High Difficulty Summary Read the original abstract here |
| Medium | GrooveSquid.com (original content) | Medium Difficulty Summary This paper explores constraint-based structure learning in Markov networks, focusing on theoretical limits for two critical aspects: the number of conditional independence tests and the size of conditioning sets. The authors demonstrate that the graph parameter maximum pairwise connectivity (κ) determines the minimum size of conditioning sets required to learn the graph, showing that at least one test with a conditioning set of size at least κ is necessary. Conversely, any graph can be learned by performing tests with conditioning sets of sizes at most κ. Additionally, the authors establish upper and lower bounds on the number of tests required to learn graphs of varying treewidths and maximum degrees. Specifically, they show that every n-vertex graph can be learned by at most nκ tests with conditioning sets of sizes at most κ, while there exist graphs requiring at least nΩ(κ) tests even when the treewidth is bounded. Furthermore, graphs of bounded treewidth can be learned by a polynomial number of tests with conditioning sets of sizes at most 2κ. |
| Low | GrooveSquid.com (original content) | Low Difficulty Summary In this paper, researchers work on understanding how to learn the structure of Markov networks using only data and no prior knowledge. They find that the maximum pairwise connectivity (κ) between nodes in the network is important for learning its structure. The authors show that you need at least one test with a certain size to learn the graph, but also that some graphs can be learned quickly by doing fewer tests. They also discover that there are limits on how fast or slow this process can be based on the complexity of the graph. |
