Smoothness and Structure Learning by Proxy.

Area of Science:

• Machine Learning
• Computational Statistics
• Data Mining

Background:

• Learning structures from large datasets is computationally intensive.
• Bayesian networks possess a super-exponentially large search space for structure learning.
• Existing methods struggle with scalability due to extensive search and scoring requirements.

Purpose of the Study:

• To develop a computationally efficient method for Bayesian network structure learning.
• To validate the use of proxy scoring functions to accelerate the search process.
• To demonstrate the effectiveness of Gaussian Process regressors as proxy scoring functions.

Main Methods:

• Implemented a proxy-based search strategy using Gaussian Process regressors.
• Trained the proxy on a selection of sampled Bayesian networks.
• Proved the smoothness of a common scoring function for Bayesian networks.
• Compared proxy-based search against exact scoring methods on multiple datasets.

Main Results:

• The proxy-based search method significantly reduces computation time.
• Achieved equivalent or superior network scores compared to exact scoring methods.
• Demonstrated the theoretical foundation for using proxy functions through smoothness bounds.
• Successfully applied the method to various datasets, showing practical efficiency gains.

Conclusions:

• Proxy-based search using Gaussian Process regressors is a well-founded and effective approach for Bayesian network structure learning.
• This method offers a substantial speedup for learning from large datasets.
• The findings pave the way for more scalable and efficient machine learning algorithms.