Learning Minimal Latent Directed Information Polytrees.

Area of Science:

• Causal inference and machine learning
• Probabilistic graphical models
• Information theory

Background:

• Stochastic systems involve complex causal dynamics among random processes.
• Existing methods for causal discovery often require complete data, limiting their applicability.
• Directed information trees offer a framework for modeling these dynamics.

Purpose of the Study:

• To propose a novel approach for learning latent directed polytrees.
• To enable causal discovery in systems where only a subset of processes are observed.
• To establish theoretical guarantees for the proposed learning method.

Main Methods:

• Developing a learning algorithm for latent directed polytrees based on discrepancy measures.
• Utilizing directed information to capture causal relationships among processes.
• Proving the consistency of the learning approach for minimal latent directed trees.

Main Results:

• Demonstrated a consistent approach for learning minimal latent directed trees.
• Showcased the applicability of the method for directed information polytrees with partial observations.
• Analyzed the sample complexity using mutual information as the discrepancy measure.

Conclusions:

• The proposed approach enables effective learning of latent directed polytrees from partial data.
• This work advances causal discovery in complex stochastic systems.
• The findings have implications for understanding and modeling dynamic systems.