Deep network embedding with dimension selection.

Area of Science:

• Machine Learning
• Network Science
• Statistical Inference

Background:

• Network embedding converts complex network data into a format suitable for machine learning.
• Existing methods often use heuristics for embedding dimensions, leading to bias.
• Deep learning embedding methods face nonidentifiability issues.

Purpose of the Study:

• To develop a statistically rigorous framework for network embedding.
• To address bias and nonidentifiability issues in current network embedding techniques.
• To establish theoretical foundations for network embedding using missing data imputation.

Main Methods:

• Network embedding vectors are treated as missing data.
• A sparse decoder reconstructs network features.
• An adaptive stochastic gradient Markov chain Monte Carlo (MCMC) algorithm is used for imputation and decoder training.

Main Results:

• The sparse decoder enables parsimonious mapping, aiding embedding dimension selection.
• Nonidentifiability issues in deep embedding methods are overcome.
• Embedding vectors converge to a desired posterior distribution, mitigating bias.

Conclusions:

• This work provides the first theoretical foundation for network embedding within a missing data imputation framework.
• The proposed method offers improved statistical rigor and overcomes limitations of existing techniques.
• This approach enhances the reliability of downstream statistical inference on network data.