Multitask Learning Over Adaptive Networks With Grouping Strategies

Considering groups of parameters rather than individual parameters can be beneficial for estimation accuracy if structural relationships between parameters exist (e.g., spatial, hierarchical, or related to the physics of the problem). Group sparsity-estimators are typical examples that benefit from such prior information. Building on this principle, we show that the diffusion LMS algorithm used for distributed inference over adaptive networks can be extended to deal with structured criteria built upon groups of variables, leading to a flexible framework that can encode various relationships in the parameters to estimate. We also introduce online strategies to group the parameters to estimate in an unsupervised manner, and to promote or inhibit collaborations between nodes depending on whether these groups are locally or globally applicable. Simulations illustrate the theoretical findings and the estimation strategies.