14:00 – 15:00 – Malgorzata Bogdan (University of Wroclaw)
Title: Model Patterns Induced by Convex Penalties
Abstract: Regularization is commonly viewed as a tool for controlling model complexity, but it can also be interpreted as a mechanism for learning structural patterns in model parameters. In this talk, I adopt a geometric perspective in which model patterns are characterized through the subdifferential of the penalty, providing a unified way to understand how regularizers encode structural information and induce dimensionality reduction beyond classical sparsity.
Using LASSO and SLOPE-type penalties as guiding examples, I illustrate how different regularization schemes promote distinct forms of structure, including variable selection, coefficient clustering, and hierarchical organization. From this viewpoint, shrinkage emerges not simply as a constraint but as a statistically beneficial operation: directing estimates toward structured regions of the parameter space can substantially improve estimation stability and predictive accuracy.
To formalize these ideas, I outline a general asymptotic framework for pattern recovery in penalized estimators with non-differentiable penalties. The results describe conditions governing successful recovery, clarify the role of regularizer-specific assumptions such as irrepresentability, and motivate two-step strategies that achieve reliable pattern identification under weaker conditions.
Refreshments available between 16:00 – 16:30, Huxley Common Room (HXLY 549)