Andrew McInerney: A Smooth Information Criterion for Selection and Fusion of Categorical Predictors

Categorical predictors often contain levels with indistinguishable effects on the response, motivating the fusion of category coefficients to obtain parsimonious and interpretable models.  Classical approaches to fusion typically rely on penalised likelihood methods that require the selection of tuning parameters, while discrete optimisation via information criteria becomes computationally infeasible as the number of possible fusion structures grows combinatorially.  In this talk, we propose a smooth information-criterion-based method for simultaneous parameter estimation, factor selection, and fusion of categorical effects within generalized linear models.  The method replaces the discrete L0 penalty underlying the Bayesian information criterion (BIC) with a continuously differentiable surrogate that correctly accounts for the degrees of freedom induced by fusion. This yields a tractable optimisation problem that directly targets the information-criterion objective and eliminates the need for tuning-parameter selection. Simulation studies demonstrate that the proposed approach achieves substantially lower false positive rates for factor selection and level fusion compared with existing penalised methods, while exhibiting behaviour comparable to exhaustive BIC selection when discrete search is feasible. An application to real data illustrates the practical benefits of the method in producing interpretable models.