Classification with Mixed-Type Predictors and Doubly Adaptive Group-Fused Regularisation

Classification with mixed-type predictors—continuous, categorical, and functional—is central to modern sensing and healthcare applications, yet existing estimators address this heterogeneity only partially: sparse linear methods presume a fixed functional form, nonparametric kernel classifiers degrade sharply with dimension, and nonparametric spline smoothing treats each functional predictor as a separate one-dimensional problem without an inherent mechanism for excluding an entire predictor block. None of these approaches jointly estimates feature sparsity and cross-class coefficient homogeneity. This article brings these paradigms under a common additive decomposition and proposes Doubly Adaptive Group-Fused Regularisation (DAGFR), a convex multinomial estimator that jointly pursues group-wise sparsity and pairwise cross-class coefficient fusion. Under fixed-dimensional regularity conditions, including the availability of a shared n-consistent initial estimator, DAGFR is shown to possess the Group-wise Adaptive Fusion Oracle Property under a shared-window regularisation-rate condition. Controlled simulations examine the finite-sample behaviour predicted by the oracle result. On the MotionSense human activity benchmark, DAGFR achieves a test accuracy of 77.0%, log-loss of 0.8073, and macro-F1 of 0.7174. Under a common reference-category parameterisation, DAGFR retains 197 free parameters out of 1265, achieving a 6.4-fold parameter compression factor and a feature-column reduction ratio of 0.714. Across the investigated simulations and the fixed MotionSense split, DAGFR produced a compact structured model and the strongest reported predictive metrics among the four fitted procedures.