Data-Driven Constraints on Magnetar Population: No Evidence for a Distinct White Dwarf Channel

Magnetars are usually interpreted as highly magnetized neutron stars, yet a small subset of low spin-down sources has motivated alternative scenarios involving highly magnetized white dwarfs. We test whether the observed magnetar sample is consistent with a single neutron-star population or whether the data favor an additional compact-object channel. We combine exploratory machine-learning diagnostics with hierarchical Bayesian population modeling. First, we apply principal component analysis and K-means clustering in $(P,\dot{P},L_X)$ space, and then train a Random Forest classifier with leave-one-out cross-validation to identify the observables driving the empirical split. We subsequently construct a hierarchical Bayesian mixture model that links spin parameters to magnetic-field distributions through covariate-dependent mixing fractions. Posterior inference is performed with Hamiltonian Monte Carlo, and predictive performance is assessed with Pareto-smoothed importance sampling leave-one-out cross-validation. The exploratory analysis reveals a reproducible sub-structure: the Random Forest reaches $>95\mathrm{\%}$ LOOCV accuracy, with $L_X$, $\dot{P}$, and $kT$ emerging as the dominant predictors. However, the Bayesian comparison shows no statistically significant preference for a two-population model. Instead, a few low spin-down sources receive intermediate posterior membership probabilities, indicating that they are better interpreted as transitional or outlying objects than as members of a clearly distinct class. Overall, current data do not require a separate white-dwarf magnetar population. The main result is therefore conservative but strong: the observed sample is adequately described by a predominantly neutron-star population, while still allowing physically interesting deviations in specific sources.