Algorithm

Objectives

For observation \(i\) at iteration \(m\), gradients \(g_i = \partial \ell(y_i, F_i)/\partial F_i\) and Hessians \(h_i = \partial^2 \ell(y_i, F_i)/\partial F_i^2\) are computed for the current objective:

• Cox (objective = "cox"): negative Cox partial log-likelihood, Breslow handling of tied event times, with \(g_i\)/\(h_i\) derived from cumulative risk-set sums computed once per boosting round in \(O(n \log n)\) (sort once, reuse the ordering).
• AFT (objective = "aft"): negative log-likelihood of a normal location-scale accelerated failure time model, with separate closed-form gradients/Hessians for event vs. censored observations.

Split search

For every node and feature: gradient and Hessian sums are accumulated by histogram bin (continuous features are pre-binned into up to max_bins quantile-based bins, default 255), cumulative left/right statistics are computed, and every valid split point is scored by

\[ \text{Gain} = \frac12\left[\frac{G_L^2}{H_L+\lambda} + \frac{G_R^2}{H_R+\lambda} - \frac{(G_L+G_R)^2}{H_L+H_R+\lambda}\right] - \gamma, \]

with missing values evaluated as routed both left and right; the better direction is stored as the node’s default. Leaf values are \(w_j = -G_j/(H_j+\lambda)\).

Parallelism

The per-feature histogram/gain scan within each node is data-parallel (each feature’s best split is independent of the others given the node’s gradient/Hessian sums), so it is dispatched through RcppParallel::parallelFor() once the node/feature count crosses an internal threshold (below it, the same code path runs serially – dispatch overhead isn’t worth it for small nodes). Because the reduction across features is a fixed-order argmax rather than an order-dependent floating-point sum, training is bit-identical regardless of threads.

What’s not yet implemented

Leaf-wise (grow_policy = "lossguide") growth, validation-based early stopping (accepted but inactive), monotonic/interaction constraints, and AFT distributions other than the normal.