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//! Regression tree representation and prediction.
//!
//! A tree is a flat array of [`Node`]s (node `0` is the root). Internal nodes
//! carry a numeric split `x[feature] < threshold`. Instances whose feature is
//! *missing* follow the node's `default_left` direction, implementing XGBoost's
//! sparsity-aware routing. Leaf nodes carry the raw leaf weight (the learning
//! rate is applied by the boosting loop, not baked into the tree).
use crate::data::DMatrix;
use serde::{Deserialize, Serialize};
/// Sentinel used in child pointers to mark "no child" (i.e. a leaf).
const NO_CHILD: i32 = -1;
/// A single tree node.
#[derive(Debug, Clone, Copy, PartialEq, Serialize, Deserialize)]
pub struct Node {
/// Split feature index (meaningful only for internal nodes).
pub split_feature: u32,
/// Split threshold: an instance goes left when `value < split_cond`.
pub split_cond: f32,
/// Direction taken by instances with a missing value at this node.
pub default_left: bool,
/// Left child index, or `-1` for a leaf.
pub left: i32,
/// Right child index, or `-1` for a leaf.
pub right: i32,
/// Leaf weight (used only for leaves).
pub leaf_value: f32,
/// Sum of Hessians routed through this node (for cover-based importance/SHAP).
pub sum_hess: f32,
/// Loss reduction (gain) achieved by this node's split (0 for leaves).
pub split_gain: f32,
/// Whether this internal node splits on a categorical feature by set
/// membership rather than a numeric threshold. `false` for numeric splits
/// and leaves.
#[serde(default)]
pub is_categorical: bool,
/// For a categorical node, the start index into the owning tree's category
/// list of the categories routed left. Unused (`0`) otherwise.
#[serde(default)]
pub cat_begin: u32,
/// For a categorical node, the end index (exclusive) into the owning tree's
/// category list of the categories routed left. Unused (`0`) otherwise.
#[serde(default)]
pub cat_end: u32,
}
impl Node {
/// A fresh leaf node with the given weight and cover.
pub(crate) fn leaf(value: f32, sum_hess: f32) -> Self {
Node {
split_feature: 0,
split_cond: 0.0,
default_left: true,
left: NO_CHILD,
right: NO_CHILD,
leaf_value: value,
sum_hess,
split_gain: 0.0,
is_categorical: false,
cat_begin: 0,
cat_end: 0,
}
}
/// Whether this node is a leaf.
#[inline]
pub fn is_leaf(&self) -> bool {
self.left == NO_CHILD
}
}
/// A regression tree: a flat node array with node `0` as the root.
#[derive(Debug, Clone, PartialEq, Serialize, Deserialize, Default)]
pub struct RegTree {
nodes: Vec<Node>,
/// Flat pool of category values routed left by categorical nodes. Node
/// `n` (when `n.is_categorical`) owns `categories[n.cat_begin..n.cat_end]`.
/// Empty for trees with no categorical splits (including all legacy trees).
#[serde(default)]
categories: Vec<u32>,
}
impl RegTree {
/// Create an empty tree with a placeholder root leaf, ready to be grown by a
/// builder. Returns the root node id (`0`).
pub(crate) fn with_root(sum_hess: f32) -> Self {
RegTree {
nodes: vec![Node::leaf(0.0, sum_hess)],
categories: Vec::new(),
}
}
/// Number of nodes (internal + leaf).
#[inline]
pub fn num_nodes(&self) -> usize {
self.nodes.len()
}
/// Number of leaf nodes.
pub fn num_leaves(&self) -> usize {
self.nodes.iter().filter(|n| n.is_leaf()).count()
}
pub(crate) fn is_valid_for_features(&self, n_features: usize) -> bool {
let locally_valid = !self.nodes.is_empty()
&& self.nodes.iter().all(|node| {
node.sum_hess.is_finite()
&& node.leaf_value.is_finite()
&& node.split_cond.is_finite()
&& node.split_gain.is_finite()
&& (node.is_leaf()
|| ((node.split_feature as usize) < n_features
&& node.left >= 0
&& node.right >= 0
&& (node.left as usize) < self.nodes.len()
&& (node.right as usize) < self.nodes.len()
&& (!node.is_categorical
|| (node.cat_begin <= node.cat_end
&& (node.cat_end as usize) <= self.categories.len()))))
});
if !locally_valid {
return false;
}
let mut seen = vec![false; self.nodes.len()];
let mut stack = vec![0usize];
while let Some(node_id) = stack.pop() {
if seen[node_id] {
return false;
}
seen[node_id] = true;
let node = &self.nodes[node_id];
if !node.is_leaf() {
stack.push(node.left as usize);
stack.push(node.right as usize);
}
}
seen.into_iter().all(|visited| visited)
}
/// Read-only access to the node array.
#[inline]
pub fn nodes(&self) -> &[Node] {
&self.nodes
}
/// Flat pool of categories routed left by categorical nodes.
#[inline]
pub(crate) fn categories(&self) -> &[u32] {
&self.categories
}
/// Access a node by id.
#[inline]
pub fn node(&self, id: usize) -> &Node {
&self.nodes[id]
}
/// Turn leaf `nid` into an internal node by attaching two child leaves.
/// Returns `(left_id, right_id)`.
///
/// Both builders overwrite these child values in their finalize pass (which
/// recomputes every leaf from stored stats and bounds), so the values here
/// are placeholders on that path — but the parameters stay: directly built
/// trees (tests, learners) rely on them as the real leaf weights.
#[allow(clippy::too_many_arguments)]
pub(crate) fn expand(
&mut self,
nid: usize,
split_feature: u32,
split_cond: f32,
default_left: bool,
left_value: f32,
left_hess: f32,
right_value: f32,
right_hess: f32,
) -> (usize, usize) {
let left_id = self.nodes.len();
let right_id = left_id + 1;
self.nodes.push(Node::leaf(left_value, left_hess));
self.nodes.push(Node::leaf(right_value, right_hess));
let n = &mut self.nodes[nid];
n.split_feature = split_feature;
n.split_cond = split_cond;
n.default_left = default_left;
n.left = left_id as i32;
n.right = right_id as i32;
(left_id, right_id)
}
/// Turn leaf `nid` into a categorical (set-membership) internal node.
/// Instances whose value of `split_feature` is one of `cats_left` go to the
/// left child. All other (and missing) categories follow `default_left`
/// only when missing. Present categories not in the set go right.
/// Returns `(left_id, right_id)`.
///
/// As in [`expand`](Self::expand), builders overwrite the child values when
/// finalizing; the parameters serve directly built trees.
#[allow(clippy::too_many_arguments)]
pub(crate) fn expand_categorical(
&mut self,
nid: usize,
split_feature: u32,
cats_left: &[u32],
default_left: bool,
left_value: f32,
left_hess: f32,
right_value: f32,
right_hess: f32,
) -> (usize, usize) {
let left_id = self.nodes.len();
let right_id = left_id + 1;
self.nodes.push(Node::leaf(left_value, left_hess));
self.nodes.push(Node::leaf(right_value, right_hess));
let begin = self.categories.len() as u32;
self.categories.extend_from_slice(cats_left);
let end = self.categories.len() as u32;
let n = &mut self.nodes[nid];
n.split_feature = split_feature;
n.is_categorical = true;
n.cat_begin = begin;
n.cat_end = end;
n.default_left = default_left;
n.left = left_id as i32;
n.right = right_id as i32;
(left_id, right_id)
}
/// Set a leaf's weight (used to finalize leaf values after growth).
pub(crate) fn set_leaf_value(&mut self, nid: usize, value: f32) {
self.nodes[nid].leaf_value = value;
}
/// Record the loss reduction achieved by an internal node's split.
pub(crate) fn set_split_gain(&mut self, nid: usize, gain: f32) {
self.nodes[nid].split_gain = gain;
}
/// Multiply every leaf weight by `factor`. Used to apply the learning rate
/// (shrinkage) so that stored trees already carry their scaled contribution,
/// matching XGBoost's saved-model semantics.
pub fn scale_leaves(&mut self, factor: f32) {
for n in &mut self.nodes {
if n.is_leaf() {
n.leaf_value *= factor;
}
}
}
/// Route a single feature vector (via an accessor) to its leaf id.
///
/// `get` returns `None` for a missing feature. Generic over the accessor so
/// the same code serves dense rows, sparse rows, and SHAP traversals.
pub fn leaf_id_with(&self, get: impl Fn(u32) -> Option<f32>) -> usize {
let mut nid = 0usize;
loop {
let node = &self.nodes[nid];
if node.is_leaf() {
return nid;
}
let go_left = if node.is_categorical {
match get(node.split_feature) {
// Categories are integer-coded; membership in the left set
// routes left, everything else (present, not in set) right.
Some(v) => {
let c = v as u32;
self.categories[node.cat_begin as usize..node.cat_end as usize].contains(&c)
}
None => node.default_left,
}
} else {
match get(node.split_feature) {
Some(v) => v < node.split_cond,
None => node.default_left,
}
};
nid = if go_left {
node.left as usize
} else {
node.right as usize
};
}
}
/// Route a dense feature row (indexed by feature id, `missing` sentinel for
/// absent values) to its leaf id. Equivalent to
/// `leaf_id_with(|f| if is_missing(row[f]) { None } else { Some(row[f]) })`
/// without the closure/`Option` overhead.
#[inline]
pub fn leaf_id_dense(&self, row: &[f32], missing: f32) -> usize {
let nodes = &self.nodes[..];
let mut nid = 0usize;
loop {
let node = &nodes[nid];
if node.left == NO_CHILD {
return nid;
}
let v = row[node.split_feature as usize];
let go_left = if crate::data::is_missing(v, missing) {
node.default_left
} else if node.is_categorical {
let c = v as u32;
self.categories[node.cat_begin as usize..node.cat_end as usize].contains(&c)
} else {
v < node.split_cond
};
nid = if go_left {
node.left as usize
} else {
node.right as usize
};
}
}
/// Predict the raw leaf weight for row `row` of `data`.
pub fn predict_row(&self, data: &DMatrix, row: usize) -> f32 {
let leaf = self.leaf_id_with(|f| data.get(row, f as usize));
self.nodes[leaf].leaf_value
}
}
#[cfg(test)]
mod tests {
use super::*;
/// Build a small tree by hand:
/// root: feature 0 < 0.5 ? left : right, missing -> left
/// left leaf = -1.0, right leaf = +2.0
fn stump() -> RegTree {
let mut t = RegTree::with_root(10.0);
t.expand(0, 0, 0.5, true, -1.0, 5.0, 2.0, 5.0);
t
}
#[test]
fn routing_numeric() {
let t = stump();
// value 0.2 < 0.5 -> left leaf -1.0
assert_eq!(t.leaf_id_with(|_| Some(0.2)), 1);
// value 0.9 >= 0.5 -> right leaf +2.0
assert_eq!(t.leaf_id_with(|_| Some(0.9)), 2);
}
#[test]
fn routing_missing_follows_default() {
let t = stump();
// missing -> default_left = true -> left leaf
assert_eq!(t.leaf_id_with(|_| None), 1);
assert_eq!(t.node(1).leaf_value, -1.0);
}
#[test]
fn routing_categorical_set_membership() {
// Categorical split: categories {0, 2} go left, everything else right.
let mut t = RegTree::with_root(10.0);
t.expand_categorical(0, 0, &[0, 2], false, -1.0, 5.0, 2.0, 5.0);
assert!(t.node(0).is_categorical);
// In-set categories route left (leaf 1, value -1.0).
assert_eq!(t.leaf_id_with(|_| Some(0.0)), 1);
assert_eq!(t.leaf_id_with(|_| Some(2.0)), 1);
// Out-of-set present categories route right (leaf 2, value 2.0).
assert_eq!(t.leaf_id_with(|_| Some(1.0)), 2);
assert_eq!(t.leaf_id_with(|_| Some(3.0)), 2);
// Unseen category also routes right (not in the left set).
assert_eq!(t.leaf_id_with(|_| Some(9.0)), 2);
// Missing follows default_left = false -> right.
assert_eq!(t.leaf_id_with(|_| None), 2);
}
#[test]
fn predict_row_dense() {
let t = stump();
let d = DMatrix::from_dense(&[0.1, 0.9], 2, 1).unwrap();
assert_eq!(t.predict_row(&d, 0), -1.0);
assert_eq!(t.predict_row(&d, 1), 2.0);
assert_eq!(t.num_leaves(), 2);
assert_eq!(t.num_nodes(), 3);
}
}