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//! Power-transform wrapper leaf — port of skaters' `power_transform`
//! composed with an inner leaf.
//!
//! Applies a **signed power** transform on the way in, and inverses
//! (delta method) on the way out:
//!
//! ```text
//! forward: y' = sign(y) * |y|^p
//! inverse: ŷ = sign(y') * |y'|^(1/p)
//! d/dy'[inv]: = (1/p) * |y'|^(1/p - 1)
//! ```
//!
//! For `0 < p < 1` this compresses tails (log-like) but works on all
//! reals — no explosion on negatives. Skaters ships `power_transform(0.5)`
//! (the signed square-root) composed with `ema_transform(0.1)`. The
//! wrapper here is generic: pass any inner leaf.
//!
//! PR #3 of #180.
use super::super::dist::Gaussian;
use super::super::leaf::Leaf;
pub struct PowerTransformWrapper {
inner: Box<dyn Leaf + Send>,
p: f64,
inv_p: f64,
label: String,
}
impl PowerTransformWrapper {
/// Recommended: `p = 0.5` (signed square-root, matches skaters).
/// Any `p ∈ (0, 1)` is legal.
pub fn new(inner: Box<dyn Leaf + Send>, p: f64) -> Self {
let p = p.clamp(1e-4, 0.9999);
let label = format!("{}@pow{:.2}", inner.name(), p);
Self {
inner,
p,
inv_p: 1.0 / p,
label,
}
}
}
/// Signed power: `sign(x) · |x|^p`. Preserves the sign of the input.
#[inline]
fn signed_pow(x: f64, p: f64) -> f64 {
if x == 0.0 {
0.0
} else {
x.signum() * x.abs().powf(p)
}
}
impl Leaf for PowerTransformWrapper {
fn name(&self) -> &'static str {
Box::leak(self.label.clone().into_boxed_str())
}
fn predict(&self, horizon: usize) -> Vec<Gaussian> {
let inner = self.inner.predict(horizon);
inner
.into_iter()
.map(|g| {
// Inverse mean via signed-power^(1/p).
let mean_orig = signed_pow(g.mean, self.inv_p);
// Delta-method Jacobian: (1/p) * |μ|^(1/p - 1).
// Near zero the derivative is unbounded for p < 1 —
// clamp |μ| from below so σ stays finite.
let abs_mu = g.mean.abs().max(1e-6);
let jac = self.inv_p * abs_mu.powf(self.inv_p - 1.0);
let sigma = (g.std * jac.abs()).max(1e-9);
Gaussian::new(mean_orig, sigma)
})
.collect()
}
#[inline]
fn predict_one(&self) -> Gaussian {
let g = self.inner.predict_one();
let mean_orig = signed_pow(g.mean, self.inv_p);
let abs_mu = g.mean.abs().max(1e-6);
let jac = self.inv_p * abs_mu.powf(self.inv_p - 1.0);
let sigma = (g.std * jac.abs()).max(1e-9);
Gaussian::new(mean_orig, sigma)
}
fn observe(&mut self, y: f64) {
if !y.is_finite() {
return;
}
let y_trans = signed_pow(y, self.p);
if y_trans.is_finite() {
self.inner.observe(y_trans);
}
}
}
#[cfg(test)]
mod tests {
use super::super::EmaLeaf;
use super::*;
#[test]
fn round_trip_preserves_positive_values() {
// Feed positive values; power-wrapper + EMA should track them
// in original space to within EMA's expected level tracking
// (α=1 → level = last obs).
let mut w = PowerTransformWrapper::new(Box::new(EmaLeaf::new(1.0)), 0.5);
for _ in 0..10 {
w.observe(9.0); // sqrt(9)=3, EMA=3, back-square = 9
}
let g = w.predict(1)[0];
assert!(
(g.mean - 9.0).abs() < 0.5,
"round-trip mean {} not near 9",
g.mean
);
}
#[test]
fn round_trip_preserves_negative_values() {
let mut w = PowerTransformWrapper::new(Box::new(EmaLeaf::new(1.0)), 0.5);
for _ in 0..10 {
w.observe(-4.0); // signed sqrt = -2; EMA = -2; back-square = -4
}
let g = w.predict(1)[0];
assert!(
(g.mean + 4.0).abs() < 0.5,
"round-trip mean {} not near -4",
g.mean
);
}
#[test]
fn compresses_heavy_tail_variance() {
// Feed heavy-tailed inputs. Transformed-space std should be
// smaller than raw-space std (because the transform compresses).
let mut raw = EmaLeaf::new(0.1);
let mut wrapped = PowerTransformWrapper::new(Box::new(EmaLeaf::new(0.1)), 0.5);
for i in 1..=500 {
let y = if i % 50 == 0 { 100.0 } else { 1.0 };
raw.observe(y);
wrapped.observe(y);
}
// The wrapped inner sees compressed values; its std is smaller
// in transformed space. But after delta-method inversion, the
// reported std may be similar to raw. What we CAN check: the
// wrapper survives the extreme values without producing NaN
// or infinite std.
let g = wrapped.predict(1)[0];
assert!(g.mean.is_finite() && g.std.is_finite() && g.std > 0.0);
}
}