Chain fused lasso

Chain fused lasso encourages sparse, piecewise constant coefficients in the supplied feature order. Adjacent equal effects form contiguous segments. Weights default to one. .with_weights(...) takes exactly one finite, nonnegative weight per edge; a zero weight cuts the chain.

R(\beta) = \lambda_1\sum_{j=1}^p|\beta_j| + \lambda_2\sum_{j=1}^{p-1}w_j|\beta_{j+1} - \beta_j|.

Constraint region

Feasible region for chain fused lasso; the shaded set includes its boundary.

Top: $\lambda_1 = \lambda_2 = 0.5$ , $w_1 = 1$ . Bottom: $\lambda_1 = 0$ , $\lambda_2 = 1$ , $w_1 = 1$ , giving an unbounded pure-fusion strip. See the plot conventions for the fixed budget and coefficient scale.

Use the penalty

use shrinkage::{ChainFusedLasso, Penalty, ProximalPenalty};

fn main() -> Result<(), Box<dyn std::error::Error>> {
    let penalty = ChainFusedLasso::new(0.5, 0.25).with_weights(vec![1.0]);
    let coefficients = [2.0, -1.0];
    println!("Penalty: {}", penalty.value(&coefficients)?);
    let mut shrunk = [0.0; 2];
    penalty.prox(&coefficients, 1.0, &mut shrunk)?;
    println!("Proximal result: {shrunk:?}");
    Ok(())
}

Each edge contributes once. Empty and single-feature chains have no edges. Zero fusion recovers lasso. A two-feature chain has one pair, so its unit-weight constraint region coincides with clustered lasso; larger chains only fuse neighbors. Gaussian and binomial fits support proximal gradient and hybrid. See the chain fused lasso guide for segment interpretation and detailed fitting controls.

API: shrinkage::ChainFusedLasso.