optimiz-rs/docs/source/algorithms/sparse_optimization.md

Sparse Optimization

Sparse PCA, Elastic Net, and Box–Tao decomposition with Rust speed.

Sparse PCA

import numpy as np
from optimizr import sparse_pca_py

X = np.random.randn(500, 20)
components = sparse_pca_py(X, n_components=5, l1_ratio=0.15)
print(components.shape)  # (5, 20)

• Output: component matrix (n_components, n_features); rows are sparse loadings.
• Tuning: increase l1_ratio for harder sparsity; decrease to retain variance.

Elastic Net

import numpy as np
from optimizr import elastic_net_py

X = np.random.randn(200, 8)
y = np.random.randn(200)
coeffs = elastic_net_py(X, y, l1_ratio=0.3, alpha=0.01)
print(coeffs)

• Handles collinearity better than pure Lasso; use for factor shrinkage.
• Sweep alpha on a log scale (e.g., 10^{-3} to 10^{-1}) and pick via validation.

Box–Tao decomposition

from optimizr import box_tao_decomposition_py
solution = box_tao_decomposition_py(X)

Useful for constrained sparse decomposition problems; the Rust backend keeps iterations fast.

Practical notes

• Inputs must be NumPy arrays; standardize features for stable conditioning.
• For high dimensional data, start with fewer components/features to avoid over-regularization.
• Combine with risk metrics: use sparse loadings to build interpretable factors, then evaluate with compute_risk_metrics_py.