Melvin Alvarez
47 lines
1.3 KiB
Markdown
47 lines
1.3 KiB
Markdown
# Sparse Optimization
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Sparse PCA, Elastic Net, and Box–Tao decomposition with Rust speed.
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## Sparse PCA
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```python
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import numpy as np
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from optimizr import sparse_pca_py
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X = np.random.randn(500, 20)
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components = sparse_pca_py(X, n_components=5, l1_ratio=0.15)
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print(components.shape) # (5, 20)
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```
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- Output: component matrix `(n_components, n_features)`; rows are sparse loadings.
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- Tuning: increase `l1_ratio` for harder sparsity; decrease to retain variance.
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## Elastic Net
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```python
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import numpy as np
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from optimizr import elastic_net_py
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X = np.random.randn(200, 8)
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y = np.random.randn(200)
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coeffs = elastic_net_py(X, y, l1_ratio=0.3, alpha=0.01)
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print(coeffs)
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```
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- Handles collinearity better than pure Lasso; use for factor shrinkage.
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- Sweep `alpha` on a log scale (e.g., $10^{-3}$ to $10^{-1}$) and pick via validation.
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## Box–Tao decomposition
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```python
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from optimizr import box_tao_decomposition_py
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solution = box_tao_decomposition_py(X)
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```
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Useful for constrained sparse decomposition problems; the Rust backend keeps iterations fast.
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## Practical notes
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- Inputs must be NumPy arrays; standardize features for stable conditioning.
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- For high dimensional data, start with fewer components/features to avoid over-regularization.
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- Combine with risk metrics: use sparse loadings to build interpretable factors, then evaluate with `compute_risk_metrics_py`.
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