Code for Optimal spectral shrinkage via Krylov approximation
Year: 2026
Type: book
Abstract: Optimal spectral shrinkage via Krylov approximation Code for the simulations of the paper Optimal spectral shrinkage via Krylov approximation by Tianfeng Lu, Geoffrey J. Goodhill and Hong Hu. The notebook `1.ipynb` reproduces Figures 1–3, Table 2 and the simulation numbers quoted in the text. Quick start ``` pip install -r requirements.txt jupyter notebook 1.ipynb ``` Then run all cells. The notebook takes about two minutes, because the two slow simulations are read from `results/`. Figures are saved to `figures/`, and tables are printed in the notebook. We used Python 3.11 with numpy 1.26, scipy 1.17, scikit-learn 1.2, pandas 2.1 and matplotlib 3.8. What the notebook reproduces Each part of the paper has its own section in the notebook. | Paper | Output | |---|---| | Figure 1 | `figures/fig1_pls_vs_rtk.pdf` | | Figure 2 | `figures/fig_sieve.pdf` | | Table 2 | printed in the notebook | | Figure 3 | `figures/fig_shrinkage.pdf` | Each section also prints the numbers quoted in the text, and Figures 1 and 2 print their supplementary tables (Tables S2 and S3). The Figure 3 section also plots the shrinkage factors for all eleven settings of Table 2 (`figures/fig_shrinkage_sims.pdf`). Recomputing the cached results Two simulations take too long to rerun every time, so their results are stored in `results/`: - `sieve_latent.csv` (Figure 2) takes about 30 minutes to recompute. - `n1000_estimators.csv` (Table 2) takes about 5 minutes per setting. It holds all 23 settings of Table S5 in the Supplementary Material, of which Table 2 shows eleven. To recompute them, set `RERUN_SIEVE = True` or `RERUN_MAIN = True` at the top of the corresponding cell. If a file is missing, the notebook recomputes it automatically, so a run without `results/` takes about 1.5 hours. The simulations use fixed random seeds, so recomputing reproduces the stored results. The only exception is RTK-C, where rounding errors can change a single replicate's risk in the fourth decimal; this does not change any entry of Table 2. Files - `1.ipynb`: the notebook. - `spectral_shrinkage.py`: the estimator `SpectralShrinkage`, used for RTK, RTK-C, ridge, gradient descent and self-distillation. - `filters.py`: the filter dictionaries and their exact leave-one-out features. - `otherestimators.py`: principal component regression, partial least squares and the hybrid method of Chung, Nagy & O'Leary (2008). - `simulation.py`: simulation settings, data generation, exact risks and the oracle filter. - `results/`: stored simulation results. - `figures/`: figures written by the notebook. Using RTK on your own data The estimators follow the scikit-learn interface: ```python import filters as F from spectral_shrinkage import SpectralShrinkage rtk = SpectralShrinkage(F.Chebyshev(5)).fit(X, y) # RTK, m = 5 rtkc = SpectralShrinkage(F.Truncated(F.Chebyshev(5), K="resolution")).fit(X, y) # RTK-C, m = 5 y_new = rtkc.predict(X_new) ``` An intercept is fitted by default.
Author: Lu, Tianfeng
Institution: Washington University in St. Louis
Language: English
Topic: Matrix Theory and Algorithms
Subfield: Computational Theory and Mathematics
Field: Computer Science
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7225178404