pyrsdr 0.1.0

JAX-accelerated Sufficient Dimension Reduction (RSDR, SIR)

pyrsdr

JAX-accelerated Sufficient Dimension Reduction for Python.

Method	Description
RSDR	Distance-covariance SDR via Riemannian CG on the Stiefel manifold (Sheng & Yin 2016)
SIR	Sliced Inverse Regression (Li 1991)

Installation

pip install pyrsdr

Quick Start

from pyrsdr import RSDR, SIR

# RSDR — distance-covariance SDR
model = RSDR(X, Y, alpha=0.5)
model.fit(d=2)
projected = model.projected_data   # (n, d)
directions = model.dirs            # (p, d)

# SIR — sliced inverse regression
sir = SIR(nslice=10)
sir.fit(X, y, ndir=2)
directions = sir.dirs

Cross-validation

from pyrsdr import rsdr_cv

result = rsdr_cv(X, Y, d=2,
                 alpha_grid=[0.25, 0.5, 0.75, 1.0],
                 K=5, seed=42)
print(result["alpha_star"])

References

Sufficient Dimension Reduction — Foundations

• Li, K.-C. (1991). Sliced inverse regression for dimension reduction. Journal of the American Statistical Association, 86(414), 316–327.
• Cook, R. D. (1998). Regression Graphics. New York: Wiley.
• Li, B. (2018). Sufficient Dimension Reduction. Chapman & Hall/CRC.

Distance-Covariance SDR (RSDR)

• Sheng, W. & Yin, X. (2016). Sufficient Dimension Reduction via Distance Covariance. Journal of Computational and Graphical Statistics, 25(3), 684–708.

Multivariate Response & Related SDR Work

• Li, K.-C., Aragon, Y., Shedden, K., & Thomas Agnan, C. (2003). Dimension Reduction for Multivariate Response Data. JASA, 98(461), 99–109.
• Shedden, K. & Li, K.-C. (2003). Dimension reduction and spatiotemporal regression: applications to neuroimaging. Computing in Science & Engineering, 5(5), 30–36.
• Huang, S.-H., Shedden, K., & Chang, H.-W. (2023). Inference for the dimension of a regression relationship using pseudo-covariates. Biometrics, 79(3), 2394–2403.

Stiefel Manifold Optimization

• Absil, P.-A., Mahony, R., & Sepulchre, R. (2008). Optimization Algorithms on Matrix Manifolds. Princeton University Press.
• Edelman, A., Arias, T. A., & Smith, S. T. (1998). The geometry of algorithms with orthogonality constraints. SIAM J. Matrix Anal. Appl., 20(2), 303–353.

R Packages (Baselines)

• Weisberg, S. (2002). dr: Methods for Dimension Reduction for Regression. CRAN.
• Adragni, K. P. & Cook, R. D. (2014). ldr: An R Software Package for Likelihood-Based Sufficient Dimension Reduction. Journal of Statistical Software, 61(3).
• Huang, Y., Yu, Z. & Zhang, J. (2024). rSDR: Robust Sufficient Dimension Reduction. CRAN.

Related Software

• Shedden, K. — github.com/kshedden: Go/Python/Julia packages for statistical modeling, multivariate analysis, and dimension reduction.

License

MIT