Softwares

R packages

  1. “gcdl” computes the confidence interval of coefficients in the high-dimensional linear models incorporating graphical structures. “gcdl” is available at https://github.com/XiaoZhangryy/gcdl.

    • Tan, X., Zhang, X., Cui, Y. and Liu, X.* (2024). Uncertainty quantification in high-dimensional linear models incorporating graphical structures with applications to gene set analysis. Bioinformatics.

  2. “TBEinf” computes the density of TBE infinity by direct calculation, saddlepoint approximation, Fourier inversion, and related methods. “TBEinf” applys TBE1 to the generalized linear model for estimation and prediction. The estimation of coefficients is obtained through Iteratively Reweighted Least Squares. “TBEinf” is available at https://github.com/xliusufe/TBEinf.

    • Refer to Bar-Lev, S. K., Ridder, A., Liu, X.*, and Xiang, Z. (2024). Generalized Linear Model (GLM) Applications for the Exponential Dispersion Model Generated by the Landau Distribution. Mathematics. 12.

  3. The Python codes “REGS” is proposed for sampling from unnormalized densties by the techniques including Wasserstein gradient flows, numerical ODEs, density-ratio estimation and deep neural networks. REGS achieves a fantastic numerical performance on 2D mixtrues of Gaussian distributions with a large number of modes, a small variance, and a large distance between any two modes. “REGS” is available at https://github.com/xliusufe/REGS.

    • Refer to Feng X., Gao, Y., Huang, J., Jiao, Y. and Liu, X.* (2021). Relative Entropy Gradient Sampler for Unnormalized Distributions. Submitted.

  4. The R-package “rbs” select the response and estimate regression coefficients simultaneously for multivariate regression with high-dimensional response variables. “rbs” is available at https://github.com/xliusufe/rbs.

    • Refer to Hu, J., Huang, J., Liu, X. and Liu, X.* (2022). Response Best-subset Selector for Multivariate Regression with High-dimensional Response Variables. Biometrika. Accepted.

  5. The R-package “pqr” constructs confidence intervals of the coefficients of high-dimensional quantile regression via the regularized projection score estimation for the treatment effects. “pqr” is available at https://github.com/xliusufe/pqr.

    • Refer to Feng, X., Huang, J. and Liu, X.* (2020). Regularized projection score estimation of treatment effects in high-dimensional quantile regression. Statistica Sinica.

  6. The R-package “tensorMQR” estimates the coefficients as a symmetric tensor for high-dimensional multiresponse quadratic regression models incorporating Tucker decomposition for the symmetric tensor and the steepest gradient descent algorithm on Stiefel manifold. “tensorMQR” is available at https://github.com/xliusufe/tensorMQR.

    • Refer to Liu, et al. (2020). “Symmetric tensor estimation for quadratic regression”.

  7. The R-package “tensorMam” estimates the nonparametric curve for high-dimensional multivariate additive models incorporating Tucker decomposition for the tensor consisting of the coefficients. “tensorMam” is available at https://github.com/xliusufe/tensorMam.

    • Refer to Liu, X., Lian, H. and Huang, J. (2020). “A tensor estimation approach to multivariate additive models”.

  8. The R-package “RidgeVar” estimates the err variance for high-dimensional linear regression in weak signal case. “RidgeVar” is available at https://github.com/xliusufe/RidgeVar.

    • Refer to Liu, X., Zheng, S. and Feng, X.* (2020). “Estimation of error variance via ridge regression”. Biometrika.

  9. The R-package “IVGC” estimates coefficients for high-dimensional linear regression with instrument variable incorporating network structure. “IVGC” is available at https://github.com/xliusufe/IVGC.

    • Refer to Gao, et al. (2019). “Integrative analysis of genetical genomics data incorporating network structures”. Biometrics.

  10. The R-package “plvs” estimates coefficients for high-dimensional quantile regression, including composite quantile, which is implemented by combining coordinate descent and MM algorithm. “plvs” is available at https://github.com/xliusufe/plvs.

    • Refer to Liu, et al. (2018). “Ultra-high dimensional variable selection for piecewise linear loss functions”. Manuscript

  11. The R-package “FactSum” calculates the factorial of a large positive integer, that is n!, which may be much greater than the maximum memory of any data type defined by C/C++ or R. FactSum implements dramatically fast. It takes only 0.45 seconds to compute 10000! (it approximates 2.8E+35660), and 0.98 seconds to compute 10000! and sum=1!+2!+3!+…+10000! simultaneously. “FactSum” is available at https://github.com/xliusufe/FactSum. A web-based calculator can be found HERE. It is developed for teaching “Computer Programming”.

  12. The R-package “sqrtn” calculates $\sqrt{n}$ with very high precision, where n is a positive integer. “sqrtn” implements dramatically fast. It takes only less than 30 seconds to approximate $\sqrt{2}$ with 100,000 digits. “sqrtn” is available at https://github.com/xliusufe/sqrtn. A web-based calculator can be found HERE. It is developed for teaching “Computer Programming”.

  13. The R-package “PI” approximates $\pi$ with very high-precesion. It takes only 0.04 seconds to approximate $\pi$ with 1,000,000,000 digits. “PI” is available at https://github.com/xliusufe/PI. A web-based calculator can be found HERE. It is developed for teaching “Computer Programming”.

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