参考文献
Adler, Joseph. 2010. R in a Nutshell: A Desktop Quick Reference. " O’Reilly Media, Inc.".
Akaike, Hirotugu. 1974. “A New Look at the Statistical Model Identification.” IEEE Transactions on Automatic Control 19 (6): 716–23. https://doi.org/10.1109/TAC.1974.1100705.
Angelopoulos, Anastasios N., and Stephen Bates. 2021. “A Gentle Introduction to Conformal Prediction and Distribution-Free Uncertainty Quantification.” arXiv:2107.07511. https://arxiv.org/abs/2107.07511.
Angelopoulos, Anastasios N., Stephen Bates, Clara Fannjiang, Michael I. Jordan, and Tijana Zrnic. 2023. “Prediction-Powered Inference.” arXiv:2301.09633. https://arxiv.org/abs/2301.09633.
Angelopoulos, Anastasios N., John C. Duchi, and Tijana Zrnic. 2024. “PPI++: Efficient Prediction-Powered Inference.” arXiv:2311.01453. https://arxiv.org/abs/2311.01453.
Arlot, Sylvain, and Alain Celisse. 2010. “A Survey of Cross-Validation Procedures for Model Selection.” Statistics Surveys 4: 40–79. https://doi.org/10.1214/09-SS054.
Bottou, Léon. 2012. “Stochastic Gradient Descent Tricks.” In Neural Networks: Tricks of the Trade, 421–36. Springer.
Boyd, Stephen, Neal Parikh, Eric Chu, Borja Peleato, and Jonathan Eckstein. 2011. “Distributed Optimization and Statistical Learning via the Alternating Direction Method of Multipliers.” Foundations and Trends in Machine Learning 3 (1): 1–122. https://doi.org/10.1561/2200000016.
Brier, Glenn W. 1950. “Verification of Forecasts Expressed in Terms of Probability.” Monthly Weather Review 78 (1): 1–3.
Chambers, John M. 2008. Software for Data Analysis: Programming with r. New York: Springer.
Chen, Charlie, Sebastian Borgeaud, Geoffrey Irving, Jean-Baptiste Lespiau, Laurent Sifre, and John Jumper. 2023. “Accelerating Large Language Model Decoding with Speculative Sampling.” arXiv:2302.01318. https://arxiv.org/abs/2302.01318.
Dathathri, Sumanth, Abigail See, Sumedh Ghaisas, et al. 2024. “Scalable Watermarking for Identifying Large Language Model Outputs.” Nature 634: 818–23. https://doi.org/10.1038/s41586-024-08025-4.
Fanaee-T, Hadi. 2013. “Bike Sharing.” UCI Machine Learning Repository. https://doi.org/10.24432/C5W894.
Fanaee-T, Hadi, and Joao Gama. 2014. “Event Labeling Combining Ensemble Detectors and Background Knowledge.” Progress in Artificial Intelligence 2 (2–3): 113–27. https://doi.org/10.1007/s13748-013-0040-3.
Friedman, Jerome, Trevor Hastie, and Robert Tibshirani. 2010. “Regularization Paths for Generalized Linear Models via Coordinate Descent.” Journal of Statistical Software 33 (1): 1–22. https://doi.org/10.18637/jss.v033.i01.
Gelman, Andrew, John B. Carlin, Hal S. Stern, David B. Dunson, Aki Vehtari, and Donald B. Rubin. 2013. Bayesian Data Analysis. 3rd ed. Boca Raton, FL: CRC Press.
Gentle, James E. 2009. Computational Statistics. New York: Springer.
Gentleman, Robert, and Duncan Temple Lang. 2007. “Statistical Analyses and Reproducible Research.” Journal of Computational and Graphical Statistics 16 (1): 1–23.
Gneiting, Tilmann, and Adrian E. Raftery. 2007. “Strictly Proper Scoring Rules, Prediction, and Estimation.” Journal of the American Statistical Association 102 (477): 359–78. https://doi.org/10.1198/016214506000001437.
Goldberg, David. 1991. “What Every Computer Scientist Should Know about Floating-Point Arithmetic.” ACM Computing Surveys 23 (1): 5–48. https://doi.org/10.1145/103162.103163.
Golub, Gene H., and Charles F. Van Loan. 2013. Matrix Computations. 4th ed. Baltimore: Johns Hopkins University Press.
Google. 2026. “SynthID: Tools for Watermarking and Detecting LLM-Generated Text.” Responsible Generative AI Toolkit. https://ai.google.dev/responsible/docs/safeguards/synthid.
Higham, Nicholas J. 2002. Accuracy and Stability of Numerical Algorithms. 2nd ed. Philadelphia: SIAM.
Ho, Jonathan, Ajay Jain, and Pieter Abbeel. 2020. “Denoising Diffusion Probabilistic Models.” arXiv:2006.11239. https://arxiv.org/abs/2006.11239.
Hoerl, Arthur E., and Robert W. Kennard. 1970. “Ridge Regression: Biased Estimation for Nonorthogonal Problems.” Technometrics 12 (1): 55–67. https://doi.org/10.1080/00401706.1970.10488634.
Holderrieth, Peter, and Ezra Erives. 2025. “An Introduction to Flow Matching and Diffusion Models.” arXiv:2506.02070. https://arxiv.org/abs/2506.02070.
Hu, Edward J., Yelong Shen, Phillip Wallis, Zeyuan Allen-Zhu, Yuanzhi Li, Shean Wang, Lu Wang, and Weizhu Chen. 2022. “LoRA: Low-Rank Adaptation of Large Language Models.” arXiv:2106.09685. https://arxiv.org/abs/2106.09685.
Ihaka, Ross, and Robert Gentleman. 1996. “R: A Language for Data Analysis and Graphics.” Journal of Computational and Graphical Statistics 5 (3): 299–314. https://doi.org/10.1080/10618600.1996.10474713.
Leviathan, Yaniv, Matan Kalman, and Yossi Matias. 2023. “Fast Inference from Transformers via Speculative Decoding.” In Proceedings of the 40th International Conference on Machine Learning, 202:19274–86. Proceedings of Machine Learning Research. https://proceedings.mlr.press/v202/leviathan23a.html.
Li, Xiang, Feng Ruan, Huiyuan Wang, Qi Long, and Weijie J. Su. 2024. “A Statistical Framework of Watermarks for Large Language Models: Pivot, Detection Efficiency and Optimal Rules.” arXiv:2404.01245. https://arxiv.org/abs/2404.01245.
Monahan, John F. 2011. Numerical Methods of Statistics. 2nd ed. Cambridge: Cambridge University Press.
Nichol, Alexander Quinn, and Prafulla Dhariwal. 2021. “Improved Denoising Diffusion Probabilistic Models.” In Proceedings of the 38th International Conference on Machine Learning, 139:8162–71. Proceedings of Machine Learning Research. https://proceedings.mlr.press/v139/nichol21a.html.
Nocedal, Jorge, and Stephen J. Wright. 2006. Numerical Optimization. 2nd ed. New York: Springer.
Parikh, Neal, and Stephen Boyd. 2014. “Proximal Algorithms.” Foundations and Trends in Optimization 1 (3): 123–231. https://web.stanford.edu/~boyd/papers/prox_algs.html.
Peng, Roger D. 2018. “Advanced Statistical Computing.” Work in Progress. https://bookdown.org/rdpeng/advstatcomp/.
Peng, Roger D. 2011. “Reproducible Research in Computational Science.” Science 334 (6060): 1226–27. https://doi.org/10.1126/science.1213847.
Rafailov, Rafael, Archit Sharma, Eric Mitchell, Stefano Ermon, Christopher D. Manning, and Chelsea Finn. 2023. “Direct Preference Optimization: Your Language Model Is Secretly a Reward Model.” arXiv:2305.18290. https://arxiv.org/abs/2305.18290.
Robert, Christian P., and George Casella. 2004. Monte Carlo Statistical Methods. 2nd ed. New York: Springer.
Schwarz, Gideon. 1978. “Estimating the Dimension of a Model.” The Annals of Statistics 6 (2): 461–64. https://doi.org/10.1214/aos/1176344136.
Seber, George A. F., and Alan J. Lee. 2003. Linear Regression Analysis. 2nd ed. Hoboken, NJ: Wiley.
Song, Jiaming, Chenlin Meng, and Stefano Ermon. 2021. “Denoising Diffusion Implicit Models.” arXiv:2010.02502. https://arxiv.org/abs/2010.02502.
Song, Yang, Jascha Sohl-Dickstein, Diederik P. Kingma, Abhishek Kumar, Stefano Ermon, and Ben Poole. 2021. “Score-Based Generative Modeling Through Stochastic Differential Equations.” arXiv:2011.13456. https://arxiv.org/abs/2011.13456.
Stone, Mervyn. 1977. “An Asymptotic Equivalence of Choice of Model by Cross-Validation and Akaike’s Criterion.” Journal of the Royal Statistical Society: Series B (Methodological) 39 (1): 44–47.
Tibshirani, Robert. 1996. “Regression Shrinkage and Selection via the Lasso.” Journal of the Royal Statistical Society: Series B (Methodological) 58 (1): 267–88.
Wickham, Hadley. 2016. Ggplot2: Elegant Graphics for Data Analysis. Springer-Verlag New York. https://ggplot2.tidyverse.org.
Wilkinson, J. H. 1963. Rounding Errors in Algebraic Processes. London: Her Majesty’s Stationery Office.
Xie, Yihui. 2015. Dynamic Documents with r and Knitr. 2nd ed. Boca Raton, FL: Chapman; Hall/CRC.
Xie, Yihui, J. J. Allaire, and Garrett Grolemund. 2018. R Markdown: The Definitive Guide. Boca Raton, FL: Chapman; Hall/CRC. https://bookdown.org/yihui/rmarkdown/.
Zeiler, Matthew D. 2012. “Adadelta: An Adaptive Learning Rate Method.” arXiv Preprint arXiv:1212.5701.
Zou, Hui, and Trevor Hastie. 2005. “Regularization and Variable Selection via the Elastic Net.” Journal of the Royal Statistical Society: Series B (Statistical Methodology) 67 (2): 301–20. https://doi.org/10.1111/j.1467-9868.2005.00503.x.