Model selection references by Aki Vehtari.

Cross-validation

  • Bürkner, P.-C., Gabry, J., and Vehtari, A. (2020). Efficient leave-one-out cross-validation for Bayesian non-factorized normal and Student-\(t\) models. Computational Statistics, doi:10.1007/s00180-020-01045-4. arXiv preprint arXiv:1810.10559. Code.
  • Bürkner, P.-C., Gabry, J., and Vehtari, A. (2020). Approximate leave-future-out cross-validation for time series models. Journal of Statistical Computation and Simulation, 90(14):2499-2523. Online. arXiv preprint arXiv:1902.06281. Code.
  • Magnusson, M., Andersen, M.R., Jonasson, J., Vehtari, A. (2019). Bayesian leave-one-out cross-validation for large data. Thirty-sixth International Conference on Machine Learning, PMLR 97:4244–4253. Online.
  • Magnusson, M., Andersen, M.R., Jonasson, J., Vehtari, A. (2020). Leave-one-out cross-validation for Bayesian model comparison in large data. Proceedings of the 23rd International Conference on Artificial Intelligence and Statistics (AISTATS), PMLR 108:341-351. Online. preprint arXiv:2001.00980.
  • Paananen, T., Piironen, J., Bürkner, P.-C., and Vehtari, A. (2021). Implicitly adaptive importance sampling. Statistics and Computing, 31, 16. doi:10.1007/s11222-020-09982-2. arXiv preprint arXiv:1906.08850.
  • Sivula, T., Magnusson, M., and Vehtari, A. (2020). Unbiased estimator for the variance of the leave-one-out cross-validation estimator for a Bayesian normal model with fixed variance. Communications in Statistics – Theory and Methods, doi:10.1080/03610926.2021.2021240. arXiv preprint arXiv:2008.10859.
  • Sivula, T., Magnusson, M., and Vehtari, A. (2020). Uncertainty in Bayesian leave-one-out cross-validation based model comparison. arXiv preprint arXiv:2008.10296.
    Video 30min.
  • Vehtari, A., Gelman, A., Gabry, J. (2017). Practical Bayesian model evaluation using leave-one-out cross-validation and WAIC. Statistics and Computing. 27(5):1413–1432. arXiv preprint.
  • Vehtari, A., Simpson, D., Gelman, A., Yao, Y., and Gabry, J. (2019). Pareto smoothed importance sampling. arXiv preprint.
  • Vehtari, A., Mononen, T., Tolvanen, V., and Winther, O. (2016). Bayesian leave-one-out cross-validation approximations for Gaussian latent variable models. JMLR, 17(103):1–38. Online

Stacking

  • Yao, Y., Pirš, G., Vehtari, A., and Gelman, A. (2021). Bayesian hierarchical stacking: Some models are (somewhere) useful. Bayesian Analysis, doi:10.1214/21-BA1287. arXiv preprint arXiv:2101.08954.
  • Yao, Y., Vehtari, A., Simpson, D., and Gelman, A. (2017). Using stacking to average Bayesian predictive distributions. Bayesian Analysis, doi:10.1214/17-BA1091, Online
  • Yao, Y., Vehtari, A., and Gelman, A. (2022). Stacking for non-mixing Bayesian computations: The curse and blessing of multimodal posteriors. Journal of Machine Learning Research, accepted for publication. arXiv preprint arXiv:2006.12335.

Projection predictive and reference model selection

  • Afrabandpey, H., Peltola, T., Piironen, J., Vehtari, A., and Kaski, S. (2020). Making Bayesian predictive models interpretable: A decision theoretic approach. Machine Learning, 109:1855–1876. Online. arXiv preprint arXiv:1910.09358
  • Catalina, A., Bürkner, P.-C., and Vehtari, A. (2021). Latent space projection predictive inference. arXiv preprint arXiv:2109.04702.
  • Catalina, A., Bürkner, P.-C., and Vehtari, A. (2020). Projection predictive inference for generalized linear and additive multilevel models. Proceedings of the 24th International Conference on Artificial Intelligence and Statistics (AISTATS), accepted for publication. arXiv preprint arXiv:2010.06994.
  • Pavone, F., Piironen, J., Bürkner, P.-C., and Vehtari, A. (2020). Using reference models in variable selection. arXiv preprint arXiv:2004.13118
  • Piironen, J., Paasiniemi, M., and Vehtari, A. (2020). Projective Inference in High-dimensional Problems: Prediction and Feature Selection. Electronic Journal of Statistics, 14(1):2155-2197. Online. Preprint arXiv:1810.02406
  • Williams, D. R., Piironen, J., Vehtari, A., and Rast, P. (2018). Bayesian estimation of Gaussian graphical models with projection predictive selection. arXiv:1801.05725

Priors and reference models

  • Piironen, J., and Vehtari, A. (2017). On the hyperprior choice for the global shrinkage parameter in the horseshoe prior. Proceedings of the 20th International Conference on Artificial Intelligence and Statistics, PMLR 54:905-913. Online
  • Piironen, J., and Vehtari, A. (2017). Sparsity information and regularization in the horseshoe and other shrinkage priors. In Electronic Journal of Statistics, 11(2):5018-5051. Online
  • Piironen, J., and Vehtari, A. (2018). Iterative supervised principal components. Proceedings of the 21th International Conference on Artificial Intelligence and Statistics, accepted for publication. arXiv preprint arXiv:1710.06229

Miscellaneous

  • Gelman, A., Hwang, J., and Vehtari, A. (2014). Understanding predictive information criteria for Bayesian models. Statistics and Computing, 24(6):997–1016. Preprint
  • Gelman, A., Goodrich, B., Gabry, J., and Vehtari, A. (2019). R-squared for Bayesian regression models. The American Statistician, 73(3):307-309. Online. Preprint. Code.
  • Oelrich, O., Ding, S., Magnusson, M., Vehtari, A., and Villani, M. (2020). When are Bayesian model probabilities overconfident? arXiv preprint arXiv:2003.04026.
  • Piironen, J. and Vehtari, A. (2016), Comparison of Bayesian predictive methods for model selection, Statistics and Computing 27(3), 711–735. Online
  • Vehtari, A. and Ojanen, J.: 2012, A survey of Bayesian predictive methods for model assessment, selection and comparison, Statistics Surveys 6, 142–228. Online