Aki’s talk about reference models in model selection in Laplace’s demon series

I (Aki) talk about reference models in model selection in Laplace’s demon series 24 June 15UTC (Finland 18, Paris 17, New York 11). See the seminar series website for a registration link, the schedule for other talks, and the list of the recorded talks.

The short summary: 1) Why a bigger model helps inference for smaller models, 2) Bayesian decision theoretic justification, 3) Examples. There’s time for questions and discussion. Yes, it will be recorded.

The abstract:

I discuss and demonstrate the benefits of using a reference model in variable selection. A reference model acts as a noise-filter on the target variable by modeling its data generating mechanism. As a result, using the reference model predictions in the model selection procedure reduces the variability and improves stability leading to improved model selection performance and improved predictive performance of the selected model. Assuming that a Bayesian reference model describes the true distribution of future data well, the theoretically preferred usage of the reference model is to project its predictive distribution to a reduced model leading to projection predictive variable selection approach. Alternatively, reference models may also be used in an ad-hoc manner in combination with common variable selection methods.

The talk is based on work with many co-authors. The list of papers and software with links.

Juho Piironen, Markus Paasiniemi, and Aki Vehtari (2020). Projective inference in high-dimensional problems: prediction and feature selection. Electronic Journal of Statistics, 14(1):2155-2197. https://doi.org/10.1214/20-EJS1711

Federico Pavone, Juho Piironen, Paul-Christian Bürkner, and Aki Vehtari (2020). Using reference models in variable selection. arXiv preprint arXiv:2004.13118. https://arxiv.org/abs/2004.13118

Juho Piironen and Aki Vehtari (2016). Projection predictive input variable selection for Gaussian process models. 2016 IEEE 26th International Workshop on Machine Learning for Signal Processing (MLSP), doi:10.1109/MLSP.2016.7738829. https://dx.doi.org/10.1109/MLSP.2016.7738829

Juho Piironen and Aki Vehtari (2017). Comparison of Bayesian predictive methods for model selection. Statistics and Computing, 27(3):711-735. doi:10.1007/s11222-016-9649-y. https://link.springer.com/article/10.1007/s11222-016-9649-y

Homayun Afrabandpey, Tomi Peltola, Juho Piironen, Aki Vehtari, and Samuel Kaski (2019). Making Bayesian predictive models interpretable: A decision theoretic approach. arXiv preprint arXiv:1910.09358 https://arxiv.org/abs/1910.09358

Software:
Juho Piironen, Markus Paasiniemi, Alejandro Catalina and Aki Vehtari (2020). projpred: Projection Predictive Feature Selection. https://mc-stan.org/projpred