GSoc 2021 - Michael Schneider - Turing.jl case studies for Latent Variable Models

gsoc2021.md

GSoc 2021 - Turing.jl case studies for Latent Variable Models

Contributions

My contribution during GSoC 2021 is two case studies for using Turing.jl with Latent Variable Models. The models I have implemented are probabilistic PCA and Gaussian Process Latent Variable Models and a few extensions of these models. Each one is documented in a separate Github pull request (see links below).

probabilistic PCA

• Basic tutorial and model (https://www.robots.ox.ac.uk/~cvrg/hilary2006/ppca.pdf)
• Automatic Relevance Determination (Bishop, C.M., 2006. Machine learning and pattern recognition. Information science and statistics. Springer, Heidelberg; Chapter 12.2.3 (and Chapter 7.2.2))
• Residual PCA (demonstrating removal of batch effects) (https://arxiv.org/abs/1106.4333)
• Rotation Invariant Householder Parameterization for Bayesian PCA (http://proceedings.mlr.press/v97/nirwan19a.html)

Code: TuringLang/docs#121

Gaussian Process Latent Variable Model

• Basic tutorial (https://www.jmlr.org/papers/volume6/lawrence05a/lawrence05a.pdf, http://proceedings.mlr.press/v9/titsias10a/titsias10a.pdf)
• Link with pPCA via linear kernel
• Speedup of Gaussian Process Inference (not complete, https://arxiv.org/abs/2012.13962, http://proceedings.mlr.press/v5/titsias09a.html, https://arxiv.org/abs/1309.6835)

Code: TuringLang/docs#122