Overview
Gaussian process dynamical models (state-space models) builds upon a long line of work combining Gaussian processes (GP) with latent variable models for unsupervised learning tasks. Specifically, we narrow our focus on modelling high-dimensional sequential data ubiquitous in nature. The dynamics in observed space are captured by a smoothly evolving latent variable indexed by time and governed by a latent Gaussian process prior. The idea behind the project is to develop a scalable algorithm for sequential data which does not rely on holding the complete sequence in memory but can process the time-series or sequence in chunks. We also want to amortise the model with a suitable encoder like a recurrent neural network, LSTM or an Attention-based transformer.
The model is basically an extension of the model proposed here: https://gregorygundersen.com/blog/2020/07/24/gpdm/
Required reading:
[1] Gaussian process dynamical model: https://gregorygundersen.com/blog/2020/07/24/gpdm/
[2] Variational GPDM: https://proceedings.neurips.cc/paper/2011/file/af4732711661056eadbf798ba191272a-Paper.pdf
[3] Variational GPSSM: https://proceedings.neurips.cc/paper/2014/file/139f0874f2ded2e41b0393c4ac5644f7-Paper.pdf
[4] Recurrent Gaussian processes with SVI: https://arxiv.org/abs/1511.06644
[5] GPVAE for interpretable latent dynamics: http://proceedings.mlr.press/v118/pearce20a/pearce20a.pdf
