Online reaction-coordinate-learning

[maxentile]

Goal: learn optimal reaction coordinates during a simulation
Challenges: in an unbiased trajectory, you're likely to just bounce around inside a single potential well, so the principal directions are not super useful
General approaches:

• Bayesian optimization?
• Online PCA:
  • "Randomized Online PCA Algorithms with Regret Bounds that are
    Logarithmic in the Dimension" http://www.jmlr.org/papers/volume9/warmuth08a/warmuth08a.pdf
  • Approach: represent uncertainty over the best subspace as a density matrix, update this density matrix over time
  • "Online PCA for Contaminated Data" http://papers.nips.cc/paper/5135-online-pca-for-contaminated-data.pdf
  • extend this to online learning of other low-rank models? It would be really cool if you had a framework for online learning of generalized low-rank models, or learning arbitrary linear transformations (i.e. compare with the manifold-optimization-based paper?)