Learning how to learn Markov State Models of conformational dynamics

(in descending order of achievability)

• Understand how Markov State Models are constructed, fit to data, and applied
  • Collective coordinate identification
  • State space discretization
  • Transition operator estimation
  • Bayesian sampling of transition matrices
• Potential applications:
  • Alpha-synuclein?
• Explore connections between MSM challenges and relavent developments in machine learning
  • Esp. interested in Hidden Markov Models, Projected Markov Models, and Reduced-Rank Hidden Markov Models
• Understand and benchmark dimensionality reduction algorithms
  • PCA, kPCA
  • ICA, tICA, ktICA
  • Manifold-learning algorithms
    • Diffusion maps?
  • Write down design requirements for future learning algorithms
• Understand and benchmark rare-event sampling algorithms
  • Transition state theory / transition state sampling
  • Transition path theory / transition path sampling
  • String method
• Apply geometric Monte Carlo methods to transition-matrix estimation
  • Hamiltonian Monte Carlo variants by Mark Girolami and colleagues

• Minor edits, feedback, or contributions to MSMbuilder code + documentation

• Bibliography - papers read / to read
• Notebooks - IPython notebooks containing code + notes on ideas or esp. interesting papers