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Following description in http://pubs.acs.org/doi/abs/10.1021/ct5007357

Gradient-boosted feature selection:
http://www.cse.wustl.edu/~kilian/papers/gbfs.pdf

Looks very useful: linear computational complexity, reliably identifies nonlinear feature interactions

http://people.brandeis.edu/~berkes/data/papers/BlasBerkWisk_NeurComp2006.pdf

Linear SFA is formally equivalent to tICA with time-delay one.

Finding projections with high autocorrelation time:

• tICA/ktICA
• CCA with desired lag-time
• Slow Feature Analysis: http://www.cnbc.cmu.edu/~tai/readings/learning/wiskott_sejnowski_2002.pdf

Kinetic discriminatory metric learning: http://pubs.acs.org/doi/abs/10.1021/ct400132h

Questions:

• Can any aspects of the learned distance metric generalize across protein examples?

Seems like we would want to define the metastable states in terms of a probabilistic model. Consider Katherine Heller's work.

How do we visually summarize a MSM?

• Naive: draw a network where the nodes are exemplars of each state and edges are transition rates, e.g.
  (http://biomedicalcomputationreview.org/sites/default/files/u6/c_ntl9_jacs_fig3.jpg)
  (http://upload.wikimedia.org/wikipedia/commons/thumb/b/b9/[email protected]/[email protected])
  ...
  Potentially with embellishments, e.g. a "potential energy surface"
  
  (http://portfolio.scistyle.com/Protein-Folding-Funnel)
  • Benefits: direct mapping to model representation in the computer
  • Limitations:
    • State markers: a state definition isn't just a single conformation, but a group of conformations. An individual conformation is difficult to interpret using a single 2D projection
    • Transition rates: we'll experience occlusion from many overlapping edges unless we arbitrarily threshold / sparsify the transition matrix
    • Doesn't "look dynamic"
    • Requires an additional marker (e.g. node outline color) to indicate the free energy of each conformation
    • Propagating probability mass multiple time steps ahead is difficult to do visually. If I start at a node, I look for and follow the couple biggest outgoing arrows and say most of the probability mass goes to those neighbors in one time step. I do the same thing for each of those nodes to figure out where the probability mass goes in two time steps. Etc. --> It would be cool to have an interface that automatically does this propagation for you. E.g. hover over a state, and then it does a looping animation where each frame indicates how much probability mass is on each node at a given time lag.

Learning a global linear transformation with high autocorrelation doesn't necessarily help. Example potential: "X," or blobs on a hypercube-- no linear transformation will achieve high autocorrelation.

How best to describe the components then? Locally linear maps?

Implement RR-HMMs, following Siddiqi et al.'s implementation

Seems applicable, maybe worth reading carefully: https://www.stat.washington.edu/~ebfox/publications/multiResGP_NIPS_final.pdf

How can we inspect them? How are they structured in general?

How to inspect:

1. Sampling -- Collect a large number of conformations
2. Analytical -- Inspect simple models (e.g. Geometry of Random Fields book)

Previous work:
"Dynamics of hierarchical folding on energy landscapes of hexapeptides" http://wws.weizmann.ac.il/sb/faculty_pages/Levy/sites/weizmann.ac.il.sb.faculty_pages.Levy/files/ma_jcp.pdf

How can we efficiently identify metastable states?

• Specifically, can protein design algorithms be used? http://www.cs.duke.edu/donaldlab/osprey.php

John Chodera suggests:

• Multistate transition interface sampling: http://www.ncbi.nlm.nih.gov/pubmed/23901958
• Hierarchical uncoupling-coupling Monte Carlo: http://link.springer.com/chapter/10.1007%2F978-3-642-56080-4_10
• Grid-free hierarchical conformational dynamics: http://www.diss.fu-berlin.de/diss/receive/FUDISS_thesis_000000008079 Statistical Error Estimation and Grid-free Hierarchical Refinement in Conformation Dynamics.
• TRAM and dynamical reweighting:
  • http://www.choderalab.org/publications/2014/4/26/optimal-use-of-data-in-parallel-tempering-simulations-for-the-construction-of-discrete-state-markov-models-of-biomolecular-dynamics?rq=prinz
  • http://arxiv.org/abs/1407.0138
• Metadynamics and related schemes: "Schemes like metadynamics (Danny knows much more about this) can modify the dynamics significantly to "push" the simulation into new regions of space, but usually require some knowledge of relevant order parameters to do this. We've always wondered if simply using repulsive "hills" in RMSD to already-visited configurations may be sufficient to encourage the system to explore new conformations and metastable states, though it's not obvious how one would correct for this to get an initial estimate of transition rates among states or even state boundaries."

I would think TIS is a specific instance of "active learning."

Robust hierarchical clustering by active learning
http://jmlr.csail.mit.edu/proceedings/papers/v15/eriksson11a/eriksson11a.pdf

Was skimming Kevin Murphy's PhD thesis and found that Hierarchical HMMs (like SCFGs but with finite stack size / tractable inference) can be represented as dynamic Bayes nets, and therefore have linear-time inference algorithms.

Are there any limitations with the standard ways of doing this?

Standard way: Fit a Markov model to the clusters, then plot implied relaxation time scales and see how quickly they converge as you increase lag time. Faster convergence means the observations are markovian on shorter time scales,which is good.

Other ideas:

• Examine autocorrelation time of the projection directly.
  • Limitation: requires selecting a specific lagtime to optimize for.
  • Possible solution: optimize for several lagtimes simultaneously

Test cases:

• map all points to a single overlapping blob

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?)

By Frank Noe... nice! http://docs.markovmodel.org/

Coordinate transforms
1 Time-lagged independent component analysis (TICA)
Coordinate clustering
2 Regular space clustering
Markov model estimation
3 Implied timescales
4 Nonreversible Markov model estimation
5 Reversible Markov model estimation
Markov model analysis
6 Perron-cluster cluster analysis (PCCA)
7 Computational spectroscopy / dynamical fingerprints
8 Transition path theory (TPT)
Multiple thermodynamic states
9 Thermodynamic reweighting principle
10 Discrete transition-based reweighting analysis method (dTRAM)