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Model optimization and selection: Variational Approach for Markov - PowerPoint PPT Presentation

Aug 01, 2023 •259 likes •434 views

Model optimization and selection: Variational Approach for Markov Processes (VAMP) Frank No (FU Berlin) frank.noe@fu-berlin.de Motivation How many states? Which features? Which parameters? (x 1 , x 2 , , x T ) (s 1 , s 2 , , s T ) 2

  1. Model optimization and selection: Variational Approach for Markov Processes (VAMP) Frank Noé (FU Berlin) frank.noe@fu-berlin.de

  2. Motivation How many states? Which features? Which parameters? (x 1 , x 2 , …, x T ) (s 1 , s 2 , …, s T ) 2 ? Ca-coordinates ? transition matrix? 10 ? distances ? 1000 ? contacts ? Parameter optimization Hyperparameter optimization / problem model selection problem

  3. 
 
 Solving model selection problem requires two ingredients: 1) A score to rank models (MSMs, TICA, etc) by goodness 
 ==> Variational principle 2) A statistical validation method to avoid overfitting 
 ==> Cross-validation https://en.wikipedia.org/wiki/Cross-validation_(statistics)

  4. Slow processes Backward propagator Spectral decomposition Processes: Eigenvalues / timescales κ i-1 Schütte et al: J. Comput. Phys. (1999), Prinz et al.: J. Chem. Phys. 134, p174105 (2011)

  5. Part I : Variational score Noé and Nüske, MMS 11, 635-655 (2013) Nüske et al, JCTC 10, 1739-1752 (2014)

  6. Part I : Variational score Noé and Nüske, MMS 11, 635-655 (2013) Nüske et al, JCTC 10, 1739-1752 (2014)

  7. Part I : Variational score * Noé and Nüske, MMS 11, 635-655 (2013) Nüske et al, JCTC 10, 1739-1752 (2014) *Noé and Clementi, JCTC 11, 5002—5011 (2015)

  8. Variational Approach for Markov processes (VAMP) *

  9. Variational Approach for Markov processes (VAMP) Wu and Noé, arXiv: 1707.04659 (2017) * Noé and Clementi, JCTC 11, 5002-5011 (2015)

  10. Part II : Statistical validation

  11. Part II : Statistical validation

  12. Part II : Statistical validation Cross-validation

  13. Part II : Statistical validation

  14. How many states in BPTI?

  15. Which features for BPTI?

  16. Validation

  17. Acknowledgements Funding Collaborations Funding Cecilia Clementi (Rice University) Vijay Pande (Stanford) Christof Schütte (FU Berlin) Volker Haucke (FMP Berlin) Eric Vanden-Eijnden (Courant NY) Stephan Sigrist (FU Berlin) Thomas Weikl (MPI Potsdam) Oliver Daumke (MDC) Edina Rosta (King’s College London) John Chodera (MSKCC NY) Bettina Keller (FU Berlin) Gianni de Fabritiis (Barcelona)

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