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

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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

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Frank Noé (FU Berlin)

frank.noe@fu-berlin.de

Model optimization and selection: Variational Approach for Markov Processes (VAMP)

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How many states?

Motivation

Which features? 2 ? 10 ? 1000 ? Ca-coordinates ? distances ? contacts ? Which parameters? Parameter optimization problem Hyperparameter optimization / model selection problem (x1, x2, …, xT) (s1, s2, …, sT) transition matrix?

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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)

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Schütte et al: J. Comput. Phys. (1999), Prinz et al.: J. Chem. Phys. 134, p174105 (2011)

Slow processes

Eigenvalues / timescales κi-1 Backward propagator Processes: Spectral decomposition

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Part I : Variational score

Noé and Nüske, MMS 11, 635-655 (2013) Nüske et al, JCTC 10, 1739-1752 (2014)

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Part I : Variational score

Noé and Nüske, MMS 11, 635-655 (2013) Nüske et al, JCTC 10, 1739-1752 (2014)

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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) *

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Variational Approach for Markov processes (VAMP)

*

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* Noé and Clementi, JCTC 11, 5002-5011 (2015) Wu and Noé, arXiv:1707.04659 (2017)

Variational Approach for Markov processes (VAMP)

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Part II : Statistical validation

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Part II : Statistical validation

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Part II : Statistical validation

Cross-validation

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Part II : Statistical validation

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How many states in BPTI?

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Which features for BPTI?

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Validation

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Funding

Cecilia Clementi (Rice University) Christof Schütte (FU Berlin) Eric Vanden-Eijnden (Courant NY) Thomas Weikl (MPI Potsdam) Edina Rosta (King’s College London) Bettina Keller (FU Berlin)

Collaborations

Vijay Pande (Stanford) Volker Haucke (FMP Berlin) Stephan Sigrist (FU Berlin) Oliver Daumke (MDC) John Chodera (MSKCC NY) Gianni de Fabritiis (Barcelona)

Acknowledgements

Funding