The BioAnalytics Group LLC Global Optimization Toolkit Project First Prototype Delivery.

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The BioAnalytics Group LLC Global Optimization Toolkit Project First Prototype Delivery

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Outline Introductions Purposes of the Toolkit Example Workflow Modules Preliminary Results

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Purpose of the Toolkit Primary: Provide Robust, Easy-to-use Global Optimization alternatives to local optimization packages provided in MATLAB. Secondary: Provide supporting tools to use Global Optimization in biomodel parameter estimation projects.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Why is a Toolkit Needed? Local optimization routines in MATLAB leave a lot of questions unanswered. Are there other local minima that should be considered? What is the confidence region of the parameters? How good is the fit of the model to data? How do I integrate data from multiple experiments? Available global optimization packages for MATLAB are very basic or require considerable trial-and-error and experience to use.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Why Global Optimization?

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Problem Statement Minimize f(p), subject to bounds constraints on the vector p of parameters. (lb < p < ub)

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Parameter Estimation Special case of optimization f is a function of the error (ŷ-y) between simulated data ŷ and experimental measurements y, especially time-series data. Special-Special Case: ŷ is the solution to an initial value problem.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Example Workflow 1.Design a model in MATLAB. 2.Pick the parameters to be estimated. 3.Select a fitting function. 4.Import the experimental data into MATLAB. 5.Optimize the parameters to fit the data. 6.View the results. 7.Estimate confidence intervals. 8.Report results. 9.Get more data, change model, re-estimate, etc.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Modules Algorithm Selection Data Import Parameter Selection Multiple Experiments Postprocessing and Visualization

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Algorithms Adaptive Simulated Annealing Branch-and-Fit Differential Evolution Evolutionary Strategy (+Stochastic Ranking)

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Data Format Most Common Internal Format T,Y, E T is a vector of Nt measurement times Y is a matrix of Nt-by-Nm measurements E is an optional matrix of Nt-by-Nm measurement errors. Easy to import from text files, Excel, etc. using MATLAB provided functions.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Parameter Selection Most common internal parameter format: P,C, F P is a vector of Np parameter estimates C is a matrix of Np-by-Np covariance (often diagonal) F is an optional vector of Nf parameters to be estimated. P=[p1, p2, p3, p4, p5, p6, p7, p8, p9, p10] T F=[1, 8, 10, 2] (I want to fit only first, eighth, tenth, second parameters) Easy to import from text, Excel, MATLAB files with MATLAB functions.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Multiple Experiments Problem: One Model Different data sets Different parameters to be fit for each data set. Local and Global Parameters Local parameters take different (optimal) values for each data set. Global parameters have one optimal value for all data sets.

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Multiple Experiments Batch Estimation Run all data sets in a single cost function finding one optimal set of parameters. Option: Local parameters for each experiment Sequential Estimation Run each data set in sequence, improving the parameter estimate with each new data set. Find the best global parameter values Find the best local parameter values Toolkit Implements a Bayesian sequential estimator

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Postprocessing: View results

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Postprocessing: Confidence Intervals Parameter Confidence Regions

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential Preliminary Results 3 Algorithms all competitive on Novartis PERSIMrunCHIAKI test case. Differential Evolution (With TBAG modifications) Evolutionary Strategies Adaptive Simulated Annealing One algorithm not competitive: Branch-and-fit

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential

 The BioAnalytics Group LLC. All rights reserved. The BioAnalytics Group Confidential To Be Done GUI completion Benchmarks Support, Feedback and Updates External Interface: acslXtreme Follow-up work