the bioanalytics group llc global optimization toolkit project first prototype delivery

The BioAnalytics Group LLC

Global Optimization Toolkit Global Optimization Toolkit ProjectProject

First Prototype Delivery

2003-2004 The BioAnalytics Group LLC. All rights reserved.

The BioAnalytics Group

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OutlineOutline

Introductions

Purposes of the Toolkit

Example Workflow

Modules

Preliminary Results



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Purpose of the ToolkitPurpose 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.



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Why is a Toolkit Needed?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.



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Why Global Optimization?Why Global Optimization?



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Problem StatementProblem Statement

Minimize f(p), subject to bounds constraints on the vector p of parameters. (lb < p < ub)



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Parameter EstimationParameter Estimation

Special case of optimizationf 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.



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Example WorkflowExample 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.



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ModulesModules

Algorithm Selection

Data Import

Parameter Selection

Multiple Experiments

Postprocessing and Visualization



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AlgorithmsAlgorithms

Adaptive Simulated Annealing

Branch-and-Fit

Differential Evolution

Evolutionary Strategy (+Stochastic Ranking)



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Data FormatData Format

Most Common Internal FormatT,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.



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Parameter SelectionParameter 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.



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Multiple ExperimentsMultiple Experiments

Problem:One ModelDifferent data setsDifferent parameters to be fit for each data set.

Local and Global ParametersLocal parameters take different (optimal) values for each data set.Global parameters have one optimal value for all data sets.



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Multiple ExperimentsMultiple Experiments

Batch EstimationRun all data sets in a single cost function finding one optimal set of parameters.

Option: Local parameters for each experiment

Sequential EstimationRun 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



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Postprocessing: View resultsPostprocessing: View results



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Postprocessing: Confidence Postprocessing: Confidence IntervalsIntervals

Parameter Confidence Regions



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Preliminary ResultsPreliminary 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



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To Be DoneTo Be Done

GUI completion

Benchmarks

Support, Feedback and Updates

External Interface: acslXtreme

Follow-up work

the bioanalytics group llc global optimization toolkit project first prototype delivery

Documents

bioanalytics group llc

matlab files

matlab functions

simulated data

experimental data

vector p of parameters

local optimization packages

local optimization routines