FitFlow

High-level interface to constrained optimization in MATLAB with:

• named parameters
• easy addition/removal of constraints
• easy specification of the cost function
• Markov chain Monte-Carlo (MCMC) sampling under constraints for calculating confidence intervals
• Hierarchical extension of model
• and more (yet to be documented)

Dependence

• BML package : github.com/yulkang/bml

Installation

1. Download files in this repository and BML.
2. Add both directories and their subdirectories to MATLAB's path.

Tutorial

See demo.m for the script.

• Add parameters and fix one

  W = FitWorkspace;
  W.add_params({
      {'x', 0, -5, 5} % {name, th0, lb, ub}
      {'y', -5, -10, 0} % {name, th0, lb, ub}
      });
  W.cost_fun = @(W) (W.th.x - 3).^2 + (W.th.y - 6).^2;
  
  W.fix_to_th0_('x'); % Fix x to 0
  
  % Fl is a FitFlow object containing all info, including W and res.
  % res is a compact struct containing the results, suitable for saving.
  [Fl, res] = W.fit;
  disp(res.th); % res.th : Struct containing fitted x and y

  • Results

  x: 0
  y: -2.0515e-07
  

  

• Add a linear constraint

  W = FitWorkspace;
  W.add_params({
      {'x', 0, -5, 5} % {name, th0, lb, ub}
      {'y', -5, -10, 0} % {name, th0, lb, ub}
      });
  W.cost_fun = @(W) (W.th.x - 3).^2 + (W.th.y - 6).^2;
  
  W.add_constraints({
      {'A', {'x', 'y'}, {[1, -1], 1}} % x - y <= 1
      });
  
  [Fl, res] = W.fit;
  disp(res.th); % Struct containing fitted x and y

  • Results

  x: 1.0000
  y: -2.7111e-07  
  

  

• Obtain MCMC samples under the linear constraint

  CI = FitCI(Fl);
  CI.main;
  
  samp = CI.MCMC.th_samp;
  
  disp('2.5 percentile:');
  disp(CI.Fl.res.pmil0025); % 2.5 percentile (25 per mille)
  
  disp('97.5 percentile:');
  disp(CI.Fl.res.pmil0975); % 97.5 percentile (975 per mille)
  
  figure;
  plot(samp(:,1), samp(:,2), '.');
  axis equal;
  xlim([-.5, 1]);
  ylim([-1, .5]);
  xlabel('x');
  ylabel('y');

  • Results

  2.5 percentile:
    x: 0.1459
    y: -0.2234
  
  97.5 percentile:
    x: 0.9629
    y: -0.0025
  

  

License

MIT license.

Development

Contributions are welcome. Please fork the repository or contact me at yul dot kang dot on at gmail dot com for discussion.