Model fitting in ceres_solver

[Huy Nguyen‏]

I'm using ceres-solver to optimize a set of parameters (9 total) for my Monte-Carlo (MC) simulation. Basically, the MC code return an armadillo double matrix of the type results = { {1,2,3,...,19} } for every set of parameters. I have a set of corresponding data. How do I optimize the parameters using ceres-solver?

Here's the code so far:

using ceres::AutoDiffCostFunction;
using ceres::CostFunction;
using ceres::CauchyLoss;
using ceres::Problem;
using ceres::Solver;
using ceres::Solve;

struct SimulationResidual {
SimulationResidual(): y_{346.301,346.312,346.432,346.394,346.471,346.605,346.797,346.948,347.121,347.384,347.626,348.08,348.561,349.333,350.404,351.761,352.975,354.17,354.809} {};
template <typename T> bool operator()(const T* const T_params,
                                      T* residual) const {
    Tm = T_params[0];
    g31= T_params[1];
    g32= T_params[2];
    gg31= T_params[3];
    gg32= T_params[4];
    bn = T_params[5];
    bu = T_params[6];
    mn = T_params[7];
    mu = T_params[8];
    mat Tjumpave = Tjump_ave(); //  MC simulation
    residual[0] =  Tjumpave(0,0) - T(y_[0]);
    residual[1] =  Tjumpave(0,1) - T(y_[1]);
    residual[2] =  Tjumpave(0,2) - T(y_[2]);
    residual[3] =  Tjumpave(0,3) - T(y_[3]);
    residual[4] =  Tjumpave(0,4) - T(y_[4]);
    residual[5] =  Tjumpave(0,5) - T(y_[5]);
    residual[6] =  Tjumpave(0,6) - T(y_[6]);
    residual[7] =  Tjumpave(0,7) - T(y_[7]);
    residual[8] =  Tjumpave(0,8) - T(y_[8]);
    residual[9] =  Tjumpave(0,9) - T(y_[9]);
    residual[10] =  Tjumpave(0,10) - T(y_[10]);
    residual[11] =  Tjumpave(0,11) - T(y_[11]);
    residual[12] =  Tjumpave(0,12) - T(y_[12]);
    residual[13] =  Tjumpave(0,13) - T(y_[13]);
    residual[14] =  Tjumpave(0,14) - T(y_[14]);
    residual[15] =  Tjumpave(0,15) - T(y_[15]);
    residual[16] =  Tjumpave(0,16) - T(y_[16]);
    residual[17] =  Tjumpave(0,17) - T(y_[17]);
    residual[18] =  Tjumpave(0,18) - T(y_[18]);
    return true;
}
private:
    const double y_[19];
};

int main(int argc, char** argv) {
    wall_clock timer;
    timer.tic();
    google::InitGoogleLogging(argv[0]);
    double T_params[] = { Tm,g31,g32,gg31,gg32,bn,bu,mn,mu }; //  initial guess
    Problem problem;
    CostFunction* cost_function =
    new AutoDiffCostFunction<SimulationResidual, 19, 1, 1>
    ( new SimulationResidual() );
    problem.AddResidualBlock(cost_function, new CauchyLoss(0.5), &T_params);
}

When compiled in Xcode with -lceres and -lglog (and I had eigen3 installed and everything. Examples of the package ran fine without errors), I have non-matching member function for call to 'AddResidualBlock' as one of the errors. Please let me know if I need to provide more information to help you help me.
Thanks.

P/S The error is on the problem.AddResidualBlock line.

[Sameer Agarwal‏]

Huy,

Have you tried working through the tutorial? 

http://ceres-solver.org/tutorial.html 

I do not quite understand your code. As far as I can tell this code should not compile. 

In any case, 

CostFunction* cost_function =
    new AutoDiffCostFunction<SimulationResidual, 19, 1, 1>
    ( new SimulationResidual() );

is wrong. Since your functor has a 19 dimensional residual but is taking 9 dimensional parameter block as input. It should read

CostFunction* cost_function =
    new AutoDiffCostFunction<SimulationResidual, 19, 9>
    ( new SimulationResidual() );

Besides this, I expect that your montecarlo simulation is non-deterministic, which means that for the same parameters you will get different objective function values every execution, unless you are using some sort of quasi-random numbers.

This is going to be a problem, since ceres depends on its objective function  being deterministic.

Sameer

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[Huy Nguyen‏]

Hi Sameer,

Yes I have worked through some of the examples from the website, namely curve_fitting and robust_curve_fitting. Thank you for pointing out the mistake in my code. My Monte-Carlo is non-deterministic, so I don't have an analytical solution of the fit. I realize in order for the solver to work, a numerical differentiation may have to take place, but I'm not sure how the solver can get the derivative wrt the 9 parameters I'm putting in.

Is there any suggestion to have optimization work for a non-deterministic function?

Thanks,

Huy

[Sameer Agarwal‏]

Huy,

if all you are doing is calling an external monte carlo routine and comparing matrices, why not just use numeric differentiation to define the whole cost function?

in any case, numeric derivatives (and residual values) are going to be noisy because of montecarlo simulation and that is likely going to cause problems with your optimization.

Sameer

To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/9db2c454-5094-4bcd-9665-5554fda09d85%40googlegroups.com.

[Huy Nguyen‏]

Hi,

Sorry for the delay to reply. Thank you for the suggestion. I am writing the code to do optimization by numeric diff. I think I'll average more simulation runs to reduce the noise. Hopefully it will help.

Thank you,

Huy

[Sameer Agarwal‏]

Huy,

I suggest using quasi-random numbers or pseudo random numbers with a fixed seed. It will bias your simulations but it will bring down the variance to zero.

Sameer

To view this discussion on the web visit https://groups.google.com/d/msgid/ceres-solver/5157903f-030f-40c7-8095-26161919e850%40googlegroups.com.