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I'd like to train a model $\widehat{y}_i = F(x_i, \theta)$, by minimizing the sum of a loss function, $L(\widehat{y}_i, y_i, \theta)$.

I'd like to input $\{x_i, y_i\}, F, L$ into a software package and have it perform a gradient-based optimization algorithm to find a good $\theta$.

I don't want to symbolically compute the gradient/Hessian function by hand, as the software should be able to do that. I don't want the software to approximate the gradient with finite differences, since that'd be lazy on the software's part.

Can anyone recommend a good package for this? I'm having trouble finding software that does both symbolic algebra/calculus and numerical optimization.

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MATLAB does both. The symbolic toolbox does symbolic calculus, the optimization/statistic toolbox does numerical optimization, including allowing you to choose which Hessian approximation method to use (e.g. BFGS). It's also sort of the de-facto standard for optimization researchers.

Alternatively, you could hack together your own tool in SciPy/SymPy, but it's probably easier to do directly with MATLAB if you have access.

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  • $\begingroup$ I guess nothing in Python does it out of the box? What about R or C/C++? $\endgroup$
    – dshin
    Sep 19 '14 at 22:11

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