Is there any way to define a loss function in optimization problems?
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Is there any way to define a loss function when setting up an optimization problem using the optimization toolbox?
Main purpose: outlier detection.
Examples for loss functions in other optimization libraries:
- Ceres solver: http://ceres-solver.org/nnls_modeling.html?highlight=loss#lossfunction
- scipy.optimize.least_squares: https://docs.scipy.org/doc/scipy/reference/generated/scipy.optimize.least_squares.html
回答（1 个）
Matt J
2021-3-10
0 个投票
Yes, absolutely. Without a function to optimize, it's not an optimization problem.
2 个评论
Philipp Glira
2021-3-10
My questions was regarding loss functions.
The main purpose of a loss function is the detection of outliers. In other words, it makes the optimization robust against gross observation errors (=outliers).
I don't see any possibility in the documentation of the optimization toolbox to define such a loss function, but maybe I have just overlooked that part.
To clarify:
1) non-robust optimization, i.e. without loss function:
(see the 3 outliers with large y values)
2) robust optimization, i.e. with loss function:
(the 3 outliers are detected as outliers and thus have no influence on the estimated unknowns)
No, there are no outlier rejection utilities in the Optimization Toolbox solvers. The Computer Vision Toolbox, however, does have a RANSAC routine,
You could also try removing outliers with rmoutliers,
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2021-3-10
2021-3-10
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