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"the loss function max(0, -xy) is 0 if x and y are the same class and 1 if they are different" Not exactly because this would be optimizing the number of corre
by underflow 11y ago
"the loss function max(0, -xy) is 0 if x and y are the same class and 1 if they are different"
Not exactly because this would be optimizing the number of correctly classified elements.
Instead you minimize the sum of abs(WX) for each misclassified examples.
- psyklic 11y agoIn the case of these slides, the loss function is max(0, -xy) and the error function is the sum of these. So, the error function is the number of incorrectly classified examples (if x and y are different, it adds 1 to the error), which is exactly what we hope to minimize. x=1,y=1 => max(0, -(1 x 1)) = 0. x=1,y=-1 => max(0, -(-1 x 1)) = 1. x=-1,y=1 => max(0, -(1 x -1)) = 1. x=-1,y=-1 => max(0, -(-1 x -1)) = 0.
- underflow 11y agoThe transfer function is applied only at evaluation. In the formulas of the slides (and in the code), for training I compute the loss of an example X and it's expected target as: L(XW, target) What you define is minimizing L(transfer(XW), target) which is not easily optimizable.
- psyklic 11y agoIn the case of perceptrons, point taken -- I agree. However, my original statement still holds. The loss and error functions presented on the slides are still valid. Whether or not they are easily optimizable, they are still examples of loss and error functions.
- deleted 11y ago[deleted]