P13 Question

[DavidNJ]

The problem wording is to find the runs that are not linearly separable with a hard margin SVM. The expectation is that there are some.

Using LIBSVM with C=10^6, Ein is always 0; svmpredict is always 100%. The number of support vectors varies between 6 and 12, mode and median are 8.

Based on the question I was expecting some to be linearly inseparable. I increased the noise level (from .25 to 5.0). Still solved everyone, although the number of support vectors went up.

I tried 1000 points instead of 100. Eout soared, but Ein didn't budge.

[Andrs]

Originally Posted by DavidNJ

The problem wording is to find the runs that are not linearly separable with a hard margin SVM. The expectation is that there are some.

Using LIBSVM with C=10^6, Ein is always 0; svmpredict is always 100%. The number of support vectors varies between 6 and 12, mode and median are 8.

Based on the question I was expecting some to be linearly inseparable. I increased the noise level (from .25 to 5.0). Still solved everyone, although the number of support vectors went up.

I tried 1000 points instead of 100. Eout soared, but Ein didn't budge.

How many experiments are you running with 100 diff training points in each?
If you are running enough experiments, you should get some experiments with data that are not linearly separable with the rbf kernel. Are you calculating your f(x) correctly?

[MLearning]

Originally Posted by Andrs

How many experiments are you running with 100 training points?
If you are running enough experiments, you should get some experiments with data that are not linearly separable with the rbf kernel. Are you calculating your f(x) correctly?

Regardless of the number of experiments run, libsvm returns Ein=0. I tried 10000 runs and libsvm sees a linearly separable data for all the runs. On the other hand, an Octave implementation that I wrote returns Ein ~=0 most of the time (clearly qp could not handle 100X100 matrix).

[vtrajan@vtrajan.net]

Originally Posted by DavidNJ

The problem wording is to find the runs that are not linearly separable with a hard margin SVM. The expectation is that there are some.

Using LIBSVM with C=10^6, Ein is always 0; svmpredict is always 100%. The number of support vectors varies between 6 and 12, mode and median are 8.

Based on the question I was expecting some to be linearly inseparable. I increased the noise level (from .25 to 5.0). Still solved everyone, although the number of support vectors went up.

I tried 1000 points instead of 100. Eout soared, but Ein didn't budge.

My results agree with yours. I used libvsm in python (sklearn).
Rajan

[DavidNJ]

Originally Posted by MLearning

Regardless of the number of experiments run, libsvm returns Ein=0. I tried 10000 runs and libsvm sees a linearly separable data for all the runs. On the other hand, an Octave implementation that I wrote returns Ein ~=0 most of the time (clearly qp could not handle 100X100 matrix).

Which would be correct: LIBSVM or your Octave QP implementation?

Note, Eout varies, gets worse with a higher N, and with greater noise (presumably the RBF kernel is fitting the noise).

[MLearning]

Originally Posted by DavidNJ

Which would be correct: LIBSVM or your Octave QP implementation?

Note, Eout varies, gets worse with a higher N, and with greater noise (presumably the RBF kernel is fitting the noise).

In my case, when I plot the training data, I can verify that the data is linearly separable. But my Octave impelemtation fails to see it. Personally, I would rely on libsvm given the fact it is designed to handle large matrices and uses efficient optimization techniques.

[yaser]

Originally Posted by DavidNJ

The problem wording is to find the runs that are not linearly separable with a hard margin SVM. The expectation is that there are some.

There is not necessarily an expectation one way or the other. You should report whatever the data gives you.

[DavidNJ]

Originally Posted by yaser

There is not necessarily an expectation one way or the other. You should report whatever the data gives you.

Professor Yaser: A trick question? Ouch!

Originally Posted by MLearning

In my case, when I plot the training data, I can verify that the data is linearly separable.

The noise definition (.25*sin()) limits the size of the noise to fairly small values. And, this is fitting an arbitrary number of support vectors (in my test, up to 12 with .25 and up to 17 with 5.0) which greatly extends what is "linear". For comparison, question 12 could be answered on visual inspection of the plot.

[yaser]

Originally Posted by DavidNJ

Professor Yaser: A trick question? Ouch!

We have to keep everyone on their toes.