Think of it as a 2-dimensional analog to the simulator problem; we are trying to learn when the function is white or black as a function of the x, y coordinates - similar to predicting whether the result of a simulation is good or bad based on its input parameters, but easier to visualize because it's only 2-dimensional.
The toy function is trivial to solve in polar coordinates but tricky in cartesian coordinates, which is why it makes a good example.
Movie 1 shows an attempt to learn this function using Active Learning, up through 500 points. The current support vectors are shown in green - note that as new points are learned, old support vectors are sometimes dropped, too...
Movie 2 shows the first 150 points of the same simulation, but this time comparing Active Learning (on the left) with random point selection on the right. The bottom plots show the binary output, and the top plots show confidence, too.
3 shows what happens if you
use too much Active Learning - it spends all of its time focusing on
a specific region, rather than exploring the rest of the space. Our
technique needs to find a balance between focused exploration and
balanced exploration of the space. (The SVM looks different here
because this uses a Gaussian kernel, the others used a Polynomaial
kernel, but otherwise the approach is the same.)
Last updated 08-May-2002