y=log(4 + sin(4 * X1) + |X2| + X3^2 + X4^3 + X5 + 0.1*\epsilon)
Xi ~ Unif(-1, 1)
\epsilon ~ N(0, 1)
"""
# Simulation data
np.random.seed(25)
y, X = DataSimulator.SimData_Wang04(1000) # Simulate data
data = Data(y, X)
# Same kernel for all groups
kernel = Kernel('gaussian', sigma=0.5)
# Step-wise foward selection to determine group structure
res = forwardSelection(data, kernel, useLowRankApproximation=True, rank=10)
"""Simulation result:
In this example, we successfully recover the true group structure:
** SELECTED GROUP STRUCTURE: ([1], [2], [3], [4], [5])
Note: The algorithm is tested under two setting:
1) enabling low rank approximation (using Nystroem method),
2) no low rank approximation.
The performance of the algorithm under the two settings are different.
It seems that the detected structure from the first setting is closer
to the true structure than that from the second setting.