def question7():
"""
Use N=10 training data points. Get weights with Linear Regression, use those
weights to initialize a PLA and see how long it takes to converge, over 1000 runs.
"""
N = 10.0
trial = 5000
convergence_steps = np.ones((trial, 1)) * np.NAN
for i in xrange(trial):
target_fn = generate_targetFn()
data = generate_dataPoints_fromFn(N, target_fn)
w = LG(data[:, 0:2], data[:, 2])
classifier = PLA(data, weights=w)
convergence_steps[i] = classifier.train()
print "Problem 7: Average steps took for classifier convergence: %0.3f" % (convergence_steps.mean())
def runComparison(N):
"""
For training-sample size N, run experiment 1000 times, where in each iteration:
1. Create target function and training data.
2. Train PLA and SVM
3. Create ntest testing points, and compare the misclassification performance
as percentage of disagreements.
"""
ntest = 1000 # number of out-of-sample dataset points
PLA_miss = np.ones(1000)*np.NAN
SVM_miss = np.ones(1000)*np.NAN
SVM_nsupp = np.ones(1000)*np.NAN
for i in xrange(1000):
f = generate_targetFn()
trainingSet = generate_dataPoints_fromFn(N, f)
while all_same_sign(trainingSet):
trainingSet = generate_dataPoints_fromFn(N, f)
testingSet = generate_dataPoints_fromFn(ntest, f)
while all_same_sign(testingSet):
testingSet = generate_dataPoints_fromFn(ntest, f)
# train PLA
step_lim = 10000
classifier = PLA(trainingSet)
classifier.train(lim = step_lim)
# test PLA
(results, misclassified) = classifier.classify(testingSet)
PLA_miss[i] = misclassified/(ntest*1.0)
# train SVM
(w, b, SVM_nsupp[i]) = SVM(trainingSet)
# test SVM
(results, misclassified) = apply_SVM(w, b, testingSet)
SVM_miss[i] = misclassified/(ntest*1.0)
# find how often SVM is better than PLA in out-of-sample performance
print "For N=%d, SVM is better than PLA %0.3f of the times" % (N, sum(np.less(SVM_miss, PLA_miss))/1000.0)
print "For N=%d, average number of support vectors is %0.3f" % (N, np.mean(SVM_nsupp))
