def run_linear_regression(N_samples,N_points):
'''runs on N_samples and with N_points a linear regression
computes Ein by average of the samples as well as Eout
'''
print 'running Linear Regression on %s samples' %str(N_samples)
print 'Each sample has %s data points' %str(N_points)
Ein_avg = []
Eout_avg = []
for i in range(N_samples):
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d,f)
wlin,X,y = linear_regression(N_points,t_set)
Ein = compute_Ein(wlin,X,y)
Ein_avg.append(Ein)
Eout = compute_Eout(wlin,f,N_points)
Eout_avg.append(Eout)
print_avg('Ein',Ein_avg)
print_avg('Eout',Eout_avg)
def run_linear_regression(N_samples, N_points):
'''runs on N_samples and with N_points a linear regression
computes Ein by average of the samples as well as Eout
'''
print 'running Linear Regression on %s samples' % str(N_samples)
print 'Each sample has %s data points' % str(N_points)
Ein_avg = []
Eout_avg = []
for i in range(N_samples):
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d, f)
wlin, X, y = linear_regression(N_points, t_set)
Ein = compute_Ein(wlin, X, y)
Ein_avg.append(Ein)
Eout = compute_Eout(wlin, f, N_points)
Eout_avg.append(Eout)
print_avg('Ein', Ein_avg)
print_avg('Eout', Eout_avg)
def compute_Eout(wlin, f, N_points):
'number of out-of-sample points misclassifed / total number of out-of-sample points'
d = data(N_points)
t_set = build_training_set(d, f)
X_matrix = input_data_matrix(t_set)
y_vector = target_vector(t_set)
g_vector = dot(X_matrix, wlin)
for i in range(len(g_vector)):
g_vector[i] = sign(g_vector[i])
vEout = g_vector - y_vector
nEout = 0
for i in range(len(vEout)):
if vEout[i] != 0:
nEout = nEout + 1
Eout = nEout / (len(vEout) * 1.0)
return Eout
def compute_Eout(wlin,f,N_points):
'number of out-of-sample points misclassifed / total number of out-of-sample points'
d = data(N_points)
t_set = build_training_set(d,f)
X_matrix = input_data_matrix(t_set)
y_vector = target_vector(t_set)
g_vector = dot(X_matrix,wlin)
for i in range(len(g_vector)):
g_vector[i] = sign(g_vector[i])
vEout = g_vector - y_vector
nEout = 0
for i in range(len(vEout)):
if vEout[i]!=0:
nEout = nEout + 1
Eout = nEout/(len(vEout)*1.0)
return Eout
def run_lr_and_pla(N_samples, N_points):
'''runs on N_samples and with N_points a linear regresion
then from the weight vector runs PLA algorithm
compute the average number of iterations of PLA with this w vector
'''
print 'running Linear Regression on %s samples' % N_samples
print 'Each samples has %s data points' % N_points
iteration_avg = []
for i in range(N_samples):
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d, f)
wlin, X, y = linear_regression(N_points, t_set)
w_pla, iteration = PLA(N_points, wlin, f, t_set)
iteration_avg.append(iteration)
print_avg('Number of iterations', iteration_avg)
def run_lr_and_pla(N_samples, N_points):
'''runs on N_samples and with N_points a linear regresion
then from the weight vector runs PLA algorithm
compute the average number of iterations of PLA with this w vector
'''
print 'running Linear Regression on %s samples' %N_samples
print 'Each samples has %s data points' %N_points
iteration_avg = []
for i in range(N_samples):
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d,f)
wlin,X,y = linear_regression(N_points,t_set)
w_pla,iteration = PLA(N_points,wlin,f,t_set)
iteration_avg.append(iteration)
print_avg('Number of iterations',iteration_avg)
def run_PLA(N_samples, N_points):
samples = [] # vector of 1 clasified, 0 misclassified
iterations = [] #vector of iterations needed for each PLA
b_misclassified = False
diff = [] #vector of difference average between f and g
for i in range(N_samples):
# run PLA in sample
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d, f)
w = [0, 0, 0] #Start the PLA with the weight vector w being all zeros
w, iteration = PLA(N_points, w, f, t_set)
iterations.append(iteration)
# check if points are classified or not
for i in range(len(t_set)):
point = t_set[i][0]
s = h(w, point)
yn = t_set[i][1]
if yn != s:
samples.append(0)
b_misclassified = True
break
# check difference between f and g
diff.append(evaluate_diff_f_g(f, w))
if not b_misclassified: samples.append(1)
b_misclassified = False
print 'number of samples misclassified: %s ' % samples.count(0)
print 'number of classified samples: %s ' % samples.count(1)
print 'number of iteration avg: %s ' % (str(
sum(iterations) / len(iterations) * 1.0))
print 'average of difference in function g: %s' % (sum(diff) /
(len(diff) * 1.0))
def run_PLA(N_samples,N_points):
samples = []# vector of 1 clasified, 0 misclassified
iterations = []#vector of iterations needed for each PLA
b_misclassified = False
diff = []#vector of difference average between f and g
for i in range(N_samples):
# run PLA in sample
d = data(N_points)
l = randomline()
f = target_function(l)
t_set = build_training_set(d,f)
w = [0,0,0]
w,iteration = PLA(N_points,w,f,t_set)
iterations.append(iteration)
# check if points are classified or not
for i in range(len(t_set)):
point = t_set[i][0]
s = h(w,point)
yn = t_set[i][1]
if yn != s:
samples.append(0)
b_misclassified = True
break
# check difference between f and g
diff.append(evaluate_diff_f_g(f,w))
if not b_misclassified: samples.append(1)
b_misclassified = False
print 'number of samples misclassified: %s ' % samples.count(0)
print 'number of classified samples: %s ' % samples.count(1)
print 'number of iteration avg: %s ' % (str(sum(iterations)/len(iterations)*1.0))
print 'average of difference in function g: %s' % ( sum(diff)/(len(diff)*1.0) )
def run_pla_vs_svm(nbruns=1, N=10):
solvers.options['show_progress'] = False
d = []
l = 0
f = 0
t_set = []
y = []
svm_vs_pla = []
for i in range(nbruns):
onBothSides = False
while (not onBothSides):
d = data(N)
l = randomline()
f = target_function(l)
t_set = build_training_set(d, f)
y = target_vector(t_set)
if (1 in y) and (-1 in y):
onBothSides = True
else:
onBothSides = False
w = [0, 0, 0]
w_pla, iteration = PLA(N, w, f, t_set)
plaEout = evaluate_diff_f_g(f, w_pla)
X_matrix = input_data_matrix(t_set)
dimension = len(X_matrix[0])
#identity matrix of size dim X dim matrix x,I,J,typecode double
P = spmatrix(1, range(dimension), range(dimension), tc='d')
#vector of zeros of size dim, typecode double
q = matrix([0] * (dimension), tc='d')
mat = []
for t in t_set:
y = t[1]
temp = [x * -1.0 * y for x in t[0]]
mat.append(temp)
G = matrix(mat, tc='d')
G = G.trans()
# vectors of -1 of size t_set
h = matrix([-1] * len(t_set), tc='d')
#http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html
qp_sln = solvers.qp(P, q, G, h)
wsvm = list(qp_sln['x'])
# number of support vectors you can get at each run
count_sv = 0
for t in t_set:
wsvm = array(wsvm)
x = array(t[0])
y = t[1]
res = fabs(y * dot(wsvm, x) - 1)
if res < 0.001:
count_sv = count_sv + 1
#print count_sv
# Eout of svm
svmEout = computeEout_svm(f, wsvm)
#print 'svmEout: %s'%svmEout
if (svmEout < plaEout):
svm_vs_pla.append([True, count_sv])
else:
svm_vs_pla.append([False, count_sv])
print "svm win pla %f" % (len(filter(lambda a: a[0] is True, svm_vs_pla)) *
1.0 / N)
percent_svm_won = len([r[0] for r in svm_vs_pla if r[0] is True
]) * 1.0 / len(svm_vs_pla)
print "question 9: svm beat pla %f percent of the time" % (
percent_svm_won * 100)
avg_sv = sum([a[1] for a in svm_vs_pla]) * 1.0 / len(svm_vs_pla)
print "avg sv:", avg_sv
def run_pla_vs_svm(nbruns = 1, N = 10):
solvers.options['show_progress'] = False
d = []
l = 0
f = 0
t_set = []
y = []
svm_vs_pla = []
for i in range(nbruns):
onBothSides = False
while(not onBothSides):
d = data(N)
l = randomline()
f = target_function(l)
t_set = build_training_set(d,f)
y = target_vector(t_set)
if (1 in y) and (-1 in y):
onBothSides = True
else:
onBothSides = False
w = [0,0,0]
w_pla,iteration = PLA(N,w,f,t_set)
plaEout = evaluate_diff_f_g(f,w_pla)
X_matrix = input_data_matrix(t_set)
dimension = len(X_matrix[0])
#identity matrix of size dim X dim matrix x,I,J,typecode double
P = spmatrix(1, range(dimension), range(dimension), tc='d')
#vector of zeros of size dim, typecode double
q = matrix([0]*(dimension), tc='d')
mat = []
for t in t_set:
y = t[1]
temp = [x * -1.0*y for x in t[0]]
mat.append(temp)
G = matrix(mat, tc='d')
G = G.trans()
# vectors of -1 of size t_set
h = matrix([-1]*len(t_set), tc='d')
#http://abel.ee.ucla.edu/cvxopt/examples/tutorial/qp.html
qp_sln = solvers.qp(P, q, G, h)
wsvm = list(qp_sln['x'])
# number of support vectors you can get at each run
count_sv = 0
for t in t_set:
wsvm = array(wsvm)
x = array(t[0])
y = t[1]
res = fabs(y*dot(wsvm,x)-1)
if res < 0.001:
count_sv = count_sv + 1
#print count_sv
# Eout of svm
svmEout = computeEout_svm(f,wsvm)
#print 'svmEout: %s'%svmEout
if(svmEout < plaEout):
svm_vs_pla.append([True,count_sv])
else:
svm_vs_pla.append([False,count_sv])
print "svm win pla %f" % (len(filter(lambda a: a[0] is True, svm_vs_pla))*1.0/N)
percent_svm_won = len([r[0] for r in svm_vs_pla if r[0] is True])*1.0/len(svm_vs_pla)
print "question 9: svm beat pla %f percent of the time" % (percent_svm_won*100)
avg_sv = sum([a[1] for a in svm_vs_pla])*1.0/len(svm_vs_pla)
print "avg sv:", avg_sv
