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 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_nonlinear_transformation(N_samples, N_points):
'''use N_samples to have a consistent result
create a trainng set (1; x1; x2) from a constalation on N_points
runs linear regration from training set
computes Ein and averages it through all the samples
transform the training set following (1; x1; x2; x1x2; x1^2; x2^2)
run linear transformation on this transformed training set
compute Ein of transformed t_set and average through all the samples
create a hypothesis vector from the weight vector and the X matrix of the t_set transformed
Average for each function g the difference between the hypothesis vector and the function
finaly compute Eout from the f (target function) and the weight vector from training set that was not transformed
'''
Ein_avg = []
Eout_avg = []
Eintrans_avg = []
EdiffA = []
EdiffB = []
EdiffC = []
EdiffD = []
EdiffE = []
for i in range(N_samples):
t_set, f = generate_t_set(N_points)
wlin, X, y = linear_regression(N_points, t_set)
Ein = compute_Ein(wlin, X, y)
Ein_avg.append(Ein)
#transform the training data into the following nonlinear feature vector:
#(1; x1; x2; x1x2; x1^2; x2^2)
t_set_trans = transform_t_set(t_set)
wtrans, Xtrans, ytrans = linear_regression(N_points, t_set_trans)
Eintrans = compute_Ein(wtrans, Xtrans, ytrans)
Eintrans_avg.append(Eintrans)
h_vector = sign(dot(Xtrans, wtrans))
gA_vector = compute_g_vector(t_set_trans, 'a')
Ediff_a = compute_avg_difference(h_vector, gA_vector)
EdiffA.append(1 - Ediff_a)
gB_vector = compute_g_vector(t_set_trans, 'b')
Ediff_b = compute_avg_difference(h_vector, gB_vector)
EdiffB.append(1 - Ediff_b)
gC_vector = compute_g_vector(t_set_trans, 'c')
Ediff_c = compute_avg_difference(h_vector, gC_vector)
EdiffC.append(1 - Ediff_c)
gD_vector = compute_g_vector(t_set_trans, 'd')
Ediff_d = compute_avg_difference(h_vector, gD_vector)
EdiffD.append(1 - Ediff_d)
gE_vector = compute_g_vector(t_set_trans, 'e')
Ediff_e = compute_avg_difference(h_vector, gE_vector)
EdiffE.append(1 - Ediff_e)
Eout = compute_Eout_nonlineartrans(wtrans, f, N_points)
Eout_avg.append(Eout)
print_avg('Ein', Ein_avg)
print_avg('Ein Transformed', Eintrans_avg)
print_avg('P of agreeing A', EdiffA)
print_avg('P of agreeing B', EdiffB)
print_avg('P of agreeing C', EdiffC)
print_avg('P of agreeing D', EdiffD)
print_avg('P of agreeing E', EdiffE)
print_avg('Eout', Eout_avg)
def run_nonlinear_transformation(N_samples, N_points):
'''use N_samples to have a consistent result
create a trainng set (1; x1; x2) from a constalation on N_points
runs linear regration from training set
computes Ein and averages it through all the samples
transform the training set following (1; x1; x2; x1x2; x1^2; x2^2)
run linear transformation on this transformed training set
compute Ein of transformed t_set and average through all the samples
create a hypothesis vector from the weight vector and the X matrix of the t_set transformed
Average for each function g the difference between the hypothesis vector and the function
finaly compute Eout from the f (target function) and the weight vector from training set that was not transformed
'''
Ein_avg = []
Eout_avg = []
Eintrans_avg = []
EdiffA = []
EdiffB = []
EdiffC = []
EdiffD = []
EdiffE = []
for i in range(N_samples):
t_set,f = generate_t_set(N_points)
wlin,X,y = linear_regression(N_points,t_set)
Ein = compute_Ein(wlin, X, y)
Ein_avg.append(Ein)
#transform the training data into the following nonlinear feature vector:
#(1; x1; x2; x1x2; x1^2; x2^2)
t_set_trans = transform_t_set(t_set)
wtrans,Xtrans,ytrans = linear_regression(N_points,t_set_trans)
Eintrans = compute_Ein(wtrans,Xtrans,ytrans)
Eintrans_avg.append(Eintrans)
h_vector =sign(dot(Xtrans,wtrans))
gA_vector = compute_g_vector(t_set_trans,'a')
Ediff_a = compute_avg_difference(h_vector,gA_vector)
EdiffA.append(1-Ediff_a)
gB_vector = compute_g_vector(t_set_trans,'b')
Ediff_b = compute_avg_difference(h_vector,gB_vector)
EdiffB.append(1-Ediff_b)
gC_vector = compute_g_vector(t_set_trans,'c')
Ediff_c = compute_avg_difference(h_vector,gC_vector)
EdiffC.append(1-Ediff_c)
gD_vector = compute_g_vector(t_set_trans,'d')
Ediff_d = compute_avg_difference(h_vector,gD_vector)
EdiffD.append(1-Ediff_d)
gE_vector = compute_g_vector(t_set_trans,'e')
Ediff_e = compute_avg_difference(h_vector,gE_vector)
EdiffE.append(1-Ediff_e)
Eout = compute_Eout_nonlineartrans(wtrans,f,N_points)
Eout_avg.append(Eout)
print_avg('Ein',Ein_avg)
print_avg('Ein Transformed',Eintrans_avg)
print_avg('P of agreeing A',EdiffA)
print_avg('P of agreeing B',EdiffB)
print_avg('P of agreeing C',EdiffC)
print_avg('P of agreeing D',EdiffD)
print_avg('P of agreeing E',EdiffE)
print_avg('Eout',Eout_avg)
