def linear_regression_lambda(N_points,t_set,lda = 1):
'''Linear regresion algorithm with regularization
from Y and X compute the dagger or pseudo matrix
return the Xdagger.Y as the w vector
default lambda is 1.0
'''
y_vector = target_vector(t_set)
X_matrix = input_data_matrix(t_set)
# weight decay term
foo = eye(size(X_matrix,1))
bar = pinv( dot(X_matrix.T, X_matrix) + lda * foo)
return dot(dot(bar, X_matrix.T), y_vector), X_matrix, y_vector
def compute_Eout(w, test_set):
'number of out-of-sample points misclassifed/total number of out-of-sample points from data'
X_matrix = input_data_matrix(test_set)
y_vector = target_vector(test_set)
g_vector = dot(X_matrix,w)
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,N_points):
'number of out-of-sample points misclassifed / total number of out-of-sample points'
t_set = read_data_set("data/out.dta")
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_nonlineartrans(w, N_points):
'number of out-of-sample points misclassifed / total number of out-of-sample points'
# generate N fresh points (f will not change) with noise
t_set = read_data_set("data/out.dta")
t_set_trans = transform_t_set(t_set)
X_matrix = input_data_matrix(t_set_trans)
y_vector = target_vector(t_set_trans)
g_vector = dot(X_matrix,w)
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_validation(t_set, v_set, k):
'''
Run linear regression on given feature set,
and compute Ein and Eout
'''
N_points = len(t_set)
'run LR on the training set'
w, Xtrans, y = linear_regression(N_points, t_set)
' compute Ein using the validation set'
valid_set = input_data_matrix(v_set)
y_vector = target_vector(v_set)
Eval = compute_Eval(w, valid_set, y_vector)
'using the weights, compute Eval'
Eout = compute_Eout(w, k)
print 'k:' + str(k)
print 'Eval: ' + str(Eval)
print 'Eout: ' + str(Eout)