def regression_reg(lamda, deg):
validation_err = 0
for i in range(0, 10):
print(i)
rms_val_error = 0
x_val = x_train[i * 10:(i + 1) * 10, :]
t_val = t_train[i * 10:(i + 1) * 10, :]
x_train_use = np.concatenate(
(x_train[0:i * 10, :], x_train[(i + 1) * 10:, :]), 0)
t_train_use = np.concatenate(
(t_train[0:i * 10, :], t_train[(i + 1) * 10:, :]), 0)
bigphi = a1.design_matrix('polynomial', x_train_use, deg, 1)
(w, rms_train) = a1.linear_regression(x_train_use, t_train_use, bigphi,
lamda, deg, 0, 0)
#print(w)
bigfai_val = a1.design_matrix('polynomial', x_val, deg, 1)
rms_val_error = a1.evaluate_regression(bigfai_val, w, t_val)
#print(rms_val_error)
validation_err += rms_val_error
#print(validation_err)
validation_err_avg[lamda] = validation_err / 10
print(validation_err_avg)
def plot_error(normalized):
targets = values[:, 1]
if normalized == 'yes':
x = a1.normalize_data(values[:, 7:])
else:
x = values[:, 7:]
N_TRAIN = 100
x_train = x[0:N_TRAIN, :]
x_test = x[N_TRAIN:, :]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
# Complete the linear_regression and evaluate_regression functions of the assignment1.py
# Pass the required parameters to these functions
tr_dicts = {}
te_dicts = {}
keys = range(1, 7)
for degree in range(1, 7):
(w, train_err) = a1.linear_regression(x_train, t_train, 'polynomial',
0, degree, 'yes', 0, 0)
(t_est, test_err) = a1.evaluate_regression(x_test, t_test, w, degree,
'polynomial', 'yes', 0, 0)
tr_dicts[degree] = float(train_err)
te_dicts[degree] = float(test_err)
# Produce a plot of results.
plt.rcParams.update({'font.size': 15})
plt.plot(list(tr_dicts.keys()), list(tr_dicts.values()))
plt.plot(list(te_dicts.keys()), list(te_dicts.values()))
plt.ylabel('RMS')
plt.legend(['Training error', 'Testing error'])
plt.title('Fit with polynomials, no regularization')
plt.xlabel('Polynomial degree')
plt.show()
def CV(lamb):
offset, test_err = 10, 0
for i in range(0, 10):
boundA = i * offset + i
boundB = i * offset + i + offset
x_test = x[boundA:boundB]
t_test = targets[boundA:boundB]
x_train = np.concatenate((x[0:boundA - 1, :], x[boundB + 1:, :]))
t_train = np.concatenate((targets[0:boundA - 1], targets[boundB + 1:]))
(pred_train, w_train,
RMSE_train) = a1.linear_regression(x_train,
t_train,
basis='polynomial',
reg_lambda=lamb,
degree=2,
include_bias=True)
(pred_test, RMSE_test) = a1.evaluate_regression(
x_test,
t_test,
w_train,
basis='polynomial',
degree=2,
include_bias=True) # !!pass in w_train
test_err += RMSE_test # RMSE_test
return test_err / 10
def plot_multiple_error(title, bias):
#for features 8-15
for iterator in range(7, 15):
x = values[:, iterator]
x_train = x[0:N_TRAIN, :]
x_test = x[N_TRAIN:, :]
(w, train_err) = a1.linear_regression(x_train, t_train, 'polynomial',
0, 3, bias, 0, 0)
(t_est, test_err) = a1.evaluate_regression(x_test, t_test, w, 3,
'polynomial', bias, 0, 0)
#store the values in two dicts
tr_dicts[1 + iterator] = float(train_err)
te_dicts[1.35 + iterator] = float(test_err)
#print(tr_dicts)
#print(te_dicts)
# Produce a plot of results.
plt.rcParams.update({'font.size': 15})
plt.bar(list(tr_dicts.keys()), list(tr_dicts.values()), width=0.35)
plt.bar(list(te_dicts.keys()), list(te_dicts.values()), width=0.35)
plt.ylabel('RMS')
plt.legend(['Training error', 'Testing error'])
plt.title('Fit with degree=3 polynomial, no regularization,' + title)
plt.xlabel('Feature index')
plt.show()
def plot_bar_chart():
'''
Performing regression using just a single input feature
Trying features 8-15. For each (un-normalized) feature fitting a degree 3 polynomial (unregularized).
'''
for column in range(0, 8):
(w, train_error) = a1.linear_regression(x_training[:, column],
t_training, 'polynomial', 0, 3)
(_, test_error) = a1.evaluate_regression(x_testing[:, column],
t_testing, w, 'polynomial', 3)
training_error[column + 7] = train_error
testing_error[column + 7] = test_error
index = np.arange(7, 15) + 1
bar_size = 0.35
opacity = 0.8
mat_plot.bar(index,
a1.array(testing_error.values()),
bar_size,
alpha=opacity,
color=(0.3, 0.5, 0.7, 0.7))
mat_plot.bar(index + bar_size,
a1.array(training_error.values()),
bar_size,
alpha=opacity,
color=(0.9, 0.6, 0.1, 0.7))
mat_plot.ylabel('RMSE')
mat_plot.legend(['Test error', 'Training error'])
mat_plot.title('RMSE for single input feature, no regularization')
mat_plot.xlabel('Feature index')
mat_plot.show()
def PolynomialRegression(bias):
(countries, features, values) = a1.load_unicef_data()
targets = values[:, 1]
x = values[:, 7:]
x = a1.normalize_data(x)
N_TRAIN = 100
ALL = 195
x_train = x[0:N_TRAIN, :]
x_test = x[N_TRAIN:, :]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
train_error = {}
test_error = {}
for degrees in range(1, 7):
(w, t_err) = a1.linear_regression(x_train, t_train, 'polynomial', 0,
degrees, 0, 1, N_TRAIN, bias)
(t_est, te_err) = a1.evaluate_regression('polynomial', x_test, w,
t_test, degrees,
ALL - N_TRAIN, bias)
print('degree = ', degrees)
print(t_err)
train_error[degrees] = np.sqrt(np.sum(t_err) / 100)
print('sum=', np.sum(t_est, axis=0))
print('train_error = ', train_error[degrees])
test_error[degrees] = np.sqrt(np.sum(te_err) / 95)
for i in range(1, 7):
print(train_error[i])
# for i in range (1,7):
# print(test_error[i])
print(type(train_error))
plt.rcParams.update({'font.size': 15})
plt.plot([1, 2, 3, 4, 5, 6], [
train_error[1], train_error[2], train_error[3], train_error[4],
train_error[5], train_error[6]
])
plt.plot([1, 2, 3, 4, 5, 6], [
test_error[1], test_error[2], test_error[3], test_error[4],
test_error[5], test_error[6]
])
plt.ylabel('RMS')
plt.legend(['Training error', 'Testing error'])
plt.title('Fit with polynomials, no regularization, bias:' + bias)
plt.xlabel('Polynomial degree')
plt.show()
def PolynomialRegression(bias,featureNum):
(countries, features, values) = a1.load_unicef_data()
targets = values[:,1]
x = values[:,7:]
# x = a1.normalize_data(x)
N_TRAIN = 100
ALL = 195
x_train = x[0:N_TRAIN,:]
x_test = x[N_TRAIN:,:]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
train_error = {}
test_error = {}
x_trainFeature = x_train[:,featureNum]
x_testFeature = x_test[:,featureNum]
(w, t_err) = a1.linear_regression(x_trainFeature, t_train, 'polynomial', 0, 3,0 ,1 ,N_TRAIN,bias)
(t_est, te_err) = a1.evaluate_regression('polynomial',x_testFeature, w, t_test, 3, ALL-N_TRAIN, bias)
train_error = np.sqrt(np.sum(t_err)/100)
test_error = np.sqrt(np.sum(te_err)/95)
fig, (ax1, ax2) = plt.subplots(2)
fig.suptitle('Visulization of feature '+ str(featureNum+8) )
NumOfPoints = 500
x_ev1 = np.linspace(np.asscalar(min(x_trainFeature)), np.asscalar(max(x_trainFeature)), num=NumOfPoints)
x_ev1 = np.array(x_ev1).reshape(NumOfPoints,1)
phi1 = a1.design_matrix('polynomial', bias, x_ev1, NumOfPoints, 3, 0, 0 )
y1 = phi1.dot(w)
x_ev2 = np.linspace(np.asscalar(min(min(x_trainFeature),min(x_testFeature))), np.asscalar(max(max(x_trainFeature) ,max(x_testFeature) )), num=NumOfPoints)
x_ev2 = np.array(x_ev2).reshape(NumOfPoints,1)
phi2 = a1.design_matrix('polynomial', bias, x_ev2, NumOfPoints, 3, 0, 0 )
y2 = phi2.dot(w)
ax1.plot(x_ev1,y1,'r.-')
ax1.plot(x_trainFeature,t_train,'bo', color='b')
ax1.plot(x_testFeature,t_test,'bo',color='g')
ax2.plot(x_ev2,y2,'r.-')
ax2.plot(x_trainFeature,t_train,'bo', color='b')
ax2.plot(x_testFeature,t_test,'bo',color='g')
plt.show()
def PolynomialRegression(bias):
(countries, features, values) = a1.load_unicef_data()
targets = values[:,1]
x = values[:,7:]
# x = a1.normalize_data(x)
N_TRAIN = 100
ALL = 195
x_train = x[0:N_TRAIN,:]
x_test = x[N_TRAIN:,:]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
train_error = {}
test_error = {}
print(x_train)
for featureNum in range(0,8):
print('__________',featureNum,'___________________')
print(x_train[:,featureNum])
for featureNum in range(0,8):
x_trainFeature = x_train[:,featureNum]
x_testFeature = x_test[:,featureNum]
(w, t_err) = a1.linear_regression(x_trainFeature, t_train, 'polynomial', 0, 3,0 ,1 ,N_TRAIN,bias)
(t_est, te_err) = a1.evaluate_regression('polynomial',x_testFeature, w, t_test, 3, ALL-N_TRAIN, bias)
print('featureNum = ',featureNum)
print(t_err)
train_error[featureNum] = np.sqrt(np.sum(t_err)/100)
print('sum=', np.sum(t_est,axis=0))
print('train_error = ', train_error[featureNum])
test_error[featureNum] = np.sqrt(np.sum(te_err)/95)
print('train_error = ', test_error[featureNum])
print('____________________________')
x=[8,9,10,11,12,13,14,15]
x1=[8.35,9.35,10.35,11.35,12.35,13.35,14.35,15.35]
y_train = [train_error[0],train_error[1],train_error[2],train_error[3],train_error[4],train_error[5],train_error[6],train_error[7]]
y_test = [test_error[0],test_error[1],test_error[2],test_error[3],test_error[4],test_error[5],test_error[6],test_error[7]]
width = 0.35
fig, ax = plt.subplots()
ax.bar(x,y_train,width)
ax.bar(x1,y_test,0.35)
plt.ylabel('RMS')
plt.legend(['Training error','Testing error'])
plt.title('Fit with polynomials, no regularization, bias:'+bias)
plt.xlabel('Polynomial degree')
plt.show()
#x = a1.normalize_data(x)
N_TRAIN = 100
x_train = x[0:N_TRAIN,:]
x_test = x[N_TRAIN:,:]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
train_err = dict()
test_err = dict()
train_bigfai=a1.design_matrix('sigmoid',x_train,0,0)
(w,train_error)=a1.linear_regression(x,t_train,train_bigfai,-1,0,100,2000)
test_bigfai=a1.design_matrix('sigmoid',x_test,0,0)
test_error=a1.evaluate_regression(test_bigfai,w,t_test)
print(train_error)
print(test_error)
#create a plot
x_ev = np.linspace(np.asscalar(min(x_train)), np.asscalar(max(x_train)), num=500)
x_ev = np.transpose(np.asmatrix(x_ev))
bigfai=a1.design_matrix('sigmoid',x_ev,0,0)
y_ev = np.transpose(w)*np.transpose(bigfai)
N_TRAIN = 100
#Example of selecting a single feature for training
x_train = x[0:N_TRAIN, 3]
t_train = targets[0:N_TRAIN]
#Selecting a feature for both test inputs and test targets [example]
x_test = x[N_TRAIN:, 3]
t_test = targets[N_TRAIN:]
#print("x_train",x_train)
(weights, training_error) = a1.linear_regression(x_train, t_train, "ReLU", 0,
0)
tup = (weights, training_error)
(estimate, test_err) = a1.evaluate_regression(x_test, t_test, tup[0], "ReLU",
0)
tupl = (estimate, test_err)
print(tup[0])
print("training error: ", tup[1])
print("test error is: ", tupl[1])
min = np.amin(x_train)
max = np.amax(x_train)
x_ev = np.linspace(min, max, num=500)
x_ev_col = x_ev.reshape((500, 1))
#(y_ev,te_err)=a1.
(y_ev, te_err) = a1.evaluate_regression(x_ev_col, None, tup[0], "ReLU", 0)
x_train = values[0:N_TRAIN, col]
x_test = values[N_TRAIN:, col]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
(w, tr_err) = a1.linear_regression(x_train,
t_train,
'sigmoid',
bias=bias,
mu=mu,
s=s)
(t_est, te_err) = a1.evaluate_regression(x_test,
t_test,
w,
'sigmoid',
bias=bias,
mu=mu,
s=s)
# importlib.reload(a1)
## Produce a plot of results.
#plt.close('all')
#
## visualize_1d
df = {}
t2 = {}
xval = np.squeeze(x[:, col], axis=1).tolist()[0]
t = np.squeeze(targets, axis=1).tolist()[0]
(t_est, te_err) = a1.evaluate_regression(x[:, col],
for i in range(lenArg):
(w, tr_err) = a1.linear_regression(feature_list_input_train[i], t_train,
"polynomial", 0, 3)
tup = (w, tr_err)
werr.append(tup)
#print(feature_list[i].shape[0])
#print(feature_list[i].shape[1])
#for j in range(len(werr)):
#print(werr[j][0])
### List to store the following as elements (estimates, te_err)
lstZ = []
for i in range(lenArg):
(t_est, te_err) = a1.evaluate_regression(feature_list_target_test[i],
t_test, werr[i][0], "polynomial",
3)
tup2 = (t_est, te_err)
lstZ.append(tup2)
## Note: technically we do not need these list variables but we put them there for code readability
training_error_list = []
test_error_list = []
for i in range(lenArg):
#print("training error, test error: ",werr[i][1],lstZ[i][1])
training_error_list.append(werr[i][1])
test_error_list.append(lstZ[i][1])
### To do on above: refactor when have time
""" Code for barplot comment out to see barplot"""
lengthlst=len(lst)
for i in range(lengthlst):
print("---",lst[i][1])
lstZ=[]
print("length of list ",lengthlst)
for i in range(1,lengthlst+1):
#print("i",i)
#print("i-1",i-1)
#print("i-1",i-1)
#print(lst[i-1][0].shape[0])
(t_est,te_err)=a1.evaluate_regression(x_test,t_test,lst[i-1][0],"polynomial",i)
tup2=(t_est,te_err)
lstZ.append(tup2)
#for i in range(lengthlst):
#(t_est,te_err)=a1.evaluate_regression(x_test,t_test,lst[i][0],"polynomial",i+1)
#tup2=(t_est,te_err)
#lstZ.append(tup2)
#print(len(lstZ))
#for i in range(len(lstZ)):
#print(lstZ[i][1])
#(w,tr_err) = a1.linear_regression(x_train,t_train,"polynomial",0,1)
#tup=(w,tr_err)
#lst.append(tup)
targets = values[:, 1]
x = values[:, 7:]
#x = a1.normalize_data(x)
N_TRAIN = 100
# Select a single feature.
x_train = x[0:N_TRAIN, 5]
t_train = targets[0:N_TRAIN]
x_test = x[N_TRAIN:, 5]
t_test = targets[N_TRAIN:]
# Plot a curve showing learned function.
# Use linspace to get a set of samples on which to evaluate
x_ev = np.linspace(np.asscalar(min(x_train)),
np.asscalar(max(x_train)),
num=500)
shape = (len(x_ev), 1)
x_ev = x_ev.reshape(shape)
(w, tr_err, pred) = a1.linear_regression(x_train, t_train, 'polynomial', 0, 3)
(y_ev, te_err) = a1.evaluate_regression(x_ev, x_ev, w, 'polynomial', 3)
# TO DO:: Put your regression estimate here in place of x_ev.
# Evaluate regression on the linspace samples.
# y_ev, _ = a1.evaluate_regression()
plt.plot(x_train, t_train, 'bo')
plt.plot(x_test, t_test, 'go')
plt.plot(x_ev, y_ev, 'r.-')
plt.legend(['Training Data', 'Testing Data', 'Learned Polynomial'])
plt.title('13 Feature (Literacy) - regression estimate using random outputs')
plt.show()
N_TRAIN = 100
targets = values[:N_TRAIN, 1]
x = x[0:N_TRAIN, :]
lambda_list = [0, 0.01, 0.1, 1, 10, 100, 1000, 10000]
average_list = []
for i in [0, 0.01, 0.1, 1, 10, 100, 1000, 10000]:
sum = 0
for fold in range(1, 11):
x_vali = x[(fold - 1) * 10:fold * 10, :]
t_vali = targets[(fold - 1) * 10:fold * 10]
x_train = np.vstack((x[0:(fold - 1) * 10, :], x[10 * fold:, :]))
t_train = np.vstack((targets[0:(fold - 1) * 10], targets[10 * fold:]))
(w, train_err) = a1.linear_regression(x_train, t_train, 'polynomial',
i, 2, 'yes', 0, 0)
(t_est, test_err) = a1.evaluate_regression(x_vali, t_vali, w, 2,
'polynomial', 'yes', 0, 0)
#print(test_err)
sum = sum + float(test_err)
#print(sum)
average = float(sum / 10)
print(average)
average_list.append(average)
plt.rcParams.update({'font.size': 15})
plt.semilogx(lambda_list, average_list)
plt.ylabel('Average RMS')
plt.legend(['Average Validation error'])
plt.title('Fit with degree 2 polynomials')
plt.xlabel('log scale lambda')
plt.show()
x_train = x[0:N_TRAIN, :]
x_test = x[N_TRAIN:, :]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
# Complete the linear_regression and evaluate_regression functions of the assignment1.py
# Pass the required parameters to these functions
max_degree = 6
train_err = dict()
test_err = dict()
# fit a polynomial basis function for degree 1 to degree 6
for degree in range(1, max_degree+1):
(w, tr_err) = a1.linear_regression(x_train, t_train, 'polynomial', 0, degree=degree, bias=1)
# evaluate the RMS error for test data
(t_est, te_err) = a1.evaluate_regression(x_test, t_test, w, 'polynomial', degree)
train_err[degree] = tr_err
test_err[degree] = te_err
print(train_err)
print(test_err)
# Produce a plot of results.
plt.rcParams.update({'font.size': 15})
plt.plot(list(train_err.keys()), list(train_err.values()))
plt.plot(list(test_err.keys()), list(test_err.values()))
plt.ylabel('RMS')
plt.legend(['Training error', 'Testing error'])
plt.title('Fit with normalized polynomials, no regularization ')
plt.xlabel('Polynomial degree')
plt.show()
print(x_train)
i_basis = 'ReLU'
i_degree = 0
# TO DO:: Complete the linear_regression and evaluate_regression functions of the assignment1.py
train_err = []
test_err = []
(w, tr_err) = a1.linear_regression(x_train, t_train, i_basis, degree=i_degree)
train_err.append((1, tr_err))
(t_est, te_err) = a1.evaluate_regression(x_test,
t_test,
w,
i_basis,
degree=i_degree)
test_err.append((1, te_err))
train_err = np.array(train_err)
test_err = np.array(test_err)
print(train_err)
print(test_err)
# Produce a plot of results.
plt.plot(train_err[:, 0], train_err[:, 1], 'bo')
plt.plot(test_err[:, 0], test_err[:, 1], 'gx')
plt.ylabel('RMS')
plt.legend(['Training error', 'Test error'])
plt.title('Relu training and testing error')
plt.xlabel('features')
training_b_errors = []
test_b_errors = []
for feature in range(np.size(x, 1)):
# Pass the required parameters to these functions
(w, y, tr_error) = a1.linear_regression(x_train[:, feature],
t_train,
'polynomial',
0,
degree=POLYNOMIAL_DEGREE,
include_bias=False)
training_errors.append(tr_error)
(t_est, te_err) = a1.evaluate_regression(x_test[:, feature],
t_test,
w,
'polynomial',
degree=POLYNOMIAL_DEGREE,
include_bias=False)
test_errors.append(te_err)
(w_b, y_b, tr_b_error) = a1.linear_regression(x_train[:, feature],
t_train,
'polynomial',
0,
degree=POLYNOMIAL_DEGREE,
include_bias=True)
training_b_errors.append(tr_b_error)
(t_b_est, te_b_err) = a1.evaluate_regression(x_test[:, feature],
t_test,
w_b,
train_error = {}
test_error = {}
for i in range(1, 6 + 1):
#if i==3:continue
bias = True
(w, tr_err) = a1.linear_regression(x_train,
t_train,
basis='polynomial',
reg_lambda=0,
degree=i,
mu=0,
s=1,
bias_term=bias)
(test_preds, test_err) = a1.evaluate_regression(x_test,
t_test,
w,
degree=i,
bias_term=bias,
basis='polynomial')
train_error[i] = tr_err
test_error[i] = test_err
print(train_error, test_error)
# Produce a plot of results.
plt.rcParams.update({'font.size': 15})
plt.plot(list(train_error.keys()), list(train_error.values()))
plt.plot(list(test_error.keys()), list(test_error.values()))
plt.ylabel('RMSE')
plt.legend(['Training error', 'Testing error'])
title = 'Fit with polynomials of degree 1 to 6 and regularization= ' + str(
normalize)
plt.title(title)
xt=x[10:,:]
#print("xt",xt)
tv=t[0:10,:]
#print("tv",tv)
tt=t[10:,:]
#print("tt",tt)
print("lambda: ",l)
w,_=a1.linear_regression(xt,tt,"polynomial",l,2)
#print("w at i",i,w)
x=np.vstack((xt,xv))
#print("x",x)
#x=np.vstack((xv,xt))
## For debug feel free to comment out to see diagonistic information
#xv=x[0:10,:]
#tv=t[0:10:,:]
_,v_err=a1.evaluate_regression(xv,tv,w,"polynomial",2)
print("validation error",v_err)
t=np.vstack((tt,tv))
#print("t",t)
#t=np.vstack((tv,tt))
error_list.append(v_err)
#sig=sum(error_list)
#avg=sig/len(error_list)
#avg_list.append(avg)
print(v_err,"at",i)
#sig+=v_err
##print("Weight vector is: ")
##print(w)
#print("l",l,error_list)
#sig=0
#sig=sum(error_list)
t_validate=t_trainData[(10*(i-1)):i*10,:]
t_train=t_trainData[0:10*(i-1),:]
else:
x_validate=x_trainData[10*(i-1):i*10,:]
t_validate=t_trainData[10*(i-1):i*10,:]
x_train1=x_trainData[0:10*(i-1),:]
x_train2=x_trainData[(i*10):N_TRAIN,:]
x_train=np.append(x_train1,x_train2,axis=0)
t_train1=t_trainData[0:10*(i-1),:]
t_train2=t_trainData[(i*10):N_TRAIN,:]
t_train=np.append(t_train1,t_train2,axis=0)
w,t_err= a1.linear_regression(x_train,t_train,'polynomial',True,lambda_Val,2,None,None)
pred,val_err= a1.evaluate_regression(x_validate,t_validate,'polynomial',True,w,2,None,None)
#print("trainnnnnnnnnn",t_err)
#print("testtttttttttt",val_err)
val_err_List.append(val_err)
sum_of_val_err=sum(val_err_List)
avg_of_val_err=sum_of_val_err/10
if lambda_Val!=0:
avg.append(avg_of_val_err)
else:
avglamzero= avg_of_val_err
del lam[0]
print("Average",avg)
training = x[0:N_TRAIN, :]
reg_test = x[N_TRAIN:, :]
testing = targets[0:N_TRAIN]
test = targets[N_TRAIN:]
train_err = {}
test_err = {}
for val in range(1, 7):
w, tr_err = a1.linear_regression(training,
testing,
basis='polynomial',
degree=val)
train_err[val] = tr_err
test, test_error = a1.evaluate_regression(reg_test,
test,
w=w,
basis='polynomial',
degree=val)
test_err[val] = test_error
plt.plot(train_err.keys(), train_err.values())
plt.plot(test_err.keys(), test_err.values())
plt.ylabel('Root Mean Square')
plt.legend(['Test Error', 'Train Error'])
plt.title('Fit with polynomials, no Regularization')
plt.xlabel('Polynomial Degree')
plt.show()
x = a1.normalize_data(x)
training = x[0:N_TRAIN, :]
reg_test = x[N_TRAIN:, :]
N_TRAIN = 100
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
# TO DO:: Complete the linear_regression and evaluate_regression functions of the assignment1.py
train_err = []
test_err = []
feat=8
for i in range(0, 8):
x_train = x[0:N_TRAIN, i]
x_test = x[N_TRAIN:, i]
(w, tr_err) = a1.linear_regression(x_train, t_train, 'polynomial', degree=3)
train_err.append((feat, tr_err))
(t_est, te_err) = a1.evaluate_regression(x_test, t_test, w, 'polynomial', degree=3)
test_err.append((feat, te_err))
feat+=1
train_err = np.array(train_err)
test_err = np.array(test_err)
print(train_err)
print(test_err)
# Produce a plot of results.
plt.bar(train_err[:, 0], train_err[:, 1])
plt.bar(test_err[:, 0], test_err[:, 1])
plt.ylabel('RMS')
plt.legend(['Training error', 'Test error'])
plt.title('Fit with polynomials, no regularization')
plt.xlabel('features')
plt.show()
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
degree = 6
train_err = dict()
test_err = dict()
for i in range(1, degree + 1):
bigphi = a1.design_matrix('polynomial', x_train, i, 1)
(w, rms_train) = a1.linear_regression(x_train, t_train, bigphi, -1, i, 0,
0)
test_phi = a1.design_matrix('polynomial', x_test, i, 1)
rms_test = a1.evaluate_regression(test_phi, w, t_test)
train_err[i] = rms_train
test_err[i] = rms_test
# Complete the linear_regression and evaluate_regression functions of the assignment1.py
# Pass the required parameters to these functions
# (w, tr_err) = a1.linear_regression()
# (t_est, te_err) = a1.evaluate_regression()
# Produce a plot of results.
plt.rcParams.update({'font.size': 15})
plt.plot([float(k) for k in train_err.keys()],
[float(v) for v in train_err.values()])
plt.plot([float(k) for k in test_err.keys()],
[float(v) for v in test_err.values()])
axis=0)
x_validation = x_data[pos:pos + 10, :]
t_train = np.concatenate((t_data[:pos], t_data[pos + 10:]), axis=0)
t_validation = t_data[pos:pos + 10]
(w, tr_err) = a1.linear_regression(x_train,
t_train,
basis='polynomial',
reg_lambda=lambda_value,
degree=2,
mu=0,
s=1,
bias_term=True)
(test_preds, test_err) = a1.evaluate_regression(x_validation,
t_validation,
w,
degree=2,
bias_term=True,
basis='polynomial')
train_error_arr.append(tr_err)
valiation_error_arr.append(test_err)
train_error_dict[lambda_value] = np.mean(train_error_arr)
validation_error_dict[lambda_value] = np.mean(valiation_error_arr)
print('\n\n', validation_error_dict)
plt.rcParams.update({'font.size': 15})
del (validation_error_dict[0])
del (train_error_dict[0])
plt.semilogx(list(validation_error_dict.keys()),
list(validation_error_dict.values()))
plt.ylabel('validation set error')
plt.title('Average validation set error versus λ')
# TO DO:: Complete the linear_regression and evaluate_regression functions of the assignment1.py
train_err = []
test_err = []
for p in range(1, 7):
print(p)
(w, tr_err) = a1.linear_regression(x_train,
t_train,
i_basis,
reg_lambda=0,
degree=p)
train_err.append((p, tr_err))
print(tr_err)
(t_est, te_err) = a1.evaluate_regression(x_test,
t_test,
w,
i_basis,
degree=p)
print(te_err)
test_err.append((p, te_err))
train_err = np.array(train_err)
test_err = np.array(test_err)
# Produce a plot of results.
plt.plot(train_err[:, 0], train_err[:, 1])
plt.plot(test_err[:, 0], test_err[:, 1])
plt.ylabel('RMS')
plt.legend(['Training error', 'Test error'])
plt.title('Fit with polynomials, no regularization')
plt.xlabel('Polynomial degree')
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
N_TEST = x_test.shape[0]
target_value = values[:, 1]
#input_features = values[:,7:40]
feature_size = x_train.shape[1]
phi = []
#print x_train
degree = 0
# TO DO:: Complete the linear_regression and evaluate_regression functions of the assignment1.py
(w, training_err) = a1.linear_regression(x_train, t_train, 'ReLU', degree)
train_err = training_err
(t_est, testing_err) = a1.evaluate_regression(x_test, t_test, w, 'ReLU',
degree)
test_err = testing_err
print("training error is: " + str(training_err))
print("testing error is: " + str(testing_err))
x_ev = x_train[:, 0]
x_sample = np.linspace(np.asscalar(min(x_ev)), np.asscalar(max(x_ev)), num=500)
phi_sample = np.matrix([[1] + [max(0, (5000 - x_sample[i]))]
for i in range(len(x_sample))])
y_sample = phi_sample * w
#print w.shape
#print phi_sample.shape
#print y_sample.shape
plt.plot(x_sample, y_sample, 'r.-')
plt.plot(x_ev, t_train, 'bo')
plt.title(
N_TRAIN = 100
# Select a single feature.
feature_index = 11
x_train = x[0:N_TRAIN, feature_index - 8]
t_train = targets[0:N_TRAIN]
x_test = x[N_TRAIN:, feature_index - 8]
t_test = targets[N_TRAIN:]
(w, tr_err) = a1.linear_regression(x_train, t_train, 'polynomial', 0, 3)
# Plot a curve showing learned function.
# Use linspace to get a set of samples on which to evaluate
x_ev = np.linspace(np.asscalar(min(x_train)),
np.asscalar(max(x_train)),
num=500)
# TO DO:: Put your regression estimate here in place of x_ev.
# Evaluate regression on the linspace samples.
(y_ev, error) = a1.evaluate_regression(
np.matrix(x_ev).transpose(), np.zeros(500), w, 'polynomial', 3)
plt.plot(np.matrix(x_ev).transpose(), y_ev, 'g.-')
plt.plot(x_train, t_train, 'ro')
plt.plot(x_test, t_test, 'bo')
plt.legend(['learned polynomial', 'training data', 'test data'])
plt.xlabel('x')
plt.ylabel('t')
plt.title('fits for degree 3 polynomials for feature 11 (GNI)')
plt.show()
train_err = []
test_err = []
for i in range(7, 15):
targets = values[:, 1]
x = values[:, i]
N_TRAIN = 100
x_train = x[0:N_TRAIN, :]
x_test = x[N_TRAIN:, :]
t_train = targets[0:N_TRAIN]
t_test = targets[N_TRAIN:]
w, t_err = a1.linear_regression(x_train, t_train, 'polynomial', bias,
0, 3, 1)
pred, te_err = a1.evaluate_regression(x_test, t_test, 'polynomial',
bias, w, 3)
weight.append(w)
train_err.append(t_err)
test_err.append(te_err)
print("TrainError for bais =", bias, train_err)
print("TestError for bais =", bias, test_err)
# create plot
fig, ax = plt.subplots()
index = np.arange(8)
bar_width = 0.35
opacity = 0.8
rects1 = plt.bar(index,
train_err,
#lamda_val = [0]
avg_lambda_err = []
# Produce a plot of results.
for i in lamda_val:
er = []
for j in range(10, 101, 10):
x_val_set = x_train[j - 10:j, :]
val_1 = x_train[0:j - 10, :]
val_2 = x_train[j:100, :]
x_train_set = np.vstack((val_1, val_2))
t_val_set = t_train[j - 10:j, :]
val_1 = t_train[0:j - 10, :]
val_2 = t_train[j:100, :]
t_train_set = np.vstack((val_1, val_2))
(w, tr_err, pred) = a1.linear_regression(x_train_set, t_train_set,
'polynomial', i, 2)
(y_ev, te_err) = a1.evaluate_regression(x_val_set, t_val_set, w,
'polynomial', 2)
er.append(te_err)
avg_lambda_err.append(np.mean(er))
# TO DO:: Put your regression estimate here in place of x_ev.
# Evaluate regression on the linspace samples.
# y_ev, _ = a1.evaluate_regression()
plt.semilogx(lamda_val, avg_lambda_err)
plt.ylabel('Average Vaildation Set Error')
plt.title('Regularized Polynomial Regression 10 Fold')
plt.xlabel('Lambda on log scale')
plt.show()
