def select_polynomial_degree(train_data, val_data):
model_by_degree = {}
rss_all = {}
list_of_degrees = range(1,16)
for degree in list_of_degrees:
data_n_train = reg.polynomial_sframe(train_data['sqft_living'],degree)
features_names = data_n_train.column_names()
data_n_train['price'] = train_data['price']
model_n = gp.create_linear_regression(data_n_train,target='price',features=features_names)
data_n_val = reg.polynomial_sframe(val_data['sqft_living'],degree)
data_n_val['price'] = val_data['price']
rss_n = reg.get_model_residual_sum_of_squares(model_n,data_n_val,data_n_val['price'])
rss_all[degree] = rss_n
# print 'RSS(%s): %s' % (degree,rss_n)
model_by_degree[degree] = model_n
return gp.find_key_min(rss_all), model_by_degree
def create_regression_model_by_degree(sales, list_of_degrees, sales_col='sqft_living', target='price'):
poly_n_data= {}
for degree in list_of_degrees:
polyn_data = reg.polynomial_sframe(sales[sales_col], degree)
features_names = polyn_data.column_names()
# print features_names
polyn_data[target] = sales[target]
model_n = gp.create_linear_regression(polyn_data, target=target, features = features_names)
# model_n.get("coefficients").print_rows(16)
power_n = 'power_%s'%degree
poly_n_data[power_n] = {'model':model_n, 'coefficients':model_n.get("coefficients"),'data': polyn_data}
# plt.plot(polyn_data[power_n],polyn_data['price'],'.',polyn_data[power_n], model_n.predict(polyn_data),'-')
# plt.show()
return poly_n_data
def quiz_1_selecting_l2_penalty(sales): print "\n**********************************" print "* k-Fold validation *" print "**********************************\n" (train_valid,test) = sales.random_split(.9,seed=1) all_l2_rss_avg = selecting_l2_via_cross_validation(train_valid) best_l2_penalty = min(all_l2_rss_avg,key=all_l2_rss_avg.get) print "\nQ6: Best L2 penalty via 10-fold validation L2 (%.2f): %s" % (best_l2_penalty,all_l2_rss_avg[best_l2_penalty]) degree = 15 model_train_valid,poly_sframe_train_valid = reg.polynomial_ridge_regression(train_valid,degree,target='price',l2_penalty=float(best_l2_penalty)) poly_sframe_test = reg.polynomial_sframe(test['sqft_living'],degree) poly_sframe_test['price'] = test['price'] rss_n = reg.get_model_residual_sum_of_squares(model_train_valid,poly_sframe_test,poly_sframe_test['price']) print "\nQ7: Predictions for degree=%s TEST error (RSS)=%s" % (degree,rss_n) print "\t- Between 8e13 and 4e14"
def selecting_l2_via_cross_validation(train_valid):
train_valid_shuffled = gp.graphlab.toolkits.cross_validation.shuffle(train_valid,random_seed=1)
k,target,l2_penalties = 10,'price',np_utils.np.logspace(1,7,num=13)
poly_sframe = reg.polynomial_sframe(train_valid_shuffled['sqft_living'],degree=15)
features_list = poly_sframe.column_names()
poly_sframe[target] = train_valid_shuffled[target]
l2_rss_avg = compute_k_fold_cross_validation(k,poly_sframe,target,features_list,l2_penalties)
plt.figure(figsize=(10,8))
reg.plot_k_cross_vs_penalty(l2_penalties, l2_rss_avg)
plt.savefig('../graphs/k_fold_vd_penalty_l2.png')
plt.close()
all_l2_rss_avg = dict(zip(l2_penalties,l2_rss_avg))
return all_l2_rss_avg
def main():
try:
print "\n**********************************"
print "* Polynomial Regression Model *"
print "**********************************\n"
sales = gp.load_data('../../data_sets/kc_house_data.gl/')
train,test = sales.random_split(0.5,seed=0)
set_1,set_2 = train.random_split(0.5,seed=0)
set_3,set_4 = test.random_split(0.5,seed=0)
list_of_degrees = [15] #[1,3,5,15]
list_of_sets = [set_1,set_2,set_3,set_4]
polynomial_regressions = get_polynomial_regression_by_sets(list_of_degrees, list_of_sets)
print "\nQ1: power_15 for all four models:"
pw_degree = 'power_15'
for idx,sets in enumerate(list_of_sets):
idx_set = 'set_%s' % (idx + 1)
poly_n_coeff = polynomial_regressions[idx_set][pw_degree]['coefficients']
coeff_dict = gp.convert_sframe_to_simple_dict(poly_n_coeff,'name','value')
print "\t- %s: %s"%(idx_set, coeff_dict[pw_degree])
print "\nQ2: fitted lines all look the same plots: FALSE"
training, test_data = sales.random_split(0.9,seed=1)
train_data, val_data = training.random_split(0.5,seed=1)
best_degree, model_by_degree = select_polynomial_degree(train_data,val_data)
print "\nQ3: the lowest RSS on Validation data is degree:%s" % best_degree
data_n_test = reg.polynomial_sframe(test_data['sqft_living'],best_degree)
data_n_test['price'] = test_data['price']
rss_n = reg.get_model_residual_sum_of_squares(model_by_degree[best_degree],data_n_test,data_n_test['price'])
print "\nQ4: RSS on TEST with the degree:%s from Validation data is:%s" % (best_degree,rss_n)
except Exception as details:
print "Error >> %s" % details
traceback.print_exc()