def gradient_descent_model(train_data, test_data): print "\n**********************************" print "* Gradient Descent Model *" print "**********************************\n" gradient = GrandientDescent() # Model 1: #==================================================== simple_features, my_output = ['sqft_living'], 'price' initial_weights = np_utils.np.array([-47000.,1.]) step_size, tolerance = 7e-12, 2.5e7 parameters = [initial_weights,step_size,tolerance] # TRAINING data simple_weights = calculate_weights(gradient, train_data, simple_features, my_output, parameters) # TEST data model1_predictions = get_predictions(test_data, simple_features, my_output, simple_weights) model1_pred_house1 = round(model1_predictions[0],1) print "Quiz_2 (week_2):" print "\nQ1: weight for sqft_living (model 1) is: %s" % round(simple_weights[-1],1) print "\nQ2: predicted price 1st house in TEST data (model 1) is: %s" % model1_pred_house1 # Model 2: #==================================================== model_features, my_output_m2 = ['sqft_living', 'sqft_living15'],'price' initial_weights_m2 = np_utils.np.array([-100000., 1., 1.]) step_size_m2,tolerance_m2 = 4e-12, 1e9 parameters_m2 = [initial_weights_m2,step_size_m2,tolerance_m2] # TRAINING data estimated_weights = calculate_weights(gradient, train_data, model_features, my_output_m2, parameters_m2) # TEST data model2_predictions = get_predictions(test_data, model_features, my_output_m2, estimated_weights) model2_pred_house1 = round(model2_predictions[0],1) print "\nQ3: predicted price 1st house in TEST data (model 2) is: %s" % model2_pred_house1 true_price_house1 = test_data['price'][0] print "\nQ4: True price for the 1st house on the TEST data is: %s" % true_price_house1 print "\t->diff model1: %s" % abs(model1_pred_house1-true_price_house1) print "\t->diff model2: %s" % abs(model2_pred_house1-true_price_house1) RSS1 = reg.compute_RSS(model1_predictions,test_data['price']) RSS2 = reg.compute_RSS(model2_predictions,test_data['price']) print "\nQ5: Which model (1 or 2) has lowest RSS on all of the TEST data" print "\t->RSS model1: %s" % RSS1 print "\t->RSS model2: %s" % RSS2
def find_rss_on_validation_test(training, validation, all_features,
l1_penalties, max_nonzeros):
RSS_best, L1_best, best_model = None, None, None
for l1_penalty in l1_penalties:
current_model = gp.graphlab.linear_regression.create(
training,
target='price',
features=all_features,
validation_set=None,
verbose=False,
l2_penalty=0.,
l1_penalty=l1_penalty)
current_num_nnz = current_model.coefficients['value'].nnz()
# print "\t\tNon-Zeros: %s" % current_num_nnz
if current_num_nnz == max_nonzeros:
predictions = current_model.predict(validation)
RSS = reg.compute_RSS(predictions, validation['price'])
print "L1 penalty (%.2f)\t\tRSS=%s" % (l1_penalty, RSS)
if RSS_best is None or RSS < RSS_best:
RSS_best = RSS
L1_best = l1_penalty
best_model = current_model
lasso_info = {
'RSS_best': RSS_best,
'L1_best': L1_best,
'Best model': best_model
}
return lasso_info
def more_features_with_lasso_coordinate(lasso, sales):
train_data, test_data = sales.random_split(.8, seed=0)
all_features = [
'bedrooms', 'bathrooms', 'sqft_living', 'sqft_lot', 'floors',
'waterfront', 'view', 'condition', 'grade', 'sqft_above',
'sqft_basement', 'yr_built', 'yr_renovated'
]
feature_matrix_norm, train_output, train_norms = np_utils.get_normalized_data(
train_data, all_features, 'price')
initial_weights = np_utils.np.zeros(len(all_features) + 1)
weights_info, nnz_features = {}, {}
penalty_tolerance = [[1e7, 1.0], [1e8, 1.0], [1e4, 5e5]]
penalty_str = {1e7: '1e7', 1e8: '1e8', 1e4: '1e4'}
print "\nFeatures assigned for Q5,Q6,Q7:"
for penalty, tolerance in penalty_tolerance:
weights = lasso.lasso_cyclical_coordinate_descent(
feature_matrix_norm, train_output, initial_weights, penalty,
tolerance)
# print weights
weights_normalized = weights / train_norms
weights_info[penalty] = weights_normalized
dict_weights = dict(
zip(['constant'] + all_features, weights_normalized))
nnz_features[penalty] = filter(lambda x: dict_weights[x] > 0,
dict_weights)
print "\n\tL1_penalty_%s: %s" % (penalty_str[penalty],
nnz_features[penalty])
print "\nQ8: three models RSS on the TEST data:"
test_feature_matrix, test_output = np_utils.get_numpy_data(
test_data, all_features, 'price')
for penalty, tolerance in penalty_tolerance:
current_predictions = np_utils.predict_output(test_feature_matrix,
weights_info[penalty])
RSS = reg.compute_RSS(current_predictions, test_output)
print "\n\tL1_penalty_%s: %s" % (penalty_str[penalty], RSS)
def evaluate_lasso_coordinate(lasso, sales):
simple_features = ['sqft_living', 'bedrooms']
my_output = 'price'
initial_weights = np_utils.np.zeros(3)
l1_penalty = 1e7
tolerance = 1.0
feature_matrix_norm, output, norms = np_utils.get_normalized_data(
sales, simple_features, my_output)
weights = lasso.lasso_cyclical_coordinate_descent(feature_matrix_norm,
output, initial_weights,
l1_penalty, tolerance)
# print weights
current_predictions = np_utils.predict_output(feature_matrix_norm, weights)
RSS = reg.compute_RSS(current_predictions, output)
print "\nQ3: Lasso-coordinate with normalized dataset RSS is: %s" % RSS
print "\nQ4: Features assigned a zero weight at convergence: %s" % simple_features[
-1]
print "\t->%s" % weights
def compute_ridge_rss(weights_list, feature_matrix, test_data): for weights_vals in weights_list: current_predictions = np_utils.predict_output(feature_matrix,weights_vals) RSS1 = reg.compute_RSS(current_predictions,test_data['price']) # print 'RSS1: %s' % (RSS1) print "\n\tTEST error (RSS) is: %s" % (RSS1)