class TestLassoRegression(unittest.TestCase):
"""Tests for TestLassoRegression.
Uses housing data to test LassoRegression.
Statics:
_multiprocess_can_split_ (bool): Flag for nose tests to run tests in parallel.
"""
_multiprocess_can_split_ = True
def setUp(self):
"""Constructor for TestLassoRegression.
Loads housing data, and creates training and testing data.
"""
self.convert_numpy = ConvertNumpy()
self.normalize_features = NormalizeFeatures()
self.lasso = LassoRegression()
self.predict_output = PredictOutput()
self.residual_sum_squares = ResidualSumSquares()
self.k_fold_cross_validation = KFoldCrossValidation()
# Create a dictionary type to store relevant data types so that our pandas
# will read the correct information
dtype_dict = {'bathrooms': float, 'waterfront': int, 'sqft_above': int, 'sqft_living15': float,
'grade': int, 'yr_renovated': int, 'price': float, 'bedrooms': float, 'zipcode': str,
'long': float, 'sqft_lot15': float, 'sqft_living': float, 'floors': str, 'condition': int,
'lat': float, 'date': str, 'sqft_basement': int, 'yr_built': int, 'id': str, 'sqft_lot': int,
'view': int}
# Create a kc_house that encompasses all test and train data
self.kc_house = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_data.csv', dtype=dtype_dict)
# Create a kc_house_test_frame that encompasses only train data
self.kc_house_train = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_train_data.csv',
dtype=dtype_dict)
# Create a kc_house_frames that encompasses only test data
self.kc_house_test = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_test_data.csv',
dtype=dtype_dict)
# Convert all the frames with the floors to float type
self.kc_house['floors'] = self.kc_house['floors'].astype(float)
self.kc_house_train['floors'] = self.kc_house['floors'].astype(float)
self.kc_house_test['floors'] = self.kc_house['floors'].astype(float)
# Then back to int type
self.kc_house['floors'] = self.kc_house['floors'].astype(int)
self.kc_house_train['floors'] = self.kc_house['floors'].astype(int)
self.kc_house_test['floors'] = self.kc_house['floors'].astype(int)
def test_01_normalize_features(self):
"""Tests normalizing features.
Test normalization features, and compare it with known values.
"""
# Normalize the features, and also return the norms
features, norms = self.normalize_features.l2_norm(np.array([[3., 6., 9.], [4., 8., 12.]]))
# Assert that the np array is equal to features
self.assertTrue(np.array_equal(np.array([[0.6, 0.6, 0.6], [0.8, 0.8, 0.8]]), features), True)
# Assert that the np array is equal to norms
self.assertTrue(np.array_equal(np.array([5., 10., 15.]), norms), True)
def test_02_compute_ro(self):
"""Test compute ro
Test compute one round of ro.
"""
# We will use sqft_iving, and sqft_living15
features = ['sqft_living', 'bedrooms']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house, features, output, 1)
# Create our initial weights
normalized_feature_matrix, _ = self.normalize_features.l2_norm(feature_matrix)
# Set initial weights
weights = np.array([1., 4., 1.])
# Compute ro_j
ro_j = self.lasso.compute_ro_j(normalized_feature_matrix, output, weights)
# Assert the output of ro_j
self.assertTrue(np.allclose(ro_j, np.array([79400300.03492916, 87939470.77299108, 80966698.67596565])))
def test_03_compute_coordinate_descent_step(self):
"""Test one coordinate descent step.
Test one coordinate descent step and compare it with known values.
"""
# Assert that both are equal
self.assertEquals(round(self.lasso.lasso_coordinate_descent_step({"i": 1,
"weights": np.array([1., 4.])},
np.array([[3./math.sqrt(13),
1./math.sqrt(10)],
[2./math.sqrt(13),
3./math.sqrt(10)]]),
np.array([1., 1.]),
{"l1_penalty": 0.1}), 8),
round(0.425558846691, 8))
def test_04_coordinate_descent(self):
"""Test coordinate descent.
Test coordinate descent and compare with known values.
"""
# We will use sqft_iving, and sqft_living15
features = ['sqft_living', 'bedrooms']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house, features, output, 1)
# Create our initial weights
normalized_feature_matrix, _ = self.normalize_features.l2_norm(feature_matrix)
# Set initial weights
initial_weights = np.zeros(3)
# Set l1 penalty
l1_penalty = 1e7
# Set tolerance
tolerance = 1.0
# Compute the weights using coordinate descent
weights = self.lasso.lasso_cyclical_coordinate_descent(normalized_feature_matrix, output,
{"initial_weights": initial_weights,
"l1_penalty": l1_penalty,
"tolerance": tolerance})
# Assert that these two numpy arrays are the same
self.assertTrue(np.allclose(weights, np.array([21624998.3663629, 63157246.78545423, 0.]), True))
# Predict the output
predicted_output = self.predict_output.regression(normalized_feature_matrix, weights)
# Assert that the RSS is what we wanted
self.assertEquals(round(self.residual_sum_squares.residual_sum_squares_regression(output,
predicted_output), -10),
round(1.63049248148e+15, -10))
def test_05_coordinate_descent_with_normalization(self):
"""Test coordinate descent with normalization.
Test coordinate descent and then normalize the result, so that we can use the weights on a test set.
"""
# We will use multiple features
features = ['bedrooms',
'bathrooms',
'sqft_living',
'sqft_lot',
'floors',
'waterfront',
'view',
'condition',
'grade',
'sqft_above',
'sqft_basement',
'yr_built',
'yr_renovated']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
normalized_feature_matrix, norms = self.normalize_features.l2_norm(feature_matrix)
# Compute Multiple Weights
weights1e7 = self.lasso.lasso_cyclical_coordinate_descent(normalized_feature_matrix, output,
{"initial_weights": np.zeros(len(features)+1),
"l1_penalty": 1e7,
"tolerance": 1})
weights1e8 = self.lasso.lasso_cyclical_coordinate_descent(normalized_feature_matrix, output,
{"initial_weights": np.zeros(len(features)+1),
"l1_penalty": 1e8,
"tolerance": 1})
weights1e4 = self.lasso.lasso_cyclical_coordinate_descent(normalized_feature_matrix, output,
{"initial_weights": np.zeros(len(features)+1),
"l1_penalty": 1e4,
"tolerance": 5e5})
# Compute multiple normalized
normalized_weights1e4 = weights1e4 / norms
normalized_weights1e7 = weights1e7 / norms
normalized_weights1e8 = weights1e8 / norms
# We will use multiple features
features = ['bedrooms',
'bathrooms',
'sqft_living',
'sqft_lot',
'floors',
'waterfront',
'view',
'condition',
'grade',
'sqft_above',
'sqft_basement',
'yr_built',
'yr_renovated']
# Output will use price
output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, features, output, 1)
# Predict the output
predicted_output = self.predict_output.regression(test_feature_matrix, normalized_weights1e4)
# Assert that the RSS is what we wanted
self.assertEquals(round(self.residual_sum_squares.residual_sum_squares_regression(test_output,
predicted_output), -12),
round(2.2778100476e+14, -12))
# Predict the output
predicted_output = self.predict_output.regression(test_feature_matrix, normalized_weights1e7)
# Assert that the RSS is what we wanted
self.assertEquals(round(self.residual_sum_squares.residual_sum_squares_regression(test_output,
predicted_output), -12),
round(2.75962079909e+14, -12))
# Predict the output
predicted_output = self.predict_output.regression(test_feature_matrix, normalized_weights1e8)
# Assert that the RSS is what we wanted
self.assertEquals(round(self.residual_sum_squares.residual_sum_squares_regression(test_output,
predicted_output), -12),
round(5.37049248148e+14, -12))
class LassoRegression:
"""Class to compute Lasso Regression.
Lasso Regression is essentially L1 Norm with Linear Regression. We cannot use gradient descent since the
absolute value for L1 Norm is not differentiable. Hence we use coordinate descent.
Attributes:
predict_output (PredictOutput): A PredictOutput class that can predict output given features and weights.
"""
def __init__(self):
"""Constructor for LassoRegression to setup PredictOutput.
Constructor for the LassoRegression class, mainly used to setup PredictOutput.
"""
self.predict_output = PredictOutput()
def lasso_cyclical_coordinate_descent(self, feature_matrix, output, model_parameters):
"""Coordinate descent algorithm for Lasso regression.
Performs a Lasso Cyclical Coordinate Descent, which will loop over each features and then perform
coordinate descent, and if all of the weight changes are less than the tolerance, then we will
stop.
Lasso Regression is based on: w_j = ro_j + delta/2 if ro_j < -delta/2
0 if ro_j between [-delta/2,delta/2]
ro_j - delta/2 if ro_j > delta/2
Where,
ro_j = Sigma(N, i=1, h_j(x_i)(y_i-y^_i(w_-j).
h_j(x_i): Normalized features of x_i (input features, but without j feature).
y_i: Real output.
y^_i(w_-j): Predicted output without feature j.
Args:
feature_matrix (numpy.ndarray): Feature matrix.
output (numpy.array): Real output for the feature matrix.
model_parameters (dict): A dictionary of model parameters,
{
initial_weights (numpy.array): The starting initial weights,
step_size (float): Step size,
tolerance (float or None): Tolerance (or epsilon),
l1_penalty (float): L1 penalty value,
max_iteration (int): Maximum iteration to compute.
}
Returns:
numpy.array: final weights after coordinate descent has been completed
"""
# Flag to indicate that the change is too low
low_change = False
# Set Weights to initial_weights
weights = model_parameters["initial_weights"]
# While the change is not too low (meaning lower than tolerance)
while not low_change:
# An array of boolean to detect if all the changes are less than tolerance
change = []
# Need to incorporate all the new changes to the weights
for i in range(len(weights)):
# Remember the old weights
old_weights_i = weights[i]
# Compute the current weight
weights[i] = self.lasso_coordinate_descent_step({"i": i, "weights": weights}, feature_matrix, output,
model_parameters)
# Returns true if any weight changes greater than tolerance
change.append(abs(old_weights_i-weights[i]) > model_parameters["tolerance"])
# Returns true if all the changes are less than tolerance
low_change = not any(change)
return weights
def lasso_coordinate_descent_step(self, step_parameters, feature_matrix, output, model_parameters):
"""Computes the Lasso coordinate descent step.
Computes the Lasso coordinate descent step, which is essentially computing a new ro_i, and based on the
index and ro_i, compute new w_i weight.
Args:
step_parameters (dict): A dictionary for step data,
{
i (int): Feature i,
weights (numpy.array): Current weights.
}
feature_matrix (numpy.ndarray): Feature matrix.
output (numpy.array): Real output for feature_matrix.
model_parameters (dict): A dictionary of model parameters,
{
step_size (float): Step size,
tolerance (float or None): Tolerance (or epsilon),
l1_penalty (float): L1 penalty value,
max_iteration (int): Maximum iteration to compute.
}
Returns:
new_weight_i (float): New weight for the feature i.
"""
# compute ro[i] = SUM[ [feature_i]*(output - prediction + weight[i]*[feature_i]) ]
ro_i = self.compute_ro_j(feature_matrix, output, step_parameters["weights"])[step_parameters["i"]]
# when i == 0, then it's a intercept -- do not regularize
# else
# w_i = ro_i + delta/2 if ro_i < -delta/2
# 0 if ro_i between [-delta/2,delta/2]
# ro_i - delta/2 if ro_i > delta/2
if step_parameters["i"] == 0:
new_weight_i = ro_i
elif ro_i < -model_parameters["l1_penalty"]/2.:
new_weight_i = ro_i + model_parameters["l1_penalty"]/2
elif ro_i > model_parameters["l1_penalty"]/2.:
new_weight_i = ro_i - model_parameters["l1_penalty"]/2
else:
new_weight_i = 0.
# Return the new weight for feature i
return new_weight_i
def compute_ro_j(self, feature_matrix, real_output, weights):
"""Computes ro_j.
Computes ro_j using ro_j = Sigma(N, i=1, h_j(x_i)(y_i-y^_i(w_-j).
Args:
feature_matrix (numpy.ndarray): Feature matrix.
real_output (numpy.array): Real output (not predicted) for feature_matrix.
weights (numpy.array): The current weights.
Returns:
ro (numpy.array): ro (or new weights for each feature).
"""
# Number of features (columns)
feature_num = feature_matrix.shape[1]
# Set ro to be an array that is feature_num size
ro = np.zeros(feature_num)
# Loop through feature
for j in range(feature_num):
# prediction = y_i(w_-j), prediction without feature j
prediction = self.predict_output.regression(np.delete(feature_matrix, j, axis=1),
np.delete(weights, j))
# residual = output - prediction
residual = real_output-prediction
# ro[j] = Sigma(N, i=1, feature_i) * residual
ro[j] = np.sum([feature_matrix[:, j]*residual])
return ro
class KFoldCrossValidation:
"""Class for K Fold Cross Validation.
Class for K Fold Cross Validation for selecting best parameters.
Attributes:
convert_numpy (ConvertNumpy): Pandas to Numpy conversion class.
predict_output (PredictOutput): Output prediction.
residual_sum_squares (ResidualSumSquares): Computes residual sum of squares.
"""
def __init__(self):
"""Constructor for KFoldCrossValidation.
Constructor for KFoldCrossValidation, used to setup numpy conversion, output prediction, and residual sum
of squares.
"""
self.convert_numpy = ConvertNumpy()
self.predict_output = PredictOutput()
self.residual_sum_squares = ResidualSumSquares()
def k_fold_cross_validation(self, k, model, model_parameters, data_parameters):
"""Performs K Fold Cross Validation.
Takes in our data, and splits the data to smaller subsets, and these smaller subsets are used as validation
sets, and everything else not included in the validation set is used as training sets. The model will be
trained using the training set, and the performance assessment such as RSS would be used on the validation
set against the model.
Args:
k (int): Number of folds.=
model (obj): Model used for k folds cross validation.
model_parameters (dict): Model parameters to train the specified model.
data_parameters (dict): A dictionary of data information:
{
data (pandas.DataFrame): Data used for k folds cross validation,
output (str): Output name,
features (list of str): A list of feature names.
}
Returns:
float: Average validation error.
"""
# Sum of the validation error, will divide by k (fold) later
validation_error_sum = 0
# Loop through each fold
for i in range(k):
# Computes validation, and training set
validation_set, training_set = self.create_validation_training_set(data_parameters["data"], k, i)
# Convert our pandas frame to numpy to create validation set
validation_set_matrix, validation_output = self.convert_numpy.convert_to_numpy(validation_set,
data_parameters["features"],
data_parameters["output"], 1)
# Create a model with Train Set 1 + Train Set 2
final_weights = self.create_weights(model, model_parameters, training_set, data_parameters)
# Predict the output of test features
predicted_output = self.predict_output.regression(validation_set_matrix,
final_weights)
# compute squared error (in other words, rss)
validation_error_sum += self.residual_sum_squares.residual_sum_squares_regression(validation_output,
predicted_output)
# Return the validation_error_sum divided by fold
return validation_error_sum/k
@staticmethod
def create_validation_training_set(data, k, iteration):
"""Slice data according to k, iteration, and size of data.
Computes the validation, and training set according to the k number of folds, and the current iteration.
Args:
data (pandas.DataFrame): Data used for k folds cross validation.
k (int): Number of folds.
iteration (int): Current K fold validation iteration.
Returns:
A tuple that contains training set, and validation set:
(
validation_set (pandas.DataFrame): Validation set.
training_set (pandas.DataFrame): Training set.
)
"""
length_data = len(data)
# Compute the start section of the current fold
start = int((length_data * iteration) / k)
# Compute the end section of the current fold
end = int((length_data * (iteration + 1)) / k - 1)
# Get our validation set from the start to the end+1 (+1 since we need to include the end)
# <Start : end + 1> Validation Set
validation_set = data[start:end + 1]
# The Training set the left and the right parts of the validation set
# < 0 : Start > Train Set 1
# < Start : End + 1 > Validation Set
# < End + 1 : n > Train Set 2
# Train Set 1 + Train Set 2 = All data excluding validation set
training_set = data[0:start].append(data[end + 1:length_data])
return validation_set, training_set
def create_weights(self, model, model_parameters, training_set, data_parameters):
"""Use model to create weights.
Use model, model parameters, and training set, create a set of coefficients.
Args:
model (obj): Model that can be run.
model_parameters (dict): A dictionary of model parameters.
training_set (pandas.DataFrame): Train set used for k folds cross validation.
data_parameters (dict): A dictionary of data information:
{
data (pandas.DataFrame): Data used for k folds cross validation,
output (str): Output name,
features (list of str): A list of feature names.
}
Returns:
numpy.array: numpy array of weights created by running model.
"""
# Convert our pandas frame to numpy to create training set
training_feature_matrix, training_output = self.convert_numpy.convert_to_numpy(training_set,
data_parameters["features"],
data_parameters["output"], 1)
# Create a model with Train Set 1 + Train Set 2
return model(model_parameters=model_parameters, feature_matrix=training_feature_matrix, output=training_output)
class TestRidgeRegression(unittest.TestCase):
"""Test for RidgeRegression.
Uses housing data to test RidgeRegression.
Statics:
_multiprocess_can_split_ (bool): Flag for nose tests to run tests in parallel.
"""
_multiprocess_can_split_ = True
def setUp(self):
"""Constructor for TestRidgeRegression.
Loads housing data, and creates training and testing data.
"""
self.convert_numpy = ConvertNumpy()
self.ridge_regression = RidgeRegression()
self.predict_output = PredictOutput()
self.residual_sum_squares = ResidualSumSquares()
self.k_fold_cross_validation = KFoldCrossValidation()
# Create a dictionary type to store relevant data types so that our pandas
# will read the correct information
dtype_dict = {'bathrooms': float, 'waterfront': int, 'sqft_above': int, 'sqft_living15': float,
'grade': int, 'yr_renovated': int, 'price': float, 'bedrooms': float, 'zipcode': str,
'long': float, 'sqft_lot15': float, 'sqft_living': float, 'floors': str, 'condition': int,
'lat': float, 'date': str, 'sqft_basement': int, 'yr_built': int, 'id': str, 'sqft_lot': int,
'view': int}
# Create a kc_house that encompasses all test and train data
self.kc_house = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_data.csv',
dtype=dtype_dict)
# Create a kc_house_test_frame that encompasses only train data
self.kc_house_train = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_train_data.csv',
dtype=dtype_dict)
# Create a kc_house_frames that encompasses only test data
self.kc_house_test = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_test_data.csv',
dtype=dtype_dict)
# Create a kc_house_train_valid_shuffled that encompasses both train and valid data and shuffled
self.kc_house_train_valid_shuffled = pd.read_csv('./unit_tests/test_data/regression/'
'kc_house_with_validation_k_fold/'
'wk3_kc_house_train_valid_shuffled.csv',
dtype=dtype_dict)
def test_01_gradient_descent_no_penalty(self):
"""Tests gradient descent algorithm.
Tests the result on gradient descent with low penalty.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 1000
# Tolerance
tolerance = None
# L2 Penalty
l2_penalty = 0.0
# Compute our gradient descent value
final_weights = self.ridge_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# We will use sqft_iving, and sqft_living15
test_features = ['sqft_living']
# Output will be price
test_output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, test_features,
test_output, 1)
# Predict the output of test features
predicted_output = self.predict_output.regression(test_feature_matrix, final_weights)
# Compute RSS
rss = self.residual_sum_squares.residual_sum_squares_regression(test_output, predicted_output)
# Assert that the weights is correct
self.assertEquals(round(-0.16311351478746433, 5), round(final_weights[0], 5))
self.assertEquals(round(263.02436896538489, 3), round(final_weights[1], 3))
# Assert that rss is correct
self.assertEquals(round(275723632153607.72, -5), round(rss, -5))
def test_02_gradient_descent_high_penalty(self):
"""Tests gradient descent.
Tests the result on gradient descent with high penalty.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 1000
# Tolerance
tolerance = None
# L2 Penalty
l2_penalty = 1e11
# Compute our gradient descent value
final_weights = self.ridge_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# We will use sqft_iving
test_features = ['sqft_living']
# Output will be price
test_output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, test_features,
test_output, 1)
# Predict the output of test features
predicted_output = self.predict_output.regression(test_feature_matrix, final_weights)
# Compute RSS
rss = self.residual_sum_squares.residual_sum_squares_regression(test_output, predicted_output)
# Assert that the weights is correct
self.assertEquals(round(9.7673000000000005, 5), round(final_weights[0], 5))
self.assertEquals(round(124.572, 3), round(final_weights[1], 3))
# Assert that rss is correct
self.assertEquals(round(694642101500000.0, -5), round(rss, -5))
def test_03_gradient_descent_multiple_high_penalty(self):
"""Tests gradient descent.
Tests gradient descent with multiple features, and high penalty.
"""
# We will use sqft_iving, and sqft_living15
features = ['sqft_living', 'sqft_living15']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0.0, 0.0, 0.0])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 1000
# Tolerance
tolerance = None
# L2 Penalty
l2_penalty = 1e11
# Compute our gradient descent value
final_weights = self.ridge_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# We will use sqft_iving, and sqft_living15
test_features = ['sqft_living', 'sqft_living15']
# Output will be price
test_output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, test_features,
test_output, 1)
# Predict the output of test features
predicted_output = self.predict_output.regression(test_feature_matrix, final_weights)
# Compute RSS
rss = self.residual_sum_squares.residual_sum_squares_regression(test_output, predicted_output)
# Assert that the weights is correct
self.assertEquals(round(6.7429699999999997, 5), round(final_weights[0], 5))
self.assertEquals(round(91.489000000000004, 3), round(final_weights[1], 3))
self.assertEquals(round(78.437490333967176, 3), round(final_weights[2], 3))
# Assert that rss is correct
self.assertEquals(round(500404800500842.0, -5), round(rss, -5))
# Look at the first predicted output
self.assertEquals(round(270453.53000000003, 3), round(predicted_output[0], 3))
# The first output should be 310000 in the test set
self.assertEquals(310000.0, test_output[0])
def test_04_gradient_descent_k_fold(self):
"""Tests gradient descent with K fold cross validation.
Tests best l2_penalty for ridge regression using gradient descent.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will use price
output = ['price']
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Tolerance
tolerance = None
# Max Iterations to Run
max_iterations = 1000
# Number of Folds
folds = 10
# Store Cross Validation results
cross_validation_results = []
# We want to test l2 penalty values in [10^1, 10^2, 10^3, 10^4, ..., 10^11]
for l2_penalty in np.logspace(1, 11, num=11):
# Create a dictionary of model_parameters
model_parameters = {'step_size': step_size,
'max_iteration': max_iterations,
'initial_weights': initial_weights,
'tolerance': tolerance,
'l2_penalty': l2_penalty}
# Compute the cross validation results
cv = self.k_fold_cross_validation.k_fold_cross_validation(folds, self.ridge_regression.gradient_descent,
model_parameters, {"data": self.kc_house_train,
"output": output,
"features": features})
# Append it into the results
cross_validation_results.append((l2_penalty, cv))
# Lowest Result
lowest = sorted(cross_validation_results, key=lambda x: x[1])[0]
# Assert True that 10000000 is the l2_penalty that gives the lowest cross validation error
self.assertEquals(10000000.0, lowest[0])
# Assert True that is the lowest l2_penalty
self.assertEquals(round(120916225809145.0, 0), round(lowest[1], 0))
def test_05_gradient_ascent(self):
"""Tests gradient ascent.
Tests gradient ascent and compare it with known values.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will be price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 1000
# Tolerance
tolerance = None
# L2 Penalty
l2_penalty = 0.0
# Compute our hill climbing value
final_weights = self.ridge_regression.gradient_ascent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# Assert that the weights is correct
self.assertEquals(round(-7.7535764461428101e+70, -68), round(final_weights[0], -68))
self.assertEquals(round(-1.9293745396177612e+74, -70), round(final_weights[1], -70))
def test_07_gradient_ascent_high_tolerance(self):
"""Tests gradient ascent.
Tests gradient ascent and compare it with known values.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will be price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 1000
# Tolerance
tolerance = 1
# L2 Penalty
l2_penalty = 0.0
# Compute our hill climbing value
final_weights = self.ridge_regression.gradient_ascent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# Assert that the weights is correct
self.assertEquals(0, round(final_weights[0], -68))
self.assertEquals(0, round(final_weights[1], -70))
def test_08_gradient_descent_no_penalty_high_tolerance(self):
"""Tests gradient descent algorithm.
Tests the result on gradient descent with low penalty.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([0., 0.])
# Step size
step_size = 1e-12
# Max Iterations to Run
max_iterations = 100000
# Tolerance
tolerance = 10000000000
# L2 Penalty
l2_penalty = 0.0
# Compute our gradient descent value
final_weights = self.ridge_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance,
"l2_penalty": l2_penalty,
"max_iteration": max_iterations})
# We will use sqft_iving, and sqft_living15
test_features = ['sqft_living']
# Output will be price
test_output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, test_features,
test_output, 1)
# Predict the output of test features
predicted_output = self.predict_output.regression(test_feature_matrix, final_weights)
# Compute RSS
rss = self.residual_sum_squares.residual_sum_squares_regression(test_output, predicted_output)
# Assert that the weights is correct
self.assertEquals(round(0.093859999999999999, 5), round(final_weights[0], 5))
self.assertEquals(round(262.98200000000003, 3), round(final_weights[1], 3))
# Assert that rss is correct
self.assertEquals(round(275724298300000.0, -5), round(rss, -5))
class TestLinearRegression(unittest.TestCase):
"""Test for LinearRegression.
Uses housing data to test LinearRegression.
Statics:
_multiprocess_can_split_ (bool): Flag for nose tests to run tests in parallel.
"""
_multiprocess_can_split_ = True
def setUp(self):
"""Constructor for TestLinearRegression.
Loads housing data, and creates training and testing data.
"""
self.convert_numpy = ConvertNumpy()
self.linear_regression = LinearRegression()
self.predict_output = PredictOutput()
self.residual_sum_squares = ResidualSumSquares()
# Create a dictionary type to store relevant data types so that our pandas
# will read the correct information
dtype_dict = {'bathrooms': float, 'waterfront': int, 'sqft_above': int, 'sqft_living15': float,
'grade': int, 'yr_renovated': int, 'price': float, 'bedrooms': float, 'zipcode': str,
'long': float, 'sqft_lot15': float, 'sqft_living': float, 'floors': str, 'condition': int,
'lat': float, 'date': str, 'sqft_basement': int, 'yr_built': int, 'id': str, 'sqft_lot': int,
'view': int}
# Create a kc_house that encompasses all test and train data
self.kc_house = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_data.csv', dtype=dtype_dict)
# Create a kc_house_test_frame that encompasses only train data
self.kc_house_train = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_train_data.csv',
dtype=dtype_dict)
# Create a kc_house_frames that encompasses only test data
self.kc_house_test = pd.read_csv('./unit_tests/test_data/regression/kc_house/kc_house_test_data.csv',
dtype=dtype_dict)
def test_01_gradient_descent(self):
"""Test gradient descent.
Tests gradient descent and compare it to known values.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will use price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([-47000., 1.])
# Step size
step_size = 7e-12
# Tolerance
tolerance = 2.5e7
# Compute our gradient descent value
final_weights = self.linear_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance})
# Assert that the weights is correct
self.assertEquals(round(-46999.887165546708, 3), round(final_weights[0], 3))
self.assertEquals(round(281.91211917520917, 3), round(final_weights[1], 3))
def test_02_gradient_descent_multiple(self):
"""Tests gradient descent on multiple features.
Computes gradient descent on multiple input, and computes predicted model and RSS.
"""
# We will use sqft_iving, and sqft_living15
features = ['sqft_living', 'sqft_living15']
# Output will be price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([-100000., 1., 1.])
# Step size
step_size = 4e-12
# Tolerance
tolerance = 1e9
# Compute our gradient descent value
final_weights = self.linear_regression.gradient_descent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance})
# We will use sqft_iving, and sqft_living15
test_features = ['sqft_living', 'sqft_living15']
# Output will be price
test_output = ['price']
# Convert our test pandas frame to numpy
test_feature_matrix, test_output = self.convert_numpy.convert_to_numpy(self.kc_house_test, test_features,
test_output, 1)
# Predict the output of test features
predicted_output = self.predict_output.regression(test_feature_matrix, final_weights)
# Compute RSS
rss = self.residual_sum_squares.residual_sum_squares_regression(test_output, predicted_output)
# Assert that rss is correct
self.assertEquals(round(270263443629803.41, -3), round(rss, -3))
def test_03_gradient_ascent(self):
"""Test gradient ascent.
Test gradient ascent and compare it to known values.
"""
# We will use sqft_living for our features
features = ['sqft_living']
# Output will be price
output = ['price']
# Convert our pandas frame to numpy
feature_matrix, output = self.convert_numpy.convert_to_numpy(self.kc_house_train, features, output, 1)
# Create our initial weights
initial_weights = np.array([-47000., 1.])
# Step size
step_size = 7e-12
# Tolerance
tolerance = 2.5e7
# Compute our hill climbing value
final_weights = self.linear_regression.gradient_ascent(feature_matrix, output,
{"initial_weights": initial_weights,
"step_size": step_size,
"tolerance": tolerance})
# Assert that the weights is correct
self.assertEquals(round(-47000.142201335177, 3), round(final_weights[0], 3))
self.assertEquals(round(-352.86068692252599, 3), round(final_weights[1], 3))
