def generate_prediction(x_tr_0, y_tr_0, x_tr_1, y_tr_1, x_tr_2, y_tr_2, x_tr_3,
y_tr_3, x_te_0, x_te_1, x_te_2, x_te_3, jet_num_te):
"""Generate a prediction for a test dataset already split according to jet_num
by calculating weights using a training dataset also already split."""
#compute the weights using predetermined polynomial degrees
w_0, _ = least_squares(y_tr_0, build_poly(x_tr_0, 9))
w_1, _ = least_squares(y_tr_1, build_poly(x_tr_1, 15))
w_2, _ = least_squares(y_tr_2, build_poly(x_tr_2, 13))
w_3, _ = least_squares(y_tr_3, build_poly(x_tr_3, 12))
#compute the prediction using the weights
y_te_0 = predict_labels(w_0, build_poly(x_te_0, 9))
y_te_1 = predict_labels(w_1, build_poly(x_te_1, 15))
y_te_2 = predict_labels(w_2, build_poly(x_te_2, 13))
y_te_3 = predict_labels(w_3, build_poly(x_te_3, 12))
#join the four predictions into a single one matching the original indices
predicted_y_te = []
i_0, i_1, i_2, i_3 = 0, 0, 0, 0
for jet_num in jet_num_te:
if jet_num == 0:
predicted_y_te.append(y_te_0[i_0])
i_0 += 1
elif jet_num == 1:
predicted_y_te.append(y_te_1[i_1])
i_1 += 1
elif jet_num == 2:
predicted_y_te.append(y_te_2[i_2])
i_2 += 1
else:
predicted_y_te.append(y_te_3[i_3])
i_3 += 1
return predicted_y_te
def __init__(self, model_name, w=None, learning_param=None, debug=True):
# Set weights
self.w = w
# Set debug object
if debug:
self.dbg = debugger.Debugger(['loss', 'w'])
else:
self.dbg = None
"""Depending on the chosen model, we choose the approriate output,
loss prediction, and learning functions.
"""
if model_name == 'logistic_regression':
self.model_output = misc.lr_output
self.compute_loss = cost.compute_loss_ce
self.predict_output = misc.map_prediction
max_iters = learning_param['max_iters']
gamma = learning_param['gamma']
self.learn = lambda y, x, w, dbg: impl.logistic_regression(y, x, w, max_iters, gamma, dbg)
if model_name == 'reg_logistic_regression':
self.model_output = misc.lr_output
self.compute_loss = cost.compute_loss_reg_ce
self.predict_output = misc.map_prediction
max_iters = learning_param['max_iters']
gamma = learning_param['gamma']
lambda_ = learning_param['lambda_']
self.learn = lambda y, x, w, dbg: impl.reg_logistic_regression(y, x, lambda_, w, max_iters, gamma, dbg)
if model_name == 'least_squares_GD':
self.model_output = np.dot
self.compute_loss = cost.compute_loss_ls
self.predict_output = misc.predict_ls
max_iters = learning_param['max_iters']
gamma = learning_param['gamma']
self.learn = lambda y, x, w, dbg: impl.least_squares_GD(y, x, w, max_iters, gamma, dbg)
if model_name == 'ridge_regression':
self.model_output = np.dot
self.compute_loss = cost.compute_loss_ls
self.predict_output = misc.predict_ls
lambda_ = learning_param['lambda_']
self.learn = lambda y, x, w, dbg: impl.ridge_regression(y, x, lambda_)
if model_name == 'least_squares':
self.model_output = np.dot
self.compute_loss = cost.compute_loss_ls
self.predict_output = misc.predict_ls
self.learn = lambda y, x, w, dbg: impl.least_squares(y, x)
def impute_lr(data):
#find columns that have no -999
clear_cols = [i for i in range(data.shape[1]) if -999 not in data[:,i]]
#find rows that have no -999
clear_rows = [i for i in range(data.shape[0]) if -999 not in data[i,:]]
#pdb.set_trace()
dirty_cols = [i for i in range(data.shape[1]) if i not in clear_cols]
dirty_rows = [i for i in range(data.shape[0]) if i not in clear_rows]
clear_samples = np.copy(data[clear_rows, :])
#clear_samples, mean_x, std_x = hp.standardize(clear_samples)
w_lr = list()
mse= list()
#pdb.set_trace()
for feature in dirty_cols:
wf = imp.least_squares(clear_samples[:, feature], clear_samples[:, clear_cols])
w_lr.append(wf[0])
#pdb.set_trace()
#mse.append(compute_loss(clear_samples[:, feature], clear_samples[:, clear_cols] ,wf[0]))
for sample in dirty_rows:
if data[sample,feature] == -999:
replacement = np.dot(data[sample, clear_cols].transpose(), wf[0])
data[sample, feature] = replacement
return data
def cross_validation(y, x, k_indices,k, degree,index_to_be_skewed):
"""return the loss of ridge regression."""
x_train = x[np.array([p for i in range(k_indices.shape[0]) if i != k for p in k_indices[i]])]
y_train= y[np.array([p for i in range(k_indices.shape[0]) if i != k for p in k_indices[i]])]
x_test=x[k_indices[k]]
y_test=y[k_indices[k]]
min_tr=np.min(x_train,axis=0)
max_tr=np.max(x_train,axis=0)
#Transformations to train
x_train=min_max_transform(x_train,min_tr,max_tr)
x_train[:,index_to_be_skewed]= np.log(x_train[:,index_to_be_skewed]+1)
x_train_poly,mean_train,std_train= expand_and_normalize_X(x_train,degree)
#Transformations to test, using same min, max, mean and std as in the train partition
x_test= min_max_transform(x_test,min_tr,max_tr)
x_test[:,index_to_be_skewed]= x_test[:,index_to_be_skewed]
x_test[:,index_to_be_skewed]= np.log(x_test[:,index_to_be_skewed]+1)
x_test_poly=build_poly(x_test,degree)
x_test_poly[:,1:]=(x_test_poly[:,1:]-mean_train)/std_train
w,loss=m.least_squares(y_train, x_train_poly)
loss_tr= -accuracy(y_train, predict_labels(w,x_train_poly))
loss_te= -accuracy(y_test, predict_labels(w,x_test_poly))
return loss_tr, loss_te,min_tr,max_tr
def cross_validation(y, x, degree, k, k_indices,method, error, feature_augmentation, hyperparams):
""""""
from helpers_data import feature_processing, feat_augmentation, standardize, build_poly
from implementations import ridge_regression, least_squares, least_squares_GD, least_squares_SGD, logistic_regression, reg_logistic_regression
# get k'th subgroup in test, others in train
te_indice = k_indices[k]
tr_indice = k_indices[~(np.arange(k_indices.shape[0]) == k)]
tr_indice = tr_indice.reshape(-1)
y_te = y[te_indice]
y_tr = y[tr_indice]
x_te = x[te_indice]
x_tr = x[tr_indice]
x_tr, y_tr, median = feature_processing (x_tr, y_tr, 'mean', replace_feature = True, suppr_outliers = hyperparams[-1], threshold = 3, ref_median=[])
x_te, y_te, _= feature_processing (x_te, y_te, 'mean', replace_feature = True, suppr_outliers = False, threshold = 3, ref_median=median)
tx_tr_aug = []
tx_te_aug = []
if feature_augmentation:
tx_tr_aug, index = feat_augmentation(x_tr, 0.003)
tx_te_aug, _ = feat_augmentation(x_te, 0.003, False, index)
# form data with polynomial degree
tx_tr = build_poly(x_tr, degree, feature_augmentation, tx_tr_aug)
tx_te = build_poly(x_te, degree, feature_augmentation, tx_te_aug)
tx_tr, mean, std = standardize(tx_tr)
tx_te, _, _ = standardize(tx_te, mean, std)
#print('Mean and std of each feature in train set: {} , {}'.format(tx_tr.mean(axis = 0),tx_tr.std(axis = 0)))
#print('Mean and std of each feature in test set: {} , {}'.format(tx_te.mean(axis = 0),tx_te.std(axis = 0)))
if method == 'rr': w,_ = ridge_regression(y_tr, tx_tr, hyperparams[0]) # ridge regression
elif method == 'ls': w,_ = least_squares(y_tr, tx_tr) # least square
elif method == 'lsGD': w,_ = least_squares_GD(y_tr, tx_tr, hyperparams[0], hyperparams[1], hyperparams[2]) # gradient descent
elif method == 'lsSGD': w,_ = least_squares_SGD(y_tr, tx_tr, hyperparams[0], hyperparams[1], hyperparams[2], hyperparams[3]) # stoch GD
elif method == 'log': w,_ = logistic_regression(y_tr, tx_tr, hyperparams[0], hyperparams[1], hyperparams[2]) # logistic reg
elif method == 'rlog': w,_ =reg_logistic_regression(y_tr, tx_tr, hyperparams[3], np.zeros(tx_tr.shape[1]), hyperparams[1], hyperparams[2]) # regularised logistic reg
else: raise NotImplementedError
if method == 'log':
loss_tr = cal_loglike(y_tr, tx_tr, w)
loss_te = cal_loglike(y_te, tx_te, w)
elif method == 'rlog':
loss_tr = cal_loglike_r(y_tr, tx_tr, w, hyperparams[3])
loss_te = cal_loglike_r(y_te, tx_te, w, hyperparams[3])
else :
# calculate the loss for train and test data
loss_tr = compute_loss(y_tr, tx_tr, w, error)
loss_te = compute_loss(y_te, tx_te, w, error)
y_pred = predict_labels(np.array(w).T, tx_te)
acc = accuracy(y_te,y_pred)
return loss_tr, loss_te, w, acc
def cross_validation(y,
tx,
mlfunction,
split_number=5,
lambda_=1e-6,
gamma=0.001):
'''Performs a ml_function given as parameters using cross validation on the training set split_number folds (5 as default value) '''
# define empty lists to store train/test losses and accuracy
train_loss_ = []
test_loss_ = []
train_accuracy_ = []
test_accuracy_ = []
# get k_indices
k_indices = build_k_indices(len(y), split_number)
for ki in range(len(k_indices)):
# set the k'th indices as test, and others as training set
#train_idx = np.asarray([k_indices[i] for i in np.delete( np.arange(len(k_indices)), ki)]).flatten()
test_idx = np.asarray(k_indices[ki])
train_idx = np.delete(np.arange(len(y)), test_idx)
train_tX = tx[train_idx]
train_y = y[train_idx]
test_tX = tx[test_idx]
test_y = y[test_idx]
if (mlfunction == 'ridge_regression'):
w, loss = impl.ridge_regression(train_y, train_tX, lambda_)
elif (mlfunction == 'least_squares'):
w, loss = impl.least_squares(train_y, train_tX)
elif (mlfunction == 'logistic_regression'):
w, loss = impl.logistic_regression(train_y, train_tX)
elif (mlfunction == 'reg_logistic_regression'):
w, loss = impl.reg_logistic_regression(train_y, train_tX, lambda_)
elif (mlfunction == 'least_squares_sgd'):
w, loss = impl.least_squares_SGD(train_y, train_tX, gamma)
elif (mlfunction == 'least_squares_gd'):
w, loss = impl.least_squares_GD(train_y, train_tX, gamma)
else:
print('ERROR: ml_function not recognized')
print(
'least_squares, least_squares_gd, least_squares_sgd, logistic_regression, reg_logistic_regression'
)
return None
# Calculate different losses and accuracy
train_loss_.append(impl.compute_loss_mse(train_y, train_tX, w))
test_loss_.append(impl.compute_loss_mse(test_y, test_tX, w))
train_accuracy_ = impl.compute_accuracy(train_y, train_tX, w)
test_accuracy_ = impl.compute_accuracy(test_y, test_tX, w)
return np.mean(train_loss_), np.mean(test_loss_), np.mean(
train_accuracy_), np.mean(test_accuracy_)
def get_model(model, y, tx, initial_w, max_iters, gamma, lambda_, batch_size):
""" Returns the learned weights 'w' (last weight vector) and
the corresponding loss function by a given model.
Parameters
----------
model: string
The model
y: ndarray
The labels
tx: ndarray
The feature matrix
initial_w: ndarray
The initial weights
max_iters: integer
The number of steps to run
gamma: integer
The step size
lambda_: integer
The regularization parameter
batch_size: integer
The batch size
Returns
-------
tuple
The learned weights
"""
if model == "MSE_GD":
w, _ = least_squares_GD(y, tx, initial_w, max_iters, gamma)
elif model == "MSE_SGD":
w, _ = least_squares_SGD(y, tx, initial_w, batch_size, max_iters, gamma)
elif model == "MSE_OPT":
w, _ = least_squares(y, tx)
elif model == "MSE_OPT_REG":
w, _ = ridge_regression(y, tx, lambda_)
elif model == "LOG_GD":
w, _ = logistic_regression(y, tx, initial_w, max_iters, gamma)
elif model == "LOG_REG_GD":
w, _ = reg_logistic_regression(y, tx, lambda_, initial_w, max_iters, gamma)
elif model == "LOG_REG_L1":
w, _ = reg_logistic_regression_L1(y, tx, lambda_, initial_w, max_iters, gamma)
elif model == "MSE_GD_L1":
w, _ = least_squares_GD_L1(y, tx, lambda_, initial_w, max_iters, gamma)
else:
raise UnknownModel
return w
def cross_validation_ls(y, x, k_indices, k):
"""train and test least square model using cross validation"""
x_test = x[k_indices[k]]
x_train = np.delete(x, [k_indices[k]], axis=0)
y_test = y[k_indices[k]]
y_train = np.delete(y, [k_indices[k]], axis=0)
opt_w, mse_tr = imp.least_squares(y_train,x_train)
mse_te = imp.compute_mse(y_test, x_test, opt_w)
return mse_te, opt_w
def test_least_squares(y_train, tx_train, y_test, tx_test):
"""
Tests least_squares method on the splitted data set and
reports percentage of correct predictions.
Args:
y_train: training labels after the splitting
tx_train: training features after the splitting
y_test: test labels after the splitting
tx_test: test features after the splitting
"""
print('\nTesting least_squares...')
w, _ = least_squares(y_train, tx_train)
report_prediction_accuracy(y_test, tx_test, w)
print('... testing completed.')
def find_optimal_w(tX, y, implementation, log_initial_w, log_max_iters,
log_gamma, decreasing_gamma, log_regulator, ridge_lambda):
"""
Find the optimal weights by training the data set
Parameters
----------
tX: array
The feature matrices
y: array
The output
log_initial_w: array
inital weights in order to perform GD or SGD
log_max_iters: integer
number of iterations to perform GD or SGD
log_gamma: float
gamma parameter to perform GD or SGD
log_regulator: float
lambda to perform logistic regression
ridge_lambda: float
lambda to perform ridge regression
Return
------
optimal_w = array
Optimal weights.
"""
optimal_w = None
if implementation == 0:
optimal_w, _ = impl.least_squares(y, tX)
if implementation == 1:
optimal_w, _ = impl.ridge_regression(y, tX, ridge_lambda)
if implementation == 2:
optimal_w, _ = impl.reg_logistic_regression(y, tX, log_regulator,
log_initial_w,
log_max_iters, log_gamma,
decreasing_gamma)
return optimal_w
def fill_missing_values(X_, deg=1, tresh=1, lambda_=1e-7):
# Create a dictionary to store the index of the feature with -999 value as key, and the corresponding indices as value
X = X_.copy()
unknown_dict = find_bad_features(X)
# Get bad/good features indices
bad_features = list(unknown_dict.keys())
# select feature to fill depending on the treshold
features_to_fill = [
i for i in bad_features if ((len(unknown_dict[i]) / len(X)) < tresh)
]
features_to_ignore = bad_features.copy()
for i in features_to_fill:
features_to_ignore.remove(i)
clean_features = np.delete(np.arange(len(X.T)), bad_features)
clean_X = X.T[clean_features]
# Ignoring very bad features (>tresh)
# fill missing values using least squares
for i in features_to_fill:
clean_idx = list(np.delete(np.arange(len(X)), unknown_dict[i]))
tx = clean_X.T[clean_idx]
ys = X.T[i][clean_idx]
bad_idx_by_feature = unknown_dict[i]
w, _ = impl.least_squares(ys, tx)
y_bad = np.dot(clean_X.T[bad_idx_by_feature], w)
# Predict missing values
for idx in bad_idx_by_feature:
X[idx][i] = y_bad[i]
feat_to_conserve = np.delete(np.arange(len(X.T)), features_to_ignore)
return X.T[feat_to_conserve].T
# Cross validation over lambda avg_test_accuracy_RR = cross_validation_RR(X_train, y_train, k_fold=4, seed=1) # Cross validation over gamma avg_test_accuracy_LR = cross_validation_LR(X_train, y_train, k_fold=4, seed=1) # Cross validation over both gamma and lambda g, l, avg_test_accuracy_RLR = cross_validation_RLR(X_train, y_train, k_fold=4, seed=1) #%% Testing functions #np.random.seed(42) gamma = 0.2 lambda_ = 4E-5 w, loss = least_squares(y = y_train, tx = X_train) # w, loss = least_squares_SGD(y = y_train, tx = X_train, initial_w = np.random.random(size=num_features)*0.01, max_iters = 200000, gamma = gamma) # w, loss = ridge_regression(y = y_train, tx = X_train, lambda_ = lambda_) # w, loss = logistic_regression(y = y_train, tx = X_train, initial_w = np.random.random(size=num_features)*10, max_iters = 125000, gamma = gamma) # w, loss = reg_logistic_regression(y = y_train, tx = X_train, lambda_ = lambda_, initial_w = np.random.random(size=num_features)*0.01, max_iters = 200000, gamma = gamma) plt.plot(w) #%% Predictive step y_test = X_test @ w plt.hist(y_test, bins=200)
def cross_validation(x,
y,
k,
mode,
gamma=None,
lambda_=None,
max_iters=None,
initial_w=None):
"""
INPUT:
@x : input data, dimensions (NxD)
@y : target labels, (Nx1) array
@k : number of folds
OUTPUT:
"""
D = x.shape[1]
#randomly permute data maybe?
x_split = np.array_split(x, k, axis=0)
y_split = np.array_split(y, k, axis=0)
#initialize weights and metrics
weights = list()
acc = list()
tpr = list()
fpr = list()
losses = list()
#loop over folds
for fold in range(k):
#create model
#train_ind = [i for i in range(k) if i!=fold]
#val_ind = [i for i in range(k) if i==fold]
#pdb.set_trace()
x_train = [x_split[i] for i in range(k) if i != fold]
y_train = [y_split[i] for i in range(k) if i != fold]
x_train = np.concatenate(x_train, axis=0)
y_train = np.concatenate(y_train, axis=0)
x_val = x_split[fold]
y_val = y_split[fold]
#model = Proj1_Model(x_train, y_train, mode)
#train model for fold
#weights[k] = model.train()
"""here the choice of method"""
if mode == 'linear_regression_eq':
update, loss = imp.least_squares(y_train, x_train)
predictions = np.dot(x_val, update)
pr_bool = predictions >= np.mean(predictions)
elif mode == 'ridge_regression_eq':
update, loss = imp.ridge_regression(y_train, x_train, lambda_)
predictions = np.dot(x_val, update)
pr_bool = predictions >= np.mean(predictions)
elif mode == 'linear_regression_GD':
update, loss = imp.least_squares_GD(y_train, x_train, initial_w,
max_iters, gamma)
predictions = np.dot(x_val, update)
pr_bool = predictions >= np.mean(predictions)
elif mode == 'linear_regression_SGD':
update, loss = imp.least_squares_SGD(y_train, x_train, initial_w,
max_iters, gamma)
predictions = np.dot(x_val, update)
pr_bool = predictions >= np.mean(predictions)
elif mode == 'logistic_regression':
update, loss = imp.logistic_regression(y_train, x_train, initial_w,
max_iters, gamma)
predictions = np.dot(x_val, update)
predicted_prob = H.sigmoid(predictions)
#pdb.set_trace()
pr_bool = predicted_prob > 0.5
elif mode == 'reg_logistic_regression':
update, loss = imp.reg_logistic_regression(y_train, x_train,
initial_w, max_iters,
gamma)
predictions = np.dot(x_val, update)
predicted_prob = H.sigmoid(predictions)
#pdb.set_trace()
pr_bool = predicted_prob > 0.5
weights.append(update)
losses.append(loss)
pr_bool = predictions >= np.mean(predictions)
y_bool = y_val == 1
correct = pr_bool == y_bool
tp = np.logical_and(correct, y_bool)
fp = np.logical_and(np.logical_not(correct), pr_bool)
#tp = [i for i in range(len(pr_bool)) if (pr_bool[i] == True and y_bool[i] == True)]
#all_p = [i for i in range(len(pr_bool)) if y_bool == True]
#fp = [i for i in range(len(pr_bool)) if (pr_bool == True and y_bool == False)]
#all_n = [i for i in range(len(pr_bool)) if y_bool == False]
#print('True signal samples:' + str(sum(y_val)) + ' - Predicted signal samples:' + str(sum(pr_bool)))
acc.append(sum(correct) / float(len(y_val)))
tpr.append(sum(tp) / float(sum(y_bool)))
fpr.append(sum(fp) / float(sum(np.logical_not(y_bool))))
#acc[k] = model.acc()
#tpr[k] = model.tpr()
#fpr[k] = model.fpr()
return acc, tpr, fpr, losses
from sklearn.metrics import r2_score
# Linear regression
print("Linear Regession \n ---------------- \n")
X, y = datasets.load_boston(return_X_y = True)
X, _, _ = implementations.standardize_numpy(X)
tx = np.c_[np.ones(X.shape[0]), X]
initial_w = np.zeros(tx.shape[1])
max_iters = 1000
gamma = 0.01
w_lr, loss_lr = implementations.least_squares(y, tx)
y_pred_lr = tx @ w_lr
print(f"Linear regression eq: {r2_score(y_pred_lr, y)}")
w_lr_gd, loss_lr_gd = implementations.least_squares_GD(y, tx, initial_w,
max_iters, gamma, verbose=False)
y_pred_lr_gd = tx @ w_lr_gd
print(f"Linear regression gd: {r2_score(y_pred_lr_gd, y)}")
w_lr_sgd, loss_lr_sgd = implementations.least_squares_SGD(y, tx, initial_w,
max_iters, gamma, verbose=False)
y_pred_lr_sgd = tx @ w_lr_sgd
print(f"Linear regression sgd: {r2_score(y_pred_lr_sgd, y)}")
reg = LinearRegression().fit(X, y)
y_pred_sk = reg.predict(X)
"""
Load the datasets, train a model, and create a Kaggle submission for the first
Machine Learning project
Authors: Kirill IVANOV, Matthias RAMIREZ, Nicolas TALABOT
"""
### Import modules and datasets
from proj1_helpers import load_csv_data, predict_labels, create_csv_submission
from implementations import least_squares
from utilities import split_data, preprocess_data
y_train, x_train, ids_train = load_csv_data("train.csv")
y_test, x_test, ids_test = load_csv_data("test.csv")
# Parameters
seed = 3
degree = 11
ratio = 0.66
# Learn the model
tx, x_mean, x_std = preprocess_data(x_train, degree)
x_tr, y_tr, x_te, y_te = split_data(tx, y_train, ratio, seed)
w, loss_tr = least_squares(y_tr, x_tr)
# Create a Kaggle submission
x_kaggle,_,_ = preprocess_data(x_test, degree, compute_mean_std=False, \
x_mean=x_mean, x_std=x_std)
y_pred = predict_labels(w, x_kaggle)
create_csv_submission(ids_test, y_pred, "run_submission.csv")
def cross_validation(y, tX, gamma, method='logistic_regression'):
"""Cross validation for logistic regression
@param gamma: learning rate
@return : the average accuracy over the four fold validations
"""
N, D = tX.shape
# Logistic regression parameters
max_iters = 100
batch_size = N / 100
# Cross validation parameters
seed = 1
k_fold = 4
k_indices = build_k_indices(y, k_fold, seed)
N_fold = N * (k_fold - 1) / k_fold
N_test = N / k_fold
acc = []
for k in range(k_fold):
yTr = np.array([])
xTr = np.zeros((0, D))
for i in range(k_fold):
if i == k:
yTe = y[k_indices[i]]
xTe = tX[k_indices[i]]
else:
yTr = np.append(yTr, y[k_indices[i]], axis=0)
xTr = np.append(xTr, tX[k_indices[i]], axis=0)
initial_w = np.zeros(tX.shape[1])
if method == 'logistic_regression':
initial_w = np.zeros((tX.shape[1], 1))
w, loss = logistic_regression(yTr, xTr, initial_w, max_iters,
gamma)
y_est = sigmoid(np.dot(xTe, w))
y_label = [0 if i < 0.5 else 1 for i in y_est]
elif method == 'reg_logistic_regression':
initial_w = np.zeros((tX.shape[1], 1))
lambda_ = 0.1
w, loss = reg_logistic_regression(yTr, xTr, lambda_, initial_w,
max_iters, gamma)
y_est = sigmoid(np.dot(xTe, w))
y_label = [0 if i < 0.5 else 1 for i in y_est]
elif method == 'least_squares_GD':
w, loss = least_squares_GD(yTr, xTr, initial_w, max_iters, gamma)
y_label = predict_labels(w, xTe)
elif method == 'least_squares_SGD':
w, loss = least_squares_SGD(yTr, xTr, initial_w, max_iters, gamma)
y_label = predict_labels(w, xTe)
elif method == 'least_squares':
w, loss = least_squares(yTr, xTr)
y_label = predict_labels(w, xTe)
elif method == 'ridge_regression':
w, loss = ridge_regression(yTr, xTr, 0.1)
y_label = predict_labels(w, xTe)
else:
raise Exception('Invalid method')
corr = [
True if i == yTe[ind] else False for ind, i in enumerate(y_label)
]
acc.append(sum(corr) / N_test)
# print("Fold: {f}, Accuracy: {acc}, Loss:{loss}".format(f=k, acc=acc[k], loss=loss))
return (sum(acc) / k_fold), acc
print("Starting cross validation for the tx0 dataset")
print("##################################")
min_degree0,min_loss0=cross_validation_demo(y[tX0_dropped_distribution[:,0].astype(int)], tX0_dropped_distribution[:,1:],1,16,index_to_be_skewed0)
# # Record the min, max, mean, std of the data set resulting from the best weight found so they can be re-applied to the testing set later
min0= np.min(tX0_dropped_distribution[:,1:],axis=0)
max0=np.max(tX0_dropped_distribution[:,1:],axis=0)
tx0=min_max_transform(tX0_dropped_distribution[:,1:],min0,max0)
tx0[:,index_to_be_skewed0]= np.log(tx0[:,index_to_be_skewed0]+1)
tx0_norm,mean0,std0=expand_and_normalize_X(tx0,min_degree0)
w0,loss0=m.least_squares(y[tX0_dropped_distribution[:,0].astype(int)],tx0_norm)
min_degree0,min_loss0,loss0
print("Accuracy of best w found for tx0",accuracy(y[tX0_dropped_distribution[:,0].astype(int)],predict_labels(w0,tx0_norm)))
print("##################################")
print("Starting cross validation for the tx1 dataset")
print("##################################")
min_degree1,min_loss1=cross_validation_demo(y[tX1_dropped_distribution[:,0].astype(int)], tX1_dropped_distribution[:,1:],1,16,index_to_be_skewed1)