def findLassoAlpha(alpha, y, X, returnPred=False):
X_train, X_test = X.loc['2013-10-01':'2015-04-01'], X.loc[
'2015-05-01':'2016-04-01']
y_train, y_test = y.loc['2013-10-01':'2015-04-01'], y.loc[
'2015-05-01':'2016-04-01']
datestotest = y_test.index
dt = datestotest[0]
lassoreg2 = MultiTaskLasso(alpha=alpha, max_iter=1e5)
lassoreg2.fit(X_train, y_train)
y_pred2 = lassoreg2.predict(X_test.loc[dt].reshape(1, -1))
y_pred2 = pd.DataFrame(y_pred2)
y_pred2.columns = y.columns
prediction = y_pred2
X_train = X.loc['2013-10-01':dt]
y_train = y.loc['2013-10-01':dt]
for dt in datestotest[1:]:
lassoreg2 = MultiTaskLasso(alpha=alpha, max_iter=1e5)
lassoreg2.fit(X_train, y_train)
y_pred2 = lassoreg2.predict(X_test.loc[dt].reshape(1, -1))
y_pred2 = pd.DataFrame(y_pred2)
y_pred2.columns = y.columns
prediction = pd.concat([prediction, y_pred2])
X_train = X.loc['2013-10-01':dt]
y_train = y.loc['2013-10-01':dt]
prediction.index = y_test.index
if (returnPred):
return (y_test, prediction)
else:
return mean_squared_error(y_test, prediction)
def mtlasso_model(self, X_train, y_train, X_test, y_test):
mtlasso_model = MultiTaskLasso(alpha=.005)
mtlasso_model.fit(X_train, y_train)
y_train_pred = mtlasso_model.predict(X_train)
y_test_pred = mtlasso_model.predict(X_test)
# Scoring the model
print(mtlasso_model.score(X_train, y_train))
print(mtlasso_model.score(X_test, y_test))
print('MSE train: %.6f, MSE test: %.6f' % (mean_squared_error(
y_train, y_train_pred), mean_squared_error(y_test, y_test_pred)))
print('R^2 train: %.6f, R^2 test: %.6f' %
(r2_score(y_train, y_train_pred), r2_score(y_test, y_test_pred)))
def main():
pickledname = sys.argv[1]
_qmDL = qmDL()
dataset = _qmDL.load(pickledname=pickledname)
X, Y, labels = dataset['XX'], dataset['T'], dataset['names']
#5000 training samples, with 2211 test samples
X_train, X_test, Y_train, Y_test = train_test_split(X,
Y,
test_size=2211,
random_state=42)
print 'Len X train , test:', len(X_train), len(X_test)
regressor = MultiTaskLasso().fit(X_train, Y_train)
#r = SVR()
#regressor = multiTargetRegressor(rObject=r).fit(X_train,Y_train)
Y_pred = regressor.predict(X_test)
print Y_pred
print 'Y_pred', Y_pred.shape
for i in xrange(len(labels)):
print '*** MAE ', labels[i],
print mean_absolute_error(Y_test[:, i], Y_pred[:, i])
class MultiTaskLassoImpl:
def __init__(self, **hyperparams):
self._hyperparams = hyperparams
self._wrapped_model = Op(**self._hyperparams)
def fit(self, X, y=None):
if y is not None:
self._wrapped_model.fit(X, y)
else:
self._wrapped_model.fit(X)
return self
def predict(self, X):
return self._wrapped_model.predict(X)
def run_one_configuration(
full_train_covariate_matrix,
complete_target,
new_valid_covariate_data_frames,
new_valid_target_data_frame,
std_data_frame,
target_clusters,
featurizer,
model_name,
parameters,
log_file,
):
model_baseline = dict()
model_baseline["type"] = model_name
model_baseline["target_clusters"] = target_clusters
if model_name == "multi_task_lasso":
model = MultiTaskLasso(max_iter=5000, **parameters)
elif model_name == "xgboost":
model = MultiOutputRegressor(
XGBRegressor(n_jobs=10,
objective="reg:squarederror",
verbosity=0,
**parameters))
model.fit(featurizer(full_train_covariate_matrix),
complete_target.to_numpy(copy=True))
model_baseline["model"] = lambda x: model.predict(featurizer(x))
skill, _, _, _ = location_wise_metric(
new_valid_target_data_frame,
new_valid_covariate_data_frames,
std_data_frame,
model_baseline,
"skill",
)
cos_sim, _, _, _ = location_wise_metric(
new_valid_target_data_frame,
new_valid_covariate_data_frames,
std_data_frame,
model_baseline,
"cosine-sim",
)
with open(log_file, "a") as f:
f.write(f"{len(target_clusters)} {parameters} {skill} {cos_sim}\n")
class LELM:
upper_bound = 1.
lower_bound = -1.
def __init__(self, n_hidden, C=1., max_iter=10000):
self.n_hidden = n_hidden
self.C = C
self.max_iter = max_iter
def fit(self, X, y):
# check label has form of 2-dim array
X, y, = copy.deepcopy(X), copy.deepcopy(y)
self.sample_weight = None
if y.shape.__len__() != 2:
self.classes_ = np.unique(y)
self.n_classes_ = self.classes_.__len__()
y = self.__one2array(y, self.n_classes_)
else:
self.classes_ = np.arange(y.shape[1])
self.n_classes_ = self.classes_.__len__()
self.W = np.random.uniform(self.lower_bound,
self.upper_bound,
size=(X.shape[1], self.n_hidden))
self.b = np.random.uniform(self.lower_bound,
self.upper_bound,
size=self.n_hidden)
H = expit(np.dot(X, self.W) + self.b)
self.multi_lasso = MultiTaskLasso(self.C,
max_iter=self.max_iter).fit(H, y)
def __one2array(self, y, n_dim):
y_expected = np.zeros((y.shape[0], n_dim))
for i in range(y.shape[0]):
y_expected[i][y[i]] = 1
return y_expected
def predict(self, X):
H = expit(np.dot(X, self.W) + self.b)
output = self.multi_lasso.predict(H)
return output.argmax(axis=1)
def main():
pickledname = sys.argv[1]
_qmDL = qmDL()
dataset = _qmDL.load(pickledname=pickledname)
X, Y, labels = dataset["XX"], dataset["T"], dataset["names"]
# 5000 training samples, with 2211 test samples
X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size=2211, random_state=42)
print "Len X train , test:", len(X_train), len(X_test)
regressor = MultiTaskLasso().fit(X_train, Y_train)
# r = SVR()
# regressor = multiTargetRegressor(rObject=r).fit(X_train,Y_train)
Y_pred = regressor.predict(X_test)
print Y_pred
print "Y_pred", Y_pred.shape
for i in xrange(len(labels)):
print "*** MAE ", labels[i],
print mean_absolute_error(Y_test[:, i], Y_pred[:, i])
class classSparser(object):
def __init__(self,mapperType='PIMP',support=150,projectOnSubspace=False):
#options are
#'PIMP' for Moore Penrose Pseudo Inverse
#'Regressor' for using a regression task on each dimension
self.mapperType = mapperType
self.sparsed_X = None
self.transformation_matrix = None
self.Regressor = None
self.support = support
self.projectOnSubspace = projectOnSubspace
def fit(self,X,Y):
self.sparsed_X = list()
#First, tranlate points to the origin
main_centroid = [ np.mean(x) for x in np.transpose(X) ]
print 'Main centroid:', main_centroid
X = X - main_centroid
byClassDict = defaultdict(list)
for i in xrange(len(Y)):
byClassDict[Y[i]].append(X[i])
class_centroids = dict()
centroids_matrix = list()
kindexmap = dict()
_i = 0
for k in byClassDict:
class_centroid = [ np.mean(x) for x in np.transpose(byClassDict[k]) ] #np.mean(byClassDict[k])
_norm = np.linalg.norm(class_centroid)
_scaling_factor = _norm**2#(i+1)**2 #+ (i+_norm) #Play with this using _norm, i and any otrher function/constant
_centroid = np.array(class_centroid)#*(_scaling_factor)
print '*** Class centroid:', _centroid
class_centroids[k] = _centroid
centroids_matrix.append(_centroid)
kindexmap[k] = _i
_i+=1
centroids_matrix = np.array(centroids_matrix)
ortho_centroids_matrix = np.array(gram_schmidt.gs(centroids_matrix))
ortho_centroids_matrix = normalize(ortho_centroids_matrix)
print '*Centroids matrix',centroids_matrix
print '*Ortho centroids matrix', ortho_centroids_matrix
newX, newY = list(), list()
ks = list()
for k in byClassDict:
#byClassDict[k] = np.array(byClassDict[k]) - centroids_matrix[kindexmap[k]] + np.array(ortho_centroids_matrix[kindexmap[k]]) #class_centroids[k]
#this is the basis vector corresponding to current class
classvector = np.array(ortho_centroids_matrix[kindexmap[k]])
kScalingFactor = self.support
#This section tries to get a good scaling factor for each orthonormal vector
maxks = list()
for _k in ks:
projs = [scalarProjection(x,classvector) for x in byClassDict[_k]]
maxk = max(projs)
maxks.append(maxk)
maxownk = max([scalarProjection(x,classvector) for x in byClassDict[k]])
if len(ks):
kScalingFactor = max(maxks) + abs(maxownk) + self.support
for v in byClassDict[k]:
vv = np.array(v) - centroids_matrix[kindexmap[k]] + classvector*kScalingFactor
self.sparsed_X.append(vv)
newX.append(v)
newY.append(k)
ks.append(k)
self.sparsed_X = np.array(self.sparsed_X)
if self.projectOnSubspace:
#Project on to new subspace spawned by class vectors
self.sparsed_X = np.dot(self.sparsed_X,np.transpose(centroids_matrix) )
if self.mapperType == 'PIMP':
#self.scaler = preprocessing.StandardScaler().fit(self.sparsed_X)
#self.sparsed_X = self.scaler.transform(self.sparsed_X)
self.transformation_matrix = self.sparsed_X*(np.transpose(np.linalg.pinv(X) ) )
#self.transformation_matrix = X*(np.transpose(np.linalg.pinv(self.sparsed_X) ) )
if self.mapperType == 'Regressor':
self.Regressor = MultiTaskLasso(alpha=0.00000001,max_iter=2000)
self.Regressor.fit(newX,self.sparsed_X)
return self.sparsed_X, newY
def transform(self,X):
Xs = X#self.scaler.transform(X)
if self.mapperType == 'PIMP':
transformed_data = self.transformation_matrix*Xs
#transformed_data = Xs*self.transformation_matrix
if self.mapperType == 'Regressor':
transformed_data = self.Regressor.predict(Xs)
return transformed_data
import numpy as np
from src.common.my_data import Data
from sklearn.linear_model import LassoCV
from sklearn.linear_model import MultiTaskLasso
data = Data()
agg_train_have_log = pd.read_table(data.output.sorted_train_agg_have_log_usr).drop('USRID', axis=1)
print('agg_train_have_log : ', agg_train_have_log.shape)
agg_test_have_log = pd.read_table(data.output.sorted_test_agg_have_log_usr).drop('USRID', axis=1)
print('agg_test_have_log : ', agg_test_have_log.shape)
agg_all_have_log = pd.concat([agg_train_have_log, agg_test_have_log], axis=0)
print('agg_all_have_log : ', agg_all_have_log.shape)
tf_idf_all_have_log = pd.read_table(data.feature.tf_idf_have_log_usr_evt_all)
tf_idf_all_have_log_name = tf_idf_all_have_log.head(0)
print(tf_idf_all_have_log_name)
print('tf_idf_all_have_log : ', tf_idf_all_have_log.shape)
# print(tf_idf_all)
agg_no_have_log = pd.read_table(data.output.sorted_test_agg_no_have_log_usr).drop('USRID', axis=1)
print('agg_no_have_log : ', agg_no_have_log.shape)
lasso = MultiTaskLasso()
lasso.fit(agg_all_have_log, tf_idf_all_have_log)
result_lasso = lasso.predict(agg_no_have_log)
print(result_lasso)
# result_csv = pd.DataFrame(result_lasso)
# data.to_csv(data.output.prediction_test_no_log_tf_idf, index=False, sep='\t')
k_fold = KFold(Y_train_raw.shape[0], n_folds=10)
for train, test in k_fold:
X1 = X_train_reduced[train]
Y1 = Y_train_raw[train]
X2 = X_train_reduced[test]
Y2 = Y_train_raw[test]
## Train Classifiers on fold
mcl_clf = MultiTaskLasso(alpha=.3)
mcl_clf.fit(X1, Y1)
## Score Classifiers on fold
mcl_clf_score = mcl_clf.score(X2, Y2)
print "MultiTaskLasso: ", mcl_clf_score
## Lasso CV for parameter optimization
t1 = time.time()
clf = MultiTaskLasso(alpha=.3).fit(X_train_reduced, Y_train_raw)
t_lasso_cv = time.time() - t1
print 'time to train', t_lasso_cv
Y_predicted = clf.predict(X_test_reduced)
## Save results to csv
np.savetxt('prediction.csv', Y_predicted, fmt='%.5f',delimiter=',')
n_samples = 100
n_features = 40
n_tasks = 12
rel_f = 7
coef = np.zeros((n_tasks, n_features))
times = np.linspace(0, 2 * np.pi, n_tasks)
for k in range(rel_f):
coef[:, k] = np.sin((1.0 + rr.randn(1)) * times + 3 * rr.randn(1))
X = rr.randn(n_samples, n_features)
y = np.dot(X, coef.T) + rr.randn(n_samples, n_tasks)
X_train = X[:-20]
y_train = y[:-20]
X_test = X[-20:]
y_test = y[-20:]
print("Fitting LASSO model...")
ll = Lasso(alpha=0.45)
ll.fit(X_train, y_train)
print("R2 score: {0}".format(r2_score(y_test, ll.predict(X_test))))
print("Fitting Multitask LASSO model...")
ml = MultiTaskLasso(alpha=0.45)
ml.fit(X_train, y_train)
print("R2 score: {0}".format(r2_score(y_test, ml.predict(X_test))))
print("Plotting predictions...")
plt.scatter(X[:, 1], y[:, 1])
plt.scatter(X[:, 1], ll.predict(X)[:, 1], color="blue")
plt.scatter(X[:, 1], ml.predict(X)[:, 1], color="red")
plt.show()
#
# X_train, X_test, Y_train, Y_test = train_test_split(X, Y, test_size = 0.4, random_state=0)
import sys
sys.path.insert(0, 'C:\\r workspace\\MultiSconES\\py')
from load_data import load_dataset
dataset = load_dataset()
X = dataset["data"]
Y = dataset["labels"]
X_train, X_test, Y_train, Y_test = train_test_split(X,
Y,
test_size=0.33,
random_state=42)
clf = MultiTaskLasso(alpha=1)
print "train start"
clf.fit(X_train, Y_train)
print "train end"
print "coef start"
coef_multi_task_lasso_ = clf.coef_
print "coef end"
plot_coef(coef_multi_task_lasso_)
zero_coefs = get_stats(coef_multi_task_lasso_)
print len(zero_coefs)
Y_pred = clf.predict(X_test)
clf_score = clf.score(X_test, Y_test)
score = r2_score(Y_test[:, 5], Y_pred[:, 5])
precedent[4:7, :, :, :] = block[i - 337:i - 334, :, :, :] # 前一周
precedent_frames.append(precedent)
#regr = (max_depth=8, random_state=0,n_estimators=1000)
model = MultiTaskLasso(alpha=1)
X_train, X_val, y_train, y_val = train_test_split(precedent_frames,
label_frames,
test_size=0.2,
random_state=4)
# 转化为5D的numpy数组，训练集(920,7,64,64,2)， 测试集(231,1,64,64,2)
X_train = np.array(X_train)
y_train = np.array(y_train)
X_val = np.array(X_val)
y_val = np.array(y_val)
print(X_train.shape)
print(X_val.shape)
print(y_train.shape)
print(y_val.shape)
# 把5D数据转化为randomForest输入的2D数据
X_train = X_train.reshape((920, 7 * 64 * 64 * 2))
X_val = X_val.reshape((231, 7 * 64 * 64 * 2))
y_train = y_train.reshape((920, 1 * 64 * 64 * 2))
y_val = y_val.reshape((231, 1 * 64 * 64 * 2))
model.fit(X_train, y_train)
y_pred = model.predict(X_val)
from sklearn.metrics import mean_squared_error
print(mean_squared_error(y_val, y_pred))
tss, rss, ess, r2 = xss(Y, ompCV.predict(X))
print "TSS(Total Sum of Squares): ", tss
print "RSS(Residual Sum of Squares): ", rss
print "ESS(Explained Sum of Squares): ", ess
print "R^2: ", r2
print "\n**********测试MultiTaskLasso类**********"
# 在初始化MultiTaskLasso类时, 指定参数alpha, 默认值是1.0.
multiTaskLasso = MultiTaskLasso(alpha=1.0)
# 拟合训练集
multiTaskLasso.fit(train_X, train_Y)
# 打印模型的系数
print "系数:", multiTaskLasso.coef_
print "截距:", multiTaskLasso.intercept_
print '训练集R2: ', r2_score(train_Y, multiTaskLasso.predict(train_X))
# 对于线性回归模型, 一般使用均方误差(Mean Squared Error,MSE)或者
# 均方根误差(Root Mean Squared Error,RMSE)在测试集上的表现来评该价模型的好坏.
test_Y_pred = multiTaskLasso.predict(test_X)
print "测试集得分:", multiTaskLasso.score(test_X, test_Y)
print "测试集MSE:", mean_squared_error(test_Y, test_Y_pred)
print "测试集RMSE:", np.sqrt(mean_squared_error(test_Y, test_Y_pred))
print "测试集R2:", r2_score(test_Y, test_Y_pred)
tss, rss, ess, r2 = xss(Y, multiTaskLasso.predict(X))
print "TSS(Total Sum of Squares): ", tss
print "RSS(Residual Sum of Squares): ", rss
print "ESS(Explained Sum of Squares): ", ess
print "R^2: ", r2
class classSparser(object):
def __init__(self,
mapperType='PIMP',
support=150,
projectOnSubspace=False):
#options are
#'PIMP' for Moore Penrose Pseudo Inverse
#'Regressor' for using a regression task on each dimension
self.mapperType = mapperType
self.sparsed_X = None
self.transformation_matrix = None
self.Regressor = None
self.support = support
self.projectOnSubspace = projectOnSubspace
def fit(self, X, Y):
self.sparsed_X = list()
#First, tranlate points to the origin
main_centroid = [np.mean(x) for x in np.transpose(X)]
print 'Main centroid:', main_centroid
X = X - main_centroid
byClassDict = defaultdict(list)
for i in xrange(len(Y)):
byClassDict[Y[i]].append(X[i])
class_centroids = dict()
centroids_matrix = list()
kindexmap = dict()
_i = 0
for k in byClassDict:
class_centroid = [
np.mean(x) for x in np.transpose(byClassDict[k])
] #np.mean(byClassDict[k])
_norm = np.linalg.norm(class_centroid)
_scaling_factor = _norm**2 #(i+1)**2 #+ (i+_norm) #Play with this using _norm, i and any otrher function/constant
_centroid = np.array(class_centroid) #*(_scaling_factor)
print '*** Class centroid:', _centroid
class_centroids[k] = _centroid
centroids_matrix.append(_centroid)
kindexmap[k] = _i
_i += 1
centroids_matrix = np.array(centroids_matrix)
ortho_centroids_matrix = np.array(gram_schmidt.gs(centroids_matrix))
ortho_centroids_matrix = normalize(ortho_centroids_matrix)
print '*Centroids matrix', centroids_matrix
print '*Ortho centroids matrix', ortho_centroids_matrix
newX, newY = list(), list()
ks = list()
for k in byClassDict:
#byClassDict[k] = np.array(byClassDict[k]) - centroids_matrix[kindexmap[k]] + np.array(ortho_centroids_matrix[kindexmap[k]]) #class_centroids[k]
#this is the basis vector corresponding to current class
classvector = np.array(ortho_centroids_matrix[kindexmap[k]])
kScalingFactor = self.support
#This section tries to get a good scaling factor for each orthonormal vector
maxks = list()
for _k in ks:
projs = [
scalarProjection(x, classvector) for x in byClassDict[_k]
]
maxk = max(projs)
maxks.append(maxk)
maxownk = max(
[scalarProjection(x, classvector) for x in byClassDict[k]])
if len(ks):
kScalingFactor = max(maxks) + abs(maxownk) + self.support
for v in byClassDict[k]:
vv = np.array(v) - centroids_matrix[
kindexmap[k]] + classvector * kScalingFactor
self.sparsed_X.append(vv)
newX.append(v)
newY.append(k)
ks.append(k)
self.sparsed_X = np.array(self.sparsed_X)
if self.projectOnSubspace:
#Project on to new subspace spawned by class vectors
self.sparsed_X = np.dot(self.sparsed_X,
np.transpose(centroids_matrix))
if self.mapperType == 'PIMP':
#self.scaler = preprocessing.StandardScaler().fit(self.sparsed_X)
#self.sparsed_X = self.scaler.transform(self.sparsed_X)
self.transformation_matrix = self.sparsed_X * (np.transpose(
np.linalg.pinv(X)))
#self.transformation_matrix = X*(np.transpose(np.linalg.pinv(self.sparsed_X) ) )
if self.mapperType == 'Regressor':
self.Regressor = MultiTaskLasso(alpha=0.00000001, max_iter=2000)
self.Regressor.fit(newX, self.sparsed_X)
return self.sparsed_X, newY
def transform(self, X):
Xs = X #self.scaler.transform(X)
if self.mapperType == 'PIMP':
transformed_data = self.transformation_matrix * Xs
#transformed_data = Xs*self.transformation_matrix
if self.mapperType == 'Regressor':
transformed_data = self.Regressor.predict(Xs)
return transformed_data
y_pred_lasso = lasso_model.predict(X_test)[:, 1]
for i in range(n_relevant_features):
fpr_lasso[i], tpr_lasso[i], _ = roc_curve(y_test_classes[:, i],
y_pred_lasso[:])
"""##MultiTaskLasso Model
Also computes false positive rate and true positive rate for each relevant feature
"""
multi_task_model = MultiTaskLasso(alpha=1.).fit(X, y)
multi_task_lasso_coefficients = multi_task_model.coef_
fpr_l1l2 = dict()
tpr_l1l2 = dict()
y_pred_l1l2 = multi_task_model.predict(X_test)[:, 1]
for i in range(n_relevant_features):
fpr_l1l2[i], tpr_l1l2[i], _ = roc_curve(y_test_classes[:, i],
y_pred_l1l2[:])
"""##ROC Curve
ROC Curve for GFLasso, Lasso and MultiTaskLasso Models
"""
from matplotlib import pyplot as plt
plt.plot([0, 1], [0, 1], 'k--')
plt.plot(fpr_lasso[2], tpr_lasso[2], label='Lasso')
plt.plot(fpr_l1l2[2], tpr_l1l2[2], label='l1l2')
plt.plot(fpr_gfl[2], tpr_gfl[2], label='GFLasso')
plt.xlabel('False positive rate')
path_test = 'data_test.txt'
X, Y = get_data_own(path_train)
print(X.shape)
print(Y.shape)
print("Split data for CV")
X_train, X_test , y_train, y_test = train_test_split(X, Y, test_size=0.2, random_state=1)
lasso = MultiTaskLasso(max_iter = max_iter, normalize = True)
print("Init train with multitasklassocv")
lassocv = MultiTaskLassoCV(alphas=None, cv=10, max_iter=max_iter, verbose=True, normalize=True)
lassocv.fit(X_train, y_train)
print("Fit multitasklasso with alpha from cv lasso")
lasso.set_params(alpha=lassocv.alpha_)
lasso.fit(X_train, y_train)
print("get mean square error")
mae = mean_absolute_error(y_test, lasso.predict(X_test))
print("mae: {}".format(mae))
rmsle = mean_squared_log_error(y_test, lasso.predict(X_test))
print("rmsle: {}".format(rmsle))
mape = mean_absolute_percentage_error(y_test, lasso.predict(X_test))
print("mape: {}".format(mape))
class SparseRegression:
def __init__(self,
v,
delta_v,
f,
q,
lin_args=(),
force_args=(),
split='shuffle',
split_kargs={}):
"""
v.shape = (n_steps, n_variables),
delta_v.shape = (n_steps, n_variables)
q (in [1, n_variables]) number of first variables
to fit the linear model to,
remaining n_variables-q are used as forcing
f: (n_steps, n_variables) -> (n_steps, n_features)
f will be called with f(..., *lin_args) when fitting the linear model
and with f(..., *force_args) when fitting the force
"""
if v.shape == delta_v.shape and type(q) == int and q > 0 \
and q <= v.shape[1]:
self.v, self.delta_v = self._check_reduce(v, delta_v)
self.params = [*self.v.shape, q] # [n_steps, n_vars, q]
# derivatives used for the model
self.delta_v = self.delta_v[:, :q]
# calculate features based on first q variables for linear model
self.features_lin_model = f(self.v[:, :q], *lin_args)
# calculate features based on remaining variables for forcing term
self.features_forcing = f(self.v[:, q:], *force_args)
# two different types of splitting
split_dict = {
'shuffle': self._shuffle_split,
'lorenz': self._lobes_split
}
# split the timesteps into two parts:
# first is used for fitting linear model, second for forcing
self.mask_l_m, self.mask_f = split_dict[split](**split_kargs)
# self.mask_l_m, self.mask_f = self._split_lobes(self.v[:, 0])
self.feature_generation = f
self.feature_generation_args = {
'linear': lin_args,
'forcing': force_args
}
else:
raise Exception('Error: invalid init parameter')
def _shuffle_split(self, fraction=0.5):
"""
creates two masks to split n_steps elements into two disjunct sets
where the first has length=fraction*n
"""
assert fraction > 0 and fraction < 1
n_steps = self.params[0]
n_1 = int(n_steps * fraction)
shuffled_ind = np.random.permutation(n_steps)
ind_1 = shuffled_ind[:n_1]
mask_1 = np.zeros(n_steps, dtype=np.bool)
mask_1[ind_1] = True
ind_2 = shuffled_ind[n_1:]
mask_2 = np.zeros(n_steps, dtype=np.bool)
mask_2[ind_2] = True
# each element is part of either one or the other mask
assert np.all(mask_1 ^ mask_2)
return mask_1, mask_2
def _lobes_split(self, window_pos=200, window_neg=400):
"""
use regions in which trajectories are on the lobes to fit the
linear model and the remaining steps for modeling the force
"""
v_1 = self.v[:, 0]
n_steps = self.params[0]
# find lobe switches
m_pos = v_1 > 0
m_neg = v_1 < 0
mask_switch = (m_pos[:-1] & m_neg[1:]) | (m_neg[:-1] & m_pos[1:])
switch_ind = np.nonzero(mask_switch)[0]
print('no. of lobe switches detected in v_1: {:d}'.format(
len(switch_ind)))
force_ind_list = []
for switch in switch_ind:
if switch + 1 - window_neg < 0:
l_neg = switch
else:
l_neg = window_neg
if switch + 1 + window_pos > n_steps:
l_pos = n_steps - switch
else:
l_pos = window_pos
force_ind_list.append(np.arange(switch - l_neg, switch + l_pos))
force_ind = np.concatenate(force_ind_list)
assert np.all(force_ind >= 0) and np.all(force_ind < n_steps)
mask_lobes = np.ones(n_steps, dtype=np.bool)
mask_lobes[force_ind] = False
mask_switch = np.zeros(n_steps, dtype=np.bool)
mask_switch[force_ind] = True
assert np.all(mask_lobes ^ mask_switch)
return mask_lobes, mask_switch
def _check_reduce(self, v, delta_v):
"""
check both matrices for columns containg nan and excludes them
"""
invalid_v = np.any(np.isnan(v), axis=1)
if np.any(invalid_v):
print('Warning: v matrix contains NaNs')
invalid_delta_v = np.any(np.isnan(delta_v), axis=1)
if np.any(invalid_delta_v):
print('Warning: delta_v matrix contains NaNs')
valid_steps = (~invalid_v) & (~invalid_delta_v)
valid_fraction = np.sum(valid_steps) / len(valid_steps)
if not np.isclose(valid_fraction, 1):
print('Warning: only {:.1%} of time steps are valid'.format(
valid_fraction))
if valid_fraction < 0.95:
raise Exception('Error: less than 95% of time steps are valid')
return v[valid_steps], delta_v[valid_steps]
def fit_lin_model(self, alpha=None):
"""
fit sparse linear regression on first q variables
alpha is penalization parameter, None triggers cross validation
"""
if alpha is None: # do cross validation
self.lin_model = \
MultiTaskLassoCV(eps=1e-3, n_alphas=50, cv=10, n_jobs=-1,
fit_intercept=False, normalize=False,
max_iter=3500)
else:
self.lin_model = \
MultiTaskLasso(alpha=alpha, fit_intercept=False,
normalize=False)
self.lin_model.fit(self.features_lin_model[self.mask_l_m],
self.delta_v[self.mask_l_m])
def pred_lin_model(self):
"""
calculate prediction of the linear model on the data set not used for
training it
"""
pred_d_v = self.lin_model.predict(self.features_lin_model[self.mask_f])
d_v = self.delta_v[self.mask_f]
# calculate correlation for each variable
n_variables = d_v.shape[1]
print('corr. of prediction and true delta_v:')
for i in range(n_variables):
r, p = pearsonr(pred_d_v[:, i], d_v[:, i])
print('{:d}th variable: r={:.2f} (p={:.2f})'.format(i + 1, r, p))
self.eps = d_v - pred_d_v # d_v - Af(v)
def fit_force_params(self, alpha=None):
"""
fit sparse linear regression on remaining n_variables-q variables
alpha is penalization parameter, None triggers cross validation
"""
if alpha is None: # do cross validation
self.force_model = \
MultiTaskLassoCV(eps=1e-3, n_alphas=50, cv=10, n_jobs=-1,
fit_intercept=False, normalize=False)
else:
self.force_model = \
MultiTaskLasso(alpha=alpha, fit_intercept=False,
normalize=False)
self.force_model.fit(self.features_forcing[self.mask_f], self.eps)
def fit(self, alpha_lin=None, alpha_force=None):
self.fit_lin_model(alpha=alpha_lin)
self.pred_lin_model()
self.fit_force_params(alpha=alpha_force)
def plot_coefs(self, f_descr=None):
"""
plot coef matrix of linear and force model
f_descr(n_vars, offset, *args) -> n_features
"""
n_f_lin_model = self.features_lin_model.shape[1]
n_f_forcing = self.features_forcing.shape[1]
q = self.params[-1]
if f_descr is not None:
# get names of the features
f_lin_model_str = f_descr(q, 0,
*self.feature_generation_args['linear'])
f_forcing_str = f_descr(self.v.shape[1] - q, q,
*self.feature_generation_args['forcing'])
assert len(f_lin_model_str) == n_f_lin_model
assert len(f_forcing_str) == n_f_forcing
else:
f_lin_model_str = \
[str(i) for i in range(n_f_lin_model)]
f_forcing_str = \
[str(i) for i in range(n_f_forcing)]
n_f = n_f_lin_model + n_f_forcing
fractions = (n_f_lin_model / n_f, n_f_forcing / n_f)
fig, axes = plt.subplots(ncols=2,
sharey=True,
gridspec_kw={'width_ratios': fractions})
plt.subplots_adjust(wspace=0.2)
a = self.lin_model.coef_
b = self.force_model.coef_
assert a.shape[0] == b.shape[0]
n_vars = a.shape[0]
max_abs_coef = max(abs(a.min()), abs(b.min()), a.max(), b.max())
titles = ['A', 'B']
matrices = [a, b]
ticklabels = [f_lin_model_str, f_forcing_str]
for i, ax in enumerate(axes):
ax.set_title(titles[i])
im = ax.imshow(matrices[i],
vmin=-max_abs_coef,
vmax=max_abs_coef,
origin='upper',
cmap='seismic')
ax.set_xticks(np.arange(len(ticklabels[i])))
ax.set_xticklabels(ticklabels[i], rotation=45)
ax.set_xlabel('features')
ax.set_yticks(np.arange(n_vars))
ax.set_yticklabels(
['$v_{:d}$'.format(i + 1) for i in range(n_vars)])
axes[0].set_ylabel('variables')
plt.colorbar(im, ax=axes, fraction=0.05, shrink=0.75)
def _dv(self, t, v, force):
"""
v.shape = (q,)
force(t)
"""
# linear part
lin_args = self.feature_generation_args['linear']
features_lin = \
self.feature_generation(v.reshape(1, -1), *lin_args).squeeze()
lin_contr = np.dot(self.lin_model.coef_, features_lin)
# forcing part
force_args = self.feature_generation_args['forcing']
features_force = \
self.feature_generation(force(t).reshape(1, -1),
*force_args).squeeze()
force_contr = np.dot(self.force_model.coef_, features_force)
dv = lin_contr + force_contr
return dv
def solve_model(self, dt, ind_v_init, force=None):
"""
use time serie of the force variables and simulate the system from
ind_v_init
"""
n_steps, n_vars, q = self.params
v_init = self.v[ind_v_init, :q]
# resemble the timesteps at which the original data was evaluated
n_remaining = n_steps - ind_v_init
t_remaining = dt * (n_remaining - 1)
t_eval = np.linspace(0, t_remaining, num=n_remaining)
if force is None:
def f_dummy(t):
return np.zeros(n_vars - q)
dv = partial(self._dv, force=f_dummy)
elif force.shape == (n_remaining, n_vars - q):
f_interp = interp1d(t_eval, force, axis=0, kind='quadratic')
dv = partial(self._dv, force=f_interp)
else:
raise Exception('invalid force')
result = solve_ivp(dv, [0, t_remaining],
v_init,
t_eval=t_eval,
method='RK45',
rtol=1e-6,
atol=1e-12)
print(result.message)
return result
