def optimal_machines(self, X, y, single=False, epsilon=None, info=False):
"""
Find the optimal combination of machines for testing data for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want optimal machine combinations.
y: float
Target value for query to compare.
single: boolean, optional
Option to calculate optimal machine combinations for a single query point instead.
info: bool, optional
Returns MSE dictionary for each machine combination value
epsilon: float, optional
fixed epsilon value to help determine optimal machines.
Returns
-------
MSE: dictionary mapping machines with mean squared errors
opt: optimal machines combination
"""
if epsilon is None:
epsilon = self.aggregate.epsilon
n_machines = np.arange(1, len(self.aggregate.estimators_) + 1)
MSE = {}
for num in n_machines:
machine_names = self.aggregate.estimators_.keys()
use = list(itertools.combinations(machine_names, num))
for combination in use:
machine = Cobra(random_state=self.random_state,
epsilon=epsilon)
machine.fit(self.aggregate.X_,
self.aggregate.y_,
default=False)
machine.split_data()
machine.load_default(machine_list=combination)
machine.load_machine_predictions()
if single:
result = machine.predict(X.reshape(1, -1))
MSE[combination] = np.square(y - result)
else:
results = machine.predict(X)
MSE[combination] = (mean_squared_error(y, results))
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def optimal_alpha(self, X, y, single=False, epsilon=None, info=False):
"""
Find the optimal alpha for testing data for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want optimal alpha values
y: float
Target value for query to compare.
single: boolean, optional
Option to calculate optimal alpha for a single query point instead.
info: bool, optional
Returns MSE dictionary for each alpha value
epsilon: float, optional
fixed epsilon value to help determine optimal alpha.
Returns
-------
MSE: dictionary mapping alpha with mean squared errors
opt: optimal alpha combination
"""
if epsilon is None:
epsilon = self.aggregate.epsilon
MSE = {}
for alpha in range(1, len(self.aggregate.estimators_) + 1):
machine = Cobra(random_state=self.random_state, epsilon=epsilon)
machine.fit(self.aggregate.X_, self.aggregate.y_)
# for a single data point
if single:
result = machine.predict(X, alpha=alpha)
MSE[alpha] = np.square(y - result)
else:
results = machine.predict(X, alpha=alpha)
MSE[alpha] = (mean_squared_error(y, results))
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def optimal_machines_grid(self, X, y, line_points=200, info=False):
"""
Find the optimal epsilon and machine-combination for a single query point for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want optimal machines and epsilon values
y: float
Target value for query to compare.
line_points: integer, optional
Number of epsilon values to traverse the grid.
info: bool, optional
Returns MSE dictionary for each epsilon/machine value.
Returns
-------
MSE: dictionary mapping (machine combination, epsilon) with mean squared errors
opt: optimal epislon/machine combination
"""
# code to find maximum and minimum distance between predictions to create grid
a, size = sorted(self.aggregate.all_predictions_), len(
self.aggregate.all_predictions_)
res = [a[i + 1] - a[i] for i in range(size) if i + 1 < size]
emin = min(res)
emax = max(a) - min(a)
erange = np.linspace(emin, emax, line_points)
n_machines = np.arange(1, len(self.aggregate.estimators_) + 1)
MSE = {}
for epsilon in erange:
for num in n_machines:
machine_names = self.aggregate.estimators_.keys()
use = list(itertools.combinations(machine_names, num))
for combination in use:
machine = Cobra(random_state=self.random_state,
epsilon=epsilon)
machine.fit(self.aggregate.X_,
self.aggregate.y_,
default=False)
machine.split_data()
machine.load_default(machine_list=combination)
machine.load_machine_predictions()
result = machine.predict(X.reshape(1, -1))
MSE[(combination, epsilon)] = np.square(y - result)
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def optimal_alpha_grid(self, X, y, line_points=200, info=False):
"""
Find the optimal epsilon and alpha for a single query point for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want optimal alpha and epsilon values
y: float
Target value for query to compare.
line_points: integer, optional
Number of epsilon values to traverse the grid.
info: bool, optional
Returns MSE dictionary for each epsilon/alpha value
Returns
-------
MSE: dictionary mapping (alpha, epsilon) with mean squared errors
opt: optimal epislon/alpha combination
"""
# code to find maximum and minimum distance between predictions to create grid
a, size = sorted(self.aggregate.all_predictions_), len(
self.aggregate.all_predictions_)
res = [a[i + 1] - a[i] for i in range(size) if i + 1 < size]
emin = min(res)
emax = max(a) - min(a)
erange = np.linspace(emin, emax, line_points)
n_machines = np.arange(1, len(self.aggregate.machines_) + 1)
MSE = {}
# looping over epsilon and alpha values
for epsilon in erange:
for num in n_machines:
machine = Cobra(random_state=self.random_state,
epsilon=epsilon)
machine.fit(self.aggregate.X_, self.aggregate.y_)
result = machine.predict(X.reshape(1, -1), alpha=num)
MSE[(num, epsilon)] = np.square(y - result)
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def optimal_epsilon(self, X, y, line_points=200, info=False):
"""
Find the optimal epsilon value for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want for optimal epsilon.
y: float
Target value for query to compare.
line_points: integer, optional
Number of epsilon values to traverse the grid.
info: bool, optional
Returns MSE dictionary for each epsilon value.
Returns
-------
MSE: dictionary mapping epsilon with mean squared errors
opt: optimal epsilon value
"""
a, size = sorted(self.aggregate.all_predictions_), len(
self.aggregate.all_predictions_)
res = [a[i + 1] - a[i] for i in range(size) if i + 1 < size]
emin = min(res)
emax = max(a) - min(a)
erange = np.linspace(emin, emax, line_points)
MSE = {}
for epsilon in erange:
machine = Cobra(random_state=self.random_state, epsilon=epsilon)
machine.fit(self.aggregate.X_, self.aggregate.y_)
results = machine.predict(X)
MSE[epsilon] = (mean_squared_error(y, results))
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def boxplot(self, reps=100, info=False):
"""
Plots boxplots of machines.
Parameters
----------
reps: int, optional
Number of times to repeat experiments for boxplot.
info: boolean, optional
Returns data
"""
if type(self.aggregate) is Cobra:
MSE = {k: [] for k, v in self.aggregate.machines_.items()}
MSE["COBRA"] = []
for i in range(0, reps):
cobra = Cobra(random_state=self.random_state, epsilon=self.aggregate.epsilon)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_, random_state=self.aggregate.random_state)
cobra.fit(X, y, default=False)
cobra.split_data(shuffle_data=True)
for machine in self.aggregate.machines_:
self.aggregate.machines_[machine].fit(cobra.X_k_, cobra.y_k_)
cobra.load_machine(machine, self.aggregate.machines_[machine])
cobra.load_machine_predictions()
X_test, y_test = shuffle(self.X_test, self.y_test, random_state=self.aggregate.random_state)
for machine in cobra.machines_:
MSE[machine].append(mean_squared_error(y_test, cobra.machines_[machine].predict(X_test)))
MSE["COBRA"].append(mean_squared_error(y_test, cobra.predict(X_test)))
data, labels = [], []
for machine in MSE:
data.append(MSE[machine])
labels.append(machine)
if type(self.aggregate) is Ewa:
MSE = {k: [] for k, v in self.aggregate.machines_.items()}
MSE["EWA"] = []
for i in range(0, reps):
ewa = Ewa(random_state=self.random_state, beta=self.aggregate.beta)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_, random_state=self.aggregate.random_state)
ewa.fit(X, y, default=False)
ewa.split_data(shuffle_data=True)
for machine in self.aggregate.machines_:
self.aggregate.machines_[machine].fit(ewa.X_k_, ewa.y_k_)
ewa.load_machine(machine, self.aggregate.machines_[machine])
ewa.load_machine_weights(self.aggregate.beta)
X_test, y_test = shuffle(self.X_test, self.y_test, random_state=self.aggregate.random_state)
for machine in ewa.machines_:
MSE[machine].append(mean_squared_error(y_test, ewa.machines_[machine].predict(X_test)))
MSE["EWA"].append(mean_squared_error(y_test, ewa.predict(X_test)))
data, labels = [], []
for machine in MSE:
data.append(MSE[machine])
labels.append(machine)
if type(self.aggregate) is ClassifierCobra:
errors = {k: [] for k, v in self.aggregate.machines_.items()}
errors["ClassifierCobra"] = []
for i in range(0, reps):
cc = ClassifierCobra(random_state=self.random_state)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_, random_state=self.aggregate.random_state)
cc.fit(X, y, default=False)
cc.split_data(shuffle_data=True)
for machine in self.aggregate.machines_:
self.aggregate.machines_[machine].fit(cc.X_k_, cc.y_k_)
cc.load_machine(machine, self.aggregate.machines_[machine])
cc.load_machine_predictions()
X_test, y_test = shuffle(self.X_test, self.y_test, random_state=self.aggregate.random_state)
for machine in cc.machines_:
errors[machine].append(1 - accuracy_score(y_test, cc.machines_[machine].predict(X_test)))
errors["ClassifierCobra"].append(1 - accuracy_score(y_test, cc.predict(X_test)))
data, labels = [], []
for machine in errors:
data.append(errors[machine])
labels.append(machine)
plt.figure(figsize=(self.plot_size, self.plot_size))
plt.boxplot(data, labels=labels)
plt.show()
if info:
return data
###################################################################### # Like the Cobra estimator, Ewa is also a scikit-learn compatible # estimator. It also fits into the Visualisation class, like demonstrated # in the # `notebook <https://github.com/bhargavvader/pycobra/blob/master/notebooks/visualise.ipynb>`__. # # Predicting? # ~~~~~~~~~~~ # # Like the other scikit-learn predictors, we estimate on data by simply # using the ``predict()`` method. # query = X_test[0].reshape(1, -1) cobra.predict(query) ewa.predict(query) ###################################################################### # Why pycobra? # ~~~~~~~~~~~~ # # There are scikit-learn estimators which already perform well in basic # regression tasks - why use pycobra? The Cobra estimator has the # advantage of a theoretical bound on its performance - this means it is # supposed to perform at least as well as the estimators used to create # it, up to a remainder term which decays to zero. The Ewa estimator also # benefits from similar bounds. # # pycobra also lets you compare the scikit-learn estimators used in the
def optimal_split(self,
X,
y,
split=None,
epsilon=None,
info=False,
graph=False):
"""
Find the optimal combination split (D_k, D_l) for fixed epsilon value for the COBRA predictor.
Parameteres
-----------
X: array-like, [n_features]
Vector for which we want for optimal split.
y: float
Target value for query to compare.
epsilon: float, optional.
fixed epsilon value to help determine optimal machines.
split: list, optional.
D_k, D_l break-up to calculate MSE
info: bool, optional.
Returns MSE dictionary for each split.
graph: bool, optional.
Plots graph of MSE vs split
Returns
-------
MSE: dictionary mapping split with mean squared errors
opt: optimal epsilon value
"""
if epsilon is None:
epsilon = self.aggregate.epsilon
if split is None:
split = [(0.20, 0.80), (0.40, 0.60), (0.50, 0.50), (0.60, 0.40),
(0.80, 0.20)]
MSE = {}
for k, l in split:
machine = Cobra(random_state=self.random_state, epsilon=epsilon)
machine.fit(self.aggregate.X_, self.aggregate.y_, default=False)
machine.split_data(int(k * len(self.aggregate.X_)),
int((k + l) * len(self.aggregate.X_)))
machine.load_default()
machine.load_machine_predictions()
results = machine.predict(X)
MSE[(k, l)] = (mean_squared_error(y, results))
if graph:
import matplotlib.pyplot as plt
ratio, mse = [], []
for value in split:
ratio.append(value[0])
mse.append(MSE[value])
plt.plot(ratio, mse)
if info:
return MSE
opt = min(MSE, key=MSE.get)
return opt, MSE[opt]
def boxplot(self, reps=100, info=False, dataframe=None, kind="normal"):
"""
Plots boxplots of machines.
Parameters
----------
reps: int, optional
Number of times to repeat experiments for boxplot.
info: boolean, optional
Returns data
"""
kwargs = self.kwargs
if dataframe is None:
if type(self.aggregate) is Cobra:
MSE = {k: [] for k, v in self.estimators.items()}
MSE["Cobra"] = []
for i in range(0, reps):
cobra = Cobra(epsilon=self.aggregate.epsilon)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_)
cobra.fit(X, y, default=False)
cobra.split_data(shuffle_data=True)
for machine in self.aggregate.estimators_:
self.aggregate.estimators_[machine].fit(cobra.X_k_, cobra.y_k_)
cobra.load_machine(machine, self.aggregate.estimators_[machine])
cobra.load_machine_predictions()
for machine in self.estimators:
if "Cobra" in machine:
self.estimators[machine].fit(X, y)
else:
self.estimators[machine].fit(cobra.X_k_, cobra.y_k_)
try:
if type(self.estimators[machine]) == KernelCobra:
preds = self.estimators[machine].predict(self.X_test, bandwidth=kwargs["bandwidth_kernel"])
else:
preds = self.estimators[machine].predict(self.X_test)
except KeyError:
preds = self.estimators[machine].predict(self.X_test)
MSE[machine].append(mean_squared_error(self.y_test, preds))
MSE["Cobra"].append(mean_squared_error(self.y_test, cobra.predict(self.X_test)))
try:
dataframe = pd.DataFrame(data=MSE)
except ValueError:
return MSE
if type(self.aggregate) is KernelCobra:
MSE = {k: [] for k, v in self.estimators.items()}
MSE["KernalCobra"] = []
for i in range(0, reps):
kernel = KernelCobra()
X, y = shuffle(self.aggregate.X_, self.aggregate.y_)
kernel.fit(X, y, default=False)
kernel.split_data(shuffle_data=True)
for machine in self.aggregate.estimators_:
self.aggregate.estimators_[machine].fit(kernel.X_k_, kernel.y_k_)
kernel.load_machine(machine, self.aggregate.estimators_[machine])
kernel.load_machine_predictions()
for machine in self.estimators:
if "Cobra" in machine:
self.estimators[machine].fit(X, y)
else:
self.estimators[machine].fit(cobra.X_k_, cobra.y_k_)
try:
if type(self.estimators[machine]) == KernelCobra:
preds = self.estimators[machine].predict(self.X_test, bandwidth=kwargs["bandwidth_kernel"])
else:
preds = self.estimators[machine].predict(self.X_test)
except KeyError:
preds = self.estimators[machine].predict(self.X_test)
MSE[machine].append(mean_squared_error(self.y_test, preds))
MSE["KernelCobra"].append(mean_squared_error(self.y_test, kernel.predict(self.X_test, bandwidth=kwargs[bandwidth_kernel])))
try:
dataframe = pd.DataFrame(data=MSE)
except ValueError:
return MSE
if type(self.aggregate) is Ewa:
MSE = {k: [] for k, v in self.aggregate.estimators_.items()}
MSE["EWA"] = []
for i in range(0, reps):
ewa = Ewa(random_state=self.random_state, beta=self.aggregate.beta)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_, random_state=self.aggregate.random_state)
ewa.fit(X, y, default=False)
ewa.split_data(shuffle_data=True)
for machine in self.estimators:
self.aggregate.estimators_[machine].fit(ewa.X_k_, ewa.y_k_)
ewa.load_machine(machine, self.aggregate.estimators_[machine])
ewa.load_machine_weights(self.aggregate.beta)
X_test, y_test = shuffle(self.X_test, self.y_test, random_state=self.aggregate.random_state)
for machine in self.estimators:
if "EWA" in machine:
self.estimators[machine].fit(X, y)
else:
self.estimators[machine].fit(ewa.X_k_, ewa.y_k_)
try:
if type(self.estimators[machine]) == KernelCobra:
preds = self.estimators[machine].predict(self.X_test, bandwidth=kwargs["bandwidth_kernel"])
else:
preds = self.estimators[machine].predict(self.X_test)
except KeyError:
preds = self.estimators[machine].predict(self.X_test)
MSE[machine].append(mean_squared_error(y_test, preds))
MSE["EWA"].append(mean_squared_error(y_test, ewa.predict(X_test)))
try:
dataframe = pd.DataFrame(data=MSE)
except ValueError:
return MSE
if type(self.aggregate) is ClassifierCobra:
errors = {k: [] for k, v in self.aggregate.estimators_.items()}
errors["ClassifierCobra"] = []
for i in range(0, reps):
cc = ClassifierCobra(random_state=self.random_state)
X, y = shuffle(self.aggregate.X_, self.aggregate.y_, random_state=self.aggregate.random_state)
cc.fit(X, y, default=False)
cc.split_data(shuffle_data=True)
for machine in self.aggregate.estimators_:
self.aggregate.estimators_[machine].fit(cc.X_k_, cc.y_k_)
cc.load_machine(machine, self.aggregate.estimators_[machine])
cc.load_machine_predictions()
X_test, y_test = shuffle(self.X_test, self.y_test, random_state=self.aggregate.random_state)
for machine in self.estimators:
errors[machine].append(1 - accuracy_score(y_test, self.estimators[machine].predict(X_test)))
errors["ClassifierCobra"].append(1 - accuracy_score(y_test, cc.predict(X_test)))
try:
dataframe = pd.DataFrame(data=errors)
except ValueError:
return errors
# code for different boxplot styles using the python graph gallery tutorial:
# https://python-graph-gallery.com/39-hidden-data-under-boxplot/
sns.set(style="whitegrid")
if kind == "normal":
sns.boxplot(data=dataframe)
plt.title("Boxplot")
if kind == "violin":
sns.violinplot(data=dataframe)
plt.title("Violin Plot")
if kind == "jitterplot":
ax = sns.boxplot(data=dataframe)
ax = sns.stripplot(data=dataframe, color="orange", jitter=0.2, size=2.5)
plt.title("Boxplot with jitter", loc="left")
plt.ylabel("Mean Squared Errors")
plt.xlabel("Estimators")
plt.figure(figsize=(self.plot_size, self.plot_size))
plt.show()
if info:
return dataframe
cobra.machines_['random_forest'].predict(query) ###################################################################### # Aggregate! # ---------- # # By using the aggregate function we can combine our predictors. You can # read about the aggregation procedure either in the original COBRA paper # or look around in the source code for the algorithm. # # We start by loading each machine's predictions now. # cobra.load_machine_predictions() cobra.predict(query) Y_test[9] ###################################################################### # Optimizing COBRA # ~~~~~~~~~~~~~~~~ # # To squeeze the best out of COBRA we make use of the COBRA diagnostics # class. With a grid based approach to optimizing hyperparameters, we can # find out the best epsilon value, number of machines (alpha value), and # combination of machines. # ###################################################################### # Let's check the MSE for each of COBRAs machines:
