# import dependencies
from pyomo.environ import Objective, minimize, Constraint
from . import CQER
from .constant import CET_ADDI, FUN_PROD, RTS_VRS
[docs]
class pCQR(CQER.CQR):
"""penalized convex quantile regression (pCQR)
"""
[docs]
def __init__(self, y, x, tau, eta, z=None, cet=CET_ADDI, fun=FUN_PROD, rts=RTS_VRS, penalty=1):
"""pCQR model
Args:
y (float): output variable.
x (float): input variables.
z (float, optional): Contextual variable(s). Defaults to None.
tau (float): quantile.
eta (float): tuning parameter.
cet (String, optional): CET_ADDI (additive composite error term) or CET_MULT (multiplicative composite error term). Defaults to CET_ADDI.
fun (String, optional): FUN_PROD (production frontier) or FUN_COST (cost frontier). Defaults to FUN_PROD.
rts (String, optional): RTS_VRS (variable returns to scale) or RTS_CRS (constant returns to scale). Defaults to RTS_VRS.
penalty (int, optional): penalty=1 (L1 norm), penalty=2 (L2 norm), and penalty=3 (Lipschitz norm). Defaults to 1.
"""
self.eta = eta
CQER.CQR.__init__(self, y, x, tau, z, cet, fun, rts)
if penalty == 1 or penalty == 2:
self.__model__.objective.deactivate()
if penalty == 1:
self.__model__.new_objective = Objective(rule=self.__new_objective_rule(),
sense=minimize,
doc='objective function')
elif penalty == 2:
self.__model__.new_objective = Objective(rule=self.__new_objective_rule2(),
sense=minimize,
doc='objective function')
elif penalty == 3:
self.__model__.lipschitz_norm = Constraint(self.__model__.I,
rule=self.__lipschitz_rule(),
doc='Lipschitz norm')
else:
raise ValueError('Penalty must be 1, 2, or 3.')
def __new_objective_rule(self):
"""Return the proper objective function"""
def objective_rule(model):
return self.tau * sum(model.epsilon_plus[i] for i in model.I) \
+ (1 - self.tau) * sum(model.epsilon_minus[i] for i in model.I) \
+ self.eta * sum(model.beta[ij] for ij in model.I * model.J)
return objective_rule
def __new_objective_rule2(self):
"""Return the proper objective function"""
def objective_rule(model):
return self.tau * sum(model.epsilon_plus[i] for i in model.I) \
+ (1 - self.tau) * sum(model.epsilon_minus[i] for i in model.I) \
+ self.eta * sum(model.beta[ij] **
2 for ij in model.I * model.J)
return objective_rule
def __lipschitz_rule(self):
"""Lipschitz norm"""
def lipschitz_rule(model, i):
return sum(model.beta[i, j] ** 2 for j in model.J) <= self.eta**2
return lipschitz_rule
[docs]
class pCER(CQER.CER):
"""penalized Convex Expectile Regression (pCER)
"""
[docs]
def __init__(self, y, x, tau, eta, z=None, cet=CET_ADDI, fun=FUN_PROD, rts=RTS_VRS, penalty=1):
"""pCER model
Args:
y (float): output variable.
x (float): input variables.
z (float, optional): Contextual variable(s). Defaults to None.
tau (float): expectile.
eta (float): tuning parameter.
cet (String, optional): CET_ADDI (additive composite error term) or CET_MULT (multiplicative composite error term). Defaults to CET_ADDI.
fun (String, optional): FUN_PROD (production frontier) or FUN_COST (cost frontier). Defaults to FUN_PROD.
rts (String, optional): RTS_VRS (variable returns to scale) or RTS_CRS (constant returns to scale). Defaults to RTS_VRS.
penalty (int, optional): penalty=1 (L1 norm), penalty=2 (L2 norm), and penalty=3 (Lipschitz norm). Defaults to 1.
"""
self.eta = eta
CQER.CER.__init__(self, y, x, tau, z, cet, fun, rts)
if penalty == 1 or penalty == 2:
self.__model__.squared_objective.deactivate()
if penalty == 1:
self.__model__.new_objective = Objective(rule=self.__new_squared_objective_rule(),
sense=minimize,
doc='objective function')
elif penalty == 2:
self.__model__.new_objective = Objective(rule=self.__new_squared_objective_rule2(),
sense=minimize,
doc='objective function')
elif penalty == 3:
self.__model__.lipschitz_norm = Constraint(self.__model__.I,
rule=self.__lipschitz_rule(),
doc='Lipschitz norm')
else:
raise ValueError('Penalty must be 1, 2, or 3.')
def __new_squared_objective_rule(self):
"""Return the proper objective function"""
def objective_rule(model):
return self.tau * sum(model.epsilon_plus[i] ** 2 for i in model.I) \
+ (1 - self.tau) * sum(model.epsilon_minus[i] ** 2 for i in model.I) \
+ self.eta * sum(model.beta[ij] for ij in model.I * model.J)
return objective_rule
def __new_squared_objective_rule2(self):
"""Return the proper objective function"""
def objective_rule(model):
return self.tau * sum(model.epsilon_plus[i] ** 2 for i in model.I) \
+ (1 - self.tau) * sum(model.epsilon_minus[i] ** 2 for i in model.I) \
+ self.eta * sum(model.beta[ij] **
2 for ij in model.I * model.J)
return objective_rule
def __lipschitz_rule(self):
"""Lipschitz norm"""
def lipschitz_rule(model, i):
return sum(model.beta[i, j] ** 2 for j in model.J) <= self.eta**2
return lipschitz_rule