# import dependencies
from pyomo.environ import ConcreteModel, Set, Var, Objective, minimize, Constraint
from pyomo.core.expr.numvalue import NumericValue
from .constant import FUN_PROD, FUN_COST, RTS_VRS
from . import CNLSDDF, CQER
from .utils import tools
[docs]
class CQRDDF(CNLSDDF.CNLSDDF, CQER.CQR):
"""Convex quantile regression with directional distance function
"""
[docs]
def __init__(self, y, x, b=None, gy=[1], gx=[1], gb=None, fun=FUN_PROD, tau=0.5):
"""CQR DDF
Args:
y (float): output variable.
x (float): input variables.
b (float), optional): undesirable output variables. Defaults to None.
gy (list, optional): output directional vector. Defaults to [1].
gx (list, optional): input directional vector. Defaults to [1].
gb (list, optional): undesirable output directional vector. Defaults to None.
fun (String, optional): FUN_PROD (production frontier) or FUN_COST (cost frontier). Defaults to FUN_PROD.
tau (float, optional): quantile. Defaults to 0.5.
"""
# TODO(error/warning handling): Check the configuration of the model exist
self.y, self.x, self.b, self.gy, self.gx, self.gb = tools.assert_valid_direciontal_data(
y, x, b, gy, gx, gb)
self.tau, self.fun, self.rts = tau, fun, RTS_VRS
# Initialize the CQRDDF model
self.__model__ = ConcreteModel()
# Initialize the sets
self.__model__.I = Set(initialize=range(len(self.y)))
self.__model__.J = Set(initialize=range(len(self.x[0])))
self.__model__.Q = Set(initialize=range(len(self.y[0])))
# Initialize the variables
self.__model__.alpha = Var(self.__model__.I, doc='alpha')
self.__model__.beta = Var(
self.__model__.I, self.__model__.J, bounds=(0.0, None), doc='beta')
self.__model__.gamma = Var(
self.__model__.I, self.__model__.Q, bounds=(0.0, None), doc='gamma')
self.__model__.epsilon = Var(self.__model__.I, doc='residuals')
self.__model__.epsilon_plus = Var(
self.__model__.I, bounds=(0.0, None), doc='positive error term')
self.__model__.epsilon_minus = Var(
self.__model__.I, bounds=(0.0, None), doc='negative error term')
if type(self.b) != type(None):
self.__model__.L = Set(initialize=range(len(self.b[0])))
self.__model__.delta = Var(
self.__model__.I, self.__model__.L, doc='delta')
self.__model__.objective = Objective(rule=self._CQR__objective_rule(),
sense=minimize,
doc='objective function')
self.__model__.error_decomposition = Constraint(self.__model__.I,
rule=self._CQR__error_decomposition(),
doc='decompose error term')
self.__model__.regression_rule = Constraint(self.__model__.I,
rule=self.__regression_rule(),
doc='regression equation')
self.__model__.translation_rule = Constraint(self.__model__.I,
rule=self._CNLSDDF__translation_property(),
doc='translation property')
self.__model__.afriat_rule = Constraint(self.__model__.I,
self.__model__.I,
rule=self.__afriat_rule(),
doc='afriat inequality')
# Optimize model
self.optimization_status, self.problem_status = 0, 0
def __regression_rule(self):
"""Return the proper regression constraint"""
if type(self.b) == type(None):
def regression_rule(model, i):
return sum(model.gamma[i, q] * self.y[i][q] for q in model.Q) \
== model.alpha[i] \
+ sum(model.beta[i, j] * self.x[i][j] for j in model.J) \
+ model.epsilon[i]
return regression_rule
def regression_rule(model, i):
return sum(model.gamma[i, q] * self.y[i][q] for q in model.Q) \
== model.alpha[i] \
+ sum(model.beta[i, j] * self.x[i][j] for j in model.J) \
+ sum(model.delta[i, l] * self.b[i][l] for l in model.L) \
+ model.epsilon[i]
return regression_rule
def __afriat_rule(self):
"""Return the proper afriat inequality constraint"""
if self.fun == FUN_PROD:
__operator = NumericValue.__le__
elif self.fun == FUN_COST:
__operator = NumericValue.__ge__
if type(self.b) == type(None):
def afriat_rule(model, i, h):
if i == h:
return Constraint.Skip
return __operator(model.alpha[i]
+ sum(model.beta[i, j] * self.x[i][j]
for j in model.J)
- sum(model.gamma[i, q] * self.y[i][q]
for q in model.Q),
model.alpha[h]
+ sum(model.beta[h, j] * self.x[i][j]
for j in model.J)
- sum(model.gamma[h, q] * self.y[i][q] for q in model.Q))
return afriat_rule
def afriat_rule(model, i, h):
if i == h:
return Constraint.Skip
return __operator(model.alpha[i]
+ sum(model.beta[i, j] * self.x[i][j]
for j in model.J)
+ sum(model.delta[i, l] * self.b[i][l]
for l in model.L)
- sum(model.gamma[i, q] * self.y[i][q]
for q in model.Q),
model.alpha[h]
+ sum(model.beta[h, j] * self.x[i][j]
for j in model.J)
+ sum(model.delta[h, l] * self.b[i][l]
for l in model.L)
- sum(model.gamma[h, q] * self.y[i][q] for q in model.Q))
return afriat_rule
[docs]
class CERDDF(CQRDDF):
"""Convex expectile regression with DDF formulation
"""
[docs]
def __init__(self, y, x, b=None, gy=[1], gx=[1], gb=None, fun=FUN_PROD, tau=0.5):
"""CER DDF
Args:
y (float): output variable.
x (float): input variables.
b (float), optional): undesirable output variables. Defaults to None.
gy (list, optional): output directional vector. Defaults to [1].
gx (list, optional): input directional vector. Defaults to [1].
gb (list, optional): undesirable output directional vector. Defaults to None.
fun (String, optional): FUN_PROD (production frontier) or FUN_COST (cost frontier). Defaults to FUN_PROD.
tau (float, optional): expectile. Defaults to 0.5.
"""
super().__init__(y, x, b, gy, gx, gb, fun, tau)
self.__model__.objective.deactivate()
self.__model__.squared_objective = Objective(
rule=self.__squared_objective_rule(), sense=minimize, doc='squared objective rule')
def __squared_objective_rule(self):
def squared_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)
return squared_objective_rule