def exact_moment_equations(self, maxdeg):
"""
return scipy moment equation expressions
"""
D = self.d
ws, pis = self.betas, self.weights
deg_x, deg_b = maxdeg
sigma = self.sigma_val
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas
for b in xrange(1, deg_b + 1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = expected_gaussian_moments(sigma, alphas_)
moments_y = exact_moments_y(ws, pis, moments_x, alphabs)
constrs = []
con = {}
for b in xrange(1, deg_b + 1):
for alpha in dominated_elements((deg_x for _ in xrange(D))):
eqn = describe_moment_polynomial(self.sym_betas, moments_x,
moments_y[(alpha, b)], alpha,
b)
con[(alpha, b)] = eqn
constrs.append(eqn)
return constrs, con
def empirical_moment_equations(self, xs, maxdeg):
"""
return scipy moment equation expressions
"""
xs, ys = xs
D = self.d
ws, pis = self.betas, self.weights
deg_x, deg_b = maxdeg
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas
for b in xrange(1, deg_b + 1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = compute_expected_moments(xs, alphas_)
moments_y = compute_expected_moments_y(ys, xs, alphabs)
constrs = []
for b in xrange(1, deg_b + 1):
for alpha in dominated_elements((deg_x for _ in xrange(D))):
constrs.append(
describe_moment_polynomial(self.sym_betas, moments_x,
moments_y[(alpha, b)], alpha,
b))
return constrs
def exact_moments(self, terms):
"""
Get the exact moments corresponding to a particular term
"""
terms = [
sympify(term) if isinstance(term, str) else term for term in terms
]
# Get max degree of b and x in terms
D = self.d
ws, pis = self.betas, self.weights
deg_b = max(self._y_power(term) for term in terms)
deg_x = max(max(self._x_power(term) for term in terms))
sigma = self.sigma_val
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas
for b in xrange(1, deg_b + 1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = expected_gaussian_moments(sigma, alphas_)
moments_y = exact_moments_y(ws, pis, moments_x, alphabs)
moment = {term: 0. for term in terms}
for term in terms:
b = self._y_power(term)
alpha = self._x_power(term)
moment[term] = moments_y[(alpha, b)]
return moment
def empirical_moments(self, xs, terms):
"""
Get the exact moments corresponding to a particular term
"""
terms = [
sympify(term) if isinstance(term, str) else term for term in terms
]
xs, ys = xs
D = self.d
deg_b = max(self._y_power(term) for term in terms)
deg_x = max(max(self._x_power(term) for term in terms))
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas
for b in xrange(1, deg_b + 1)]
moments_y = compute_expected_moments_y(ys, xs, alphabs)
moment = {term: 0. for term in terms}
for term in terms:
alpha, b = self._x_power(term), self._y_power(term)
moment[term] = moments_y[(alpha, b)]
return moment
def exact_moments(self, terms):
"""
Get the exact moments corresponding to a particular term
"""
terms = [sympify(term) if isinstance(term, str) else term for term in terms]
# Get max degree of b and x in terms
D = self.d
ws, pis = self.betas, self.weights
deg_b = max(self._y_power(term) for term in terms)
deg_x = max(max(self._x_power(term) for term in terms))
sigma = self.sigma_val
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas for b in xrange(1,deg_b+1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = expected_gaussian_moments(sigma, alphas_)
moments_y = exact_moments_y(ws, pis, moments_x, alphabs)
moment = {term : 0. for term in terms}
for term in terms:
b = self._y_power(term)
alpha = self._x_power(term)
moment[term] = moments_y[(alpha,b)]
return moment
def observed_monomials(self, maxdeg):
"""
return scipy moment monomials
"""
D = self.d
deg_x, deg_b = maxdeg
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas for b in xrange(1,deg_b+1)]
x = [sympify("x%d"%i) for i in xrange(D)]
y = sympify("y")
terms = map(sympify, [monomial(x, alpha) * y**b for (alpha,b) in alphabs])
return terms
def empirical_moment_equations(self, xs, maxdeg):
"""
return scipy moment equation expressions
"""
xs, ys = xs
D = self.d
ws, pis = self.betas, self.weights
deg_x, deg_b = maxdeg
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas for b in xrange(1,deg_b+1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = compute_expected_moments(xs, alphas_)
moments_y = compute_expected_moments_y(ys, xs, alphabs)
constrs = []
for b in xrange(1, deg_b+1):
for alpha in dominated_elements((deg_x for _ in xrange(D))):
constrs.append(describe_moment_polynomial(self.sym_betas, moments_x, moments_y[(alpha, b)], alpha, b))
return constrs
def empirical_moments(self, xs, terms):
"""
Get the exact moments corresponding to a particular term
"""
terms = [sympify(term) if isinstance(term, str) else term for term in terms]
xs, ys = xs
D = self.d
deg_b = max(self._y_power(term) for term in terms)
deg_x = max(max(self._x_power(term) for term in terms))
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas for b in xrange(1,deg_b+1)]
moments_y = compute_expected_moments_y(ys, xs, alphabs)
moment = {term : 0. for term in terms}
for term in terms:
alpha, b = self._x_power(term), self._y_power(term)
moment[term] = moments_y[(alpha,b)]
return moment
def observed_monomials(self, maxdeg):
"""
return scipy moment monomials
"""
D = self.d
deg_x, deg_b = maxdeg
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas
for b in xrange(1, deg_b + 1)]
x = [sympify("x%d" % i) for i in xrange(D)]
y = sympify("y")
terms = map(sympify,
[monomial(x, alpha) * y**b for (alpha, b) in alphabs])
return terms
def exact_moment_equations(self, maxdeg):
"""
return scipy moment equation expressions
"""
D = self.d
ws, pis = self.betas, self.weights
deg_x, deg_b = maxdeg
sigma = self.sigma_val
alphas = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
alphas = list(dominated_elements((deg_x for _ in xrange(D))))
alphabs = [(alpha, b) for alpha in alphas for b in xrange(1,deg_b+1)]
alphas_ = list(dominated_elements((deg_x + deg_b for _ in xrange(D))))
moments_x = expected_gaussian_moments(sigma, alphas_)
moments_y = exact_moments_y(ws, pis, moments_x, alphabs)
constrs = []
con = {}
for b in xrange(1, deg_b+1):
for alpha in dominated_elements((deg_x for _ in xrange(D))):
eqn = describe_moment_polynomial(self.sym_betas, moments_x, moments_y[(alpha, b)], alpha, b)
con[(alpha,b)] = eqn
constrs.append(eqn)
return constrs, con