def describe_moment_polynomial(syms, moments_x, moment_y, alpha, b):
"""
Computes the moment polynomial for E[x^alpha, y^b]
"""
D = len(syms)
expr = -moment_y
coeffs = sp.ntheory.multinomial_coefficients(D, b)
for beta in partitions(D, b):
expr += coeffs[beta] * monomial(syms, beta) * moments_x[tuple_add(alpha, beta)]
return expr
def describe_moment_polynomial(syms, moments_x, moment_y, alpha, b):
"""
Computes the moment polynomial for E[x^alpha, y^b]
"""
D = len(syms)
expr = -moment_y
coeffs = sp.ntheory.multinomial_coefficients(D, b)
for beta in partitions(D, b):
expr += coeffs[beta] * monomial(syms, beta) * moments_x[tuple_add(
alpha, beta)]
return expr
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 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 compute_expected_moments_y(ys, xs, alphabs):
moments = {(alpha, b): 0. for alpha, b in alphabs}
for alpha, b in alphabs:
moments[(alpha, b)] = float((monomial(xs.T, alpha) * ys**b).mean())
return moments
def compute_expected_moments(xs, alphas):
moments = {alpha: 0. for alpha in alphas}
for alpha in alphas:
m = monomial(xs.T, alpha)
moments[alpha] = m if isinstance(m, float) else float(m.mean())
return moments
def evaluate_mixture(ws, pis, beta):
r"""
Compute E_\pi[w^beta]
"""
return sum(pi * monomial(w, beta) for w, pi in zip(ws.T, pis))
def compute_expected_moments_y(ys, xs, alphabs):
moments = {(alpha, b) : 0. for alpha, b in alphabs}
for alpha, b in alphabs:
moments[(alpha,b)] = float((monomial(xs.T, alpha) * ys**b).mean())
return moments
def compute_expected_moments(xs, alphas):
moments = {alpha : 0. for alpha in alphas}
for alpha in alphas:
m = monomial(xs.T, alpha)
moments[alpha] = m if isinstance(m,float) else float(m.mean())
return moments
def evaluate_mixture(ws, pis, beta):
r"""
Compute E_\pi[w^beta]
"""
return sum(pi * monomial(w, beta) for w, pi in zip(ws.T, pis))
