def objective(X, Y, C, mu, a, b, e, f, a0, b0, e0, f0):
log2pi = np.log(2*np.pi)
N, D = X.shape
# E(lnX) = digamma(a) - ln(b) for X ~ Gamma(a,b)
E_ln_lambda = digamma(e) - np.log(f)
E_ln_alpha = digamma(a) - np.log(b)
# model likelihood
total = (N/2.0)*(E_ln_lambda - log2pi)
data_total = 0
for i in xrange(N):
delta = Y[i] - X[i].dot(mu)
data_total += delta*delta + X[i].dot(C).dot(X[i])
total -= (float(e)/f)/2.0 * data_total
# print "total after model likelihood:", total
# w likelihood
total -= (D/2.0)*log2pi
for k in xrange(D):
total += 0.5*(E_ln_alpha[k] - (float(a[k])/b[k])*(C[k,k] + mu[k]*mu[k]))
# print "total after w likelihood:", total
# lambda likelihood
total += e0*np.log(f0) - np.log(gamma(e0)) + (e0 - 1)*E_ln_lambda - f0*(float(e)/f)
# print "total after lambda likelihood:", total
# alpha likelihood
for k in xrange(D):
total += a0*np.log(b0) - np.log(gamma(a0)) + (a0 - 1)*E_ln_alpha[k] - b0*(float(a[k])/b[k])
# print "total after alpha likelihood:", total
# entropy
# TODO: calculate this manually
# total -= mvn.entropy(mean=mu, cov=C)
# e1 = mvn.entropy(cov=C)
# e2 = 0.5*np.log( np.linalg.det(2*np.pi*np.e*C) )
# print "e1:", e1, "e2:", e2
# total += 0.5*np.log( np.linalg.det(2*np.pi*np.e*C) )
total += mvn.entropy(cov=C)
# print "det(C):", np.linalg.det(C)
# print "total after lnq(w):", total
# total -= gamma_dist.entropy(e, scale=1.0/f)
# e3 = gamma_dist.entropy(e, scale=1.0/f)
# e4 = -e_ln_q_gamma(e, f)
# print "e3:", e3, "e4:", e4
# assert(np.abs(e3 - e4) < 1e-8)
total += gamma_dist.entropy(e, scale=1.0/f)
# total -= e_ln_q_gamma(e, f)
# print "total after lnq(lambda):", total
for k in xrange(D):
# total -= e_ln_q_gamma(a[k], b[k])
total += gamma_dist.entropy(a[k], scale=1.0/b[k])
return total
def objective(X, Y, C, mu, a, b, e, f, a0, b0, e0, f0):
log2pi = np.log(2*np.pi)
N, D = X.shape
# E(lnX) = digamma(a) - ln(b) for X ~ Gamma(a,b)
E_ln_lambda = digamma(e) - np.log(f)
E_ln_alpha = digamma(a) - np.log(b)
# model likelihood
total = (N/2.0)*(E_ln_lambda - log2pi)
data_total = 0
for i in xrange(N):
delta = Y[i] - X[i].dot(mu)
data_total += delta*delta + X[i].dot(C).dot(X[i])
total -= (float(e)/f)/2.0 * data_total
# print "total after model likelihood:", total
# w likelihood
total -= (D/2.0)*log2pi
for k in xrange(D):
total += 0.5*(E_ln_alpha[k] - (float(a[k])/b[k])*(C[k,k] + mu[k]*mu[k]))
# print "total after w likelihood:", total
# lambda likelihood
total += e0*np.log(f0) - np.log(gamma(e0)) + (e0 - 1)*E_ln_lambda - f0*(float(e)/f)
# print "total after lambda likelihood:", total
# alpha likelihood
for k in xrange(D):
total += a0*np.log(b0) - np.log(gamma(a0)) + (a0 - 1)*E_ln_alpha[k] - b0*(float(a[k])/b[k])
# print "total after alpha likelihood:", total
# entropy
# TODO: calculate this manually
# total -= mvn.entropy(mean=mu, cov=C)
# e1 = mvn.entropy(cov=C)
# e2 = 0.5*np.log( np.linalg.det(2*np.pi*np.e*C) )
# print "e1:", e1, "e2:", e2
# total += 0.5*np.log( np.linalg.det(2*np.pi*np.e*C) )
total += mvn.entropy(cov=C)
# print "det(C):", np.linalg.det(C)
# print "total after lnq(w):", total
# total -= gamma_dist.entropy(e, scale=1.0/f)
# e3 = gamma_dist.entropy(e, scale=1.0/f)
# e4 = -e_ln_q_gamma(e, f)
# print "e3:", e3, "e4:", e4
# assert(np.abs(e3 - e4) < 10e-8)
total += gamma_dist.entropy(e, scale=1.0/f)
# total -= e_ln_q_gamma(e, f)
# print "total after lnq(lambda):", total
for k in xrange(D):
# total -= e_ln_q_gamma(a[k], b[k])
total += gamma_dist.entropy(a[k], scale=1.0/b[k])
return total
# total += 0.5*np.log( np.linalg.det(2*np.pi*np.e*C) )
total += mvn.entropy(cov=C)
# print "det(C):", np.linalg.det(C)
# print "total after lnq(w):", total
# total -= gamma_dist.entropy(e, scale=1.0/f)
# e3 = gamma_dist.entropy(e, scale=1.0/f)
# e4 = -e_ln_q_gamma(e, f)
# print "e3:", e3, "e4:", e4
<<<<<<< HEAD
# assert(np.abs(e3 - e4) < 10e-8)
=======
# assert(np.abs(e3 - e4) < 1e-8)
>>>>>>> upstream/master
total += gamma_dist.entropy(e, scale=1.0/f)
# total -= e_ln_q_gamma(e, f)
# print "total after lnq(lambda):", total
for k in xrange(D):
# total -= e_ln_q_gamma(a[k], b[k])
total += gamma_dist.entropy(a[k], scale=1.0/b[k])
return total
def run(num=1, T=500):
X = pd.read_csv('X_set%s.csv' % num, header=None).as_matrix()
Y = pd.read_csv('y_set%s.csv' % num, header=None).as_matrix().flatten()
Z = pd.read_csv('z_set%s.csv' % num, header=None).as_matrix().flatten()
N, D = X.shape
print X.shape, Y.shape, Z.shape
def entropy(self, n, p):
ent = gamma.entropy(self, n, p)
return ent