def compute_pder(hyperparameters, i, x, z):
sigma, l = hyperparameters[0], hyperparameters[1]
tao = x - z
if i==0:
return 2*sigma*exp(-dot(tao.T, tao)/(2*l*l))
elif i==1:
r_squared = dot(tao.T, tao)
return (r_squared/l**3)*(sigma**2)*exp(-r_squared/(2*l*l))
else:
#TODO: controlar error
# print 'error'
return None
def compute_pder(hyperparameters, i, x, z):
sigma, l = hyperparameters[0], hyperparameters[1]
tao = x - z
if i == 0:
return 2 * sigma * exp(-dot(tao.T, tao) / (2 * l * l))
elif i == 1:
r_squared = dot(tao.T, tao)
return (r_squared / l**3) * (sigma**2) * exp(-r_squared /
(2 * l * l))
else:
#TODO: controlar error
# print 'error'
return None
def cov_function(hyperparameters, x, z):
# TODO:
# Comprobar que el numero de hip. es correcto
# TODO:
# Una posible mejora: hacer que todos los hypp
# puedan tomar cualquier valor real
# (p.ej. si un hyp puede tomar cualquier valor
# pos considerar el logaritmo de dicho hypp).
P, Q = self.P, self.Q
w = hyperparameters[0:Q]
mu = [[]] * Q
v = [[]] * Q
for q in range(Q):
mu[q] = hyperparameters[Q + q * P:Q + (q + 1) * P]
for q in range(Q):
v[q] = hyperparameters[Q * (1 + P) + q * P:Q * (1 + P) +
(q + 1) * P]
tao = x - z
sum = 0
for q in range(Q):
prod = w[q]
prod *= cos(TWOPI * dot(tao.T, mu[q]))
arg_exp = 0
for p in range(P):
arg_exp += ((tao[p, 0]**2) * v[q][p])
arg_exp *= (MTWOPISQ)
prod *= exp(arg_exp)
sum += prod
# TODO:
# Recomprobar que la formulita
# esta bien copiada.
return sum
def gpc_find_mode(self, tasks, hyperparameters):
try:
num_tasks = len(tasks)
# TODO: modificar esta linea (puede fallar)
n = num_cols(self.X[0])
f = np.matrix([0] * n * num_tasks).reshape((n, num_tasks))
self.mlog_ML = 0
K = [[]] * num_tasks
for task in range(num_tasks):
I = np.matrix(np.eye(n))
y = self.Y[:, task]
while True:
f_old = np.copy(f[:, task])
W = -self.sigmoid.hessian_log_likelihood(y, f[:, task])
K[task] = self.cov_function.cov_matrix(
hyperparameters, self.X[task])
sqrt_W = np.sqrt(W)
L = cholesky(I + sqrt_W * K[task] * sqrt_W)
b = W * f[:, task] + self.sigmoid.gradient_log_likelihood(
y, f[:, task])
a = b - sqrt_W * backslash(
L.T, backslash(L, sqrt_W * K[task] * b))
f[:, task] = K[task] * a
if norm(f[:, task] - f_old) < 0.01:
break
self.mlog_ML += (0.5 * dot(a.T, f[:, task]) -
self.sigmoid.log_likelihood(y, f[:, task]) +
sum(log(np.diag(L))))
self.f, self.a, self.sqrt_W, self.K, self.I = f, a, sqrt_W, K, I
return f, self.mlog_ML
except LinAlgError:
return None, np.inf
def cov_function(hyperparameters, x, z):
# TODO:
# Comprobar que el numero de hip. es correcto
# TODO:
# Una posible mejora: hacer que todos los hypp
# puedan tomar cualquier valor real
# (p.ej. si un hyp puede tomar cualquier valor
# pos considerar el logaritmo de dicho hypp).
P, Q = self.P, self.Q
w = hyperparameters[0:Q]
mu = [[]]*Q
v = [[]]*Q
for q in range(Q):
mu[q] = hyperparameters[Q+q*P:Q+(q+1)*P]
for q in range(Q):
v[q] = hyperparameters[Q*(1+P)+q*P:Q*(1+P)+(q+1)*P]
tao = x - z
sum = 0
for q in range(Q):
prod = w[q]
prod *= cos(TWOPI*dot(tao.T, mu[q]))
arg_exp = 0
for p in range(P):
arg_exp += ((tao[p,0]**2)*v[q][p])
arg_exp *= (MTWOPISQ)
prod *= exp(arg_exp)
sum += prod
# TODO:
# Recomprobar que la formulita
# esta bien copiada.
return sum
def gpc_find_mode(self, tasks, hyperparameters):
try:
num_tasks = len(tasks)
# TODO: modificar esta linea (puede fallar)
n = num_cols(self.X[0])
f = np.matrix([0]*n*num_tasks).reshape((n, num_tasks))
self.mlog_ML = 0
K = [[]]*num_tasks
for task in range(num_tasks):
I = np.matrix(np.eye(n))
y = self.Y[:,task]
while True:
f_old = np.copy(f[:,task])
W = -self.sigmoid.hessian_log_likelihood(y, f[:,task])
K[task] = self.cov_function.cov_matrix(hyperparameters, self.X[task])
sqrt_W = np.sqrt(W)
L = cholesky(I + sqrt_W*K[task]*sqrt_W)
b = W*f[:,task] + self.sigmoid.gradient_log_likelihood(y, f[:,task])
a = b - sqrt_W*backslash(L.T, backslash(L, sqrt_W*K[task]*b))
f[:,task] = K[task]*a
if norm(f[:,task]-f_old) < 0.01:
break
self.mlog_ML += (0.5*dot(a.T, f[:,task]) - self.sigmoid.log_likelihood(y, f[:,task]) + sum(log(np.diag(L))))
self.f, self.a, self.sqrt_W, self.K, self.I = f, a, sqrt_W, K, I
return f, self.mlog_ML
except LinAlgError:
return None, np.inf
def compute_pder(hyperparameters, i, x, z):
w, mu, v = hyperparameters_SMK(P, Q, hyperparameters)
tao = x - z
if i < Q:
# El parametro es una w_q
# TODO: Copypasteado (se podria hacer mejor)
q = i
prod = cos(TWOPI * dot(tao.T, mu[q]))
arg_exp = 0
for p in range(P):
arg_exp += ((tao[p, 0]**2) * v[q][p])
arg_exp *= (MTWOPISQ)
prod *= exp(arg_exp)
return prod
elif i < Q * (P + 1):
q = (i - Q) / P
p = (i - Q) % P
prod = -TWOPI * (tao[p, 0]**2) * w[q]
arg_exp = 0
for j in range(P):
arg_exp += ((tao[j, 0]**2) * v[q][p])
arg_exp *= MTWOPISQ
prod *= exp(arg_exp)
prod *= sin(TWOPI * dot(tao.T, mu[q]))
return prod
elif i < Q * (2 * P + 1):
q = (i - Q * (P + 1)) / P
p = (i - Q) % P
prod = MTWOPISQ * tao[p, 0] * w[q]
prod *= cos(TWOPI * dot(tao.T, mu[q]))
arg_exp = 0
for j in range(P):
arg_exp += ((tao[j, 0]**2) * v[q][p])
arg_exp *= MTWOPISQ
prod *= exp(arg_exp)
return prod
else:
# TODO: Implementar esto
# print 'Sin implementar (oops)'
return None
def compute_pder(hyperparameters, i, x, z):
w, mu, v = hyperparameters_SMK(P, Q, hyperparameters)
tao = x - z
if i < Q:
# El parametro es una w_q
# TODO: Copypasteado (se podria hacer mejor)
q = i
prod = cos(TWOPI*dot(tao.T, mu[q]))
arg_exp = 0
for p in range(P):
arg_exp += ((tao[p,0]**2)*v[q][p])
arg_exp *= (MTWOPISQ)
prod *= exp(arg_exp)
return prod
elif i < Q*(P+1):
q = (i-Q)/P
p = (i-Q)%P
prod = -TWOPI*(tao[p, 0]**2)*w[q]
arg_exp = 0
for j in range(P):
arg_exp += ((tao[j,0]**2)*v[q][p])
arg_exp *= MTWOPISQ
prod *= exp(arg_exp)
prod *= sin(TWOPI*dot(tao.T, mu[q]))
return prod
elif i < Q*(2*P+1):
q = (i-Q*(P+1))/P
p = (i-Q)%P
prod = MTWOPISQ*tao[p, 0]*w[q]
prod *= cos(TWOPI*dot(tao.T, mu[q]))
arg_exp = 0
for j in range(P):
arg_exp += ((tao[j,0]**2)*v[q][p])
arg_exp *= MTWOPISQ
prod *= exp(arg_exp)
return prod
else:
# TODO: Implementar esto
# print 'Sin implementar (oops)'
return None
def gpc_gradient_mlogML(self, hyperparameters, tasks):
f, a, sqrt_W, K, I = self.f, self.a, self.sqrt_W, self.K, self.I
num_tasks = len(tasks)
num_hyper = len(hyperparameters)
gradient = np.array([0.0]*num_hyper)
for task in range(num_tasks):
y = self.Y[:,task]
self.L = cholesky(I + sqrt_W*K[task]*sqrt_W)
L = self.L
R = sqrt_W*backslash(L.T, backslash(L, sqrt_W))
C = backslash(L, sqrt_W*K[task])
s2 = np.matrix(np.diag(np.diag(K[task]) - np.diag(C.T*C)))*self.sigmoid.der3_log_likelihood(y, f[:,task])
for j in range(num_hyper):
C = self.cov_function.pder_matrix(hyperparameters, j, self.X[task])
s1 = 0.5*(a.T*C*a - trace_of_prod(R, C))[0, 0]
b = C*self.sigmoid.gradient_log_likelihood(y, f[:,task])
s3 = b - K[task]*R*b
gradient[j] += (-s1 -dot(s2.T,s3))
return gradient
def gpc_gradient_mlogML(self, hyperparameters, tasks):
f, a, sqrt_W, K, I = self.f, self.a, self.sqrt_W, self.K, self.I
num_tasks = len(tasks)
num_hyper = len(hyperparameters)
gradient = np.array([0.0] * num_hyper)
for task in range(num_tasks):
y = self.Y[:, task]
self.L = cholesky(I + sqrt_W * K[task] * sqrt_W)
L = self.L
R = sqrt_W * backslash(L.T, backslash(L, sqrt_W))
C = backslash(L, sqrt_W * K[task])
s2 = np.matrix(np.diag(np.diag(K[task]) - np.diag(C.T * C))
) * self.sigmoid.der3_log_likelihood(y, f[:, task])
for j in range(num_hyper):
C = self.cov_function.pder_matrix(hyperparameters, j,
self.X[task])
s1 = 0.5 * (a.T * C * a - trace_of_prod(R, C))[0, 0]
b = C * self.sigmoid.gradient_log_likelihood(y, f[:, task])
s3 = b - K[task] * R * b
gradient[j] += (-s1 - dot(s2.T, s3))
return gradient
def compute_pder(hyperparameters, i, x, z):
l = hyperparameters[0]
return dot(x.T, z) / l
def cov_function(hyperparameters, x, z):
l = hyperparameters[0]
return log(l) * dot(x.T, z)
def cov_function(hyperparameters, x, z):
sigma, l = hyperparameters[0], hyperparameters[1]
tao = x - z
return (sigma**2) * exp(-dot(tao.T, tao) / (2 * l * l))
def compute_pder(hyperparameters, i, x, z):
l = hyperparameters[0]
return dot(x.T, z)/l
def cov_function(hyperparameters, x, z):
l = hyperparameters[0]
return log(l)*dot(x.T, z)
def cov_function(hyperparameters, x, z):
sigma, l = hyperparameters[0], hyperparameters[1]
tao = x - z
return (sigma**2)*exp(-dot(tao.T, tao)/(2*l*l))