def statistics(self, y, x, vectorize=False):
if isinstance(y, np.ndarray) and isinstance(x, np.ndarray):
idx = np.logical_and(~np.isnan(y).any(axis=1),
~np.isnan(x).any(axis=1))
y, x = y[idx], x[idx]
if self.affine:
x = np.hstack((x, np.ones((x.shape[0], 1))))
if vectorize:
contract = 'nk,nh->nkh'
n = np.ones((y.shape[0], ))
else:
contract = 'nk,nh->kh'
n = y.shape[0]
yxT = np.einsum(contract, y, x, optimize=True)
xxT = np.einsum(contract, x, x, optimize=True)
yyT = np.einsum(contract, y, y, optimize=True)
return Stats([yxT, xxT, yyT, n])
else:
func = partial(self.statistics, vectorize=vectorize)
stats = list(map(func, y, x))
return stats if vectorize else reduce(add, stats)
def weighted_statistics(self, y, x, posterior):
if isinstance(y, np.ndarray) and isinstance(x, np.ndarray)\
and not isinstance(posterior, list):
idx = np.logical_and(~np.isnan(y).any(axis=1),
~np.isnan(x).any(axis=1))
y, x = y[idx], x[idx]
if self.affine:
x = np.hstack((x, np.ones((x.shape[0], 1))))
yyT = y.T @ y
xxT = x.T @ x
xyT = x.T @ y
matnorm_stats = np.array([
posterior.M @ self.matnorm.K, self.matnorm.K,
np.trace(self.matnorm.K @ np.linalg.inv(posterior.K)) *
np.linalg.inv(posterior.V) +
posterior.M @ self.matnorm.K @ posterior.M.T, x.shape[1]
])
lingauss_stats = np.array([
0., 0., yyT - 2. * posterior.M @ xyT +
posterior.M @ xxT @ posterior.M.T +
np.trace(xxT @ np.linalg.inv(posterior.K)) *
np.linalg.inv(posterior.V), x.shape[0]
])
stats = matnorm_stats + lingauss_stats
return Stats(stats)
def weighted_statistics(self, y, x, weights, vectorize=False):
if isinstance(y, np.ndarray) and isinstance(x, np.ndarray):
idx = np.logical_and(~np.isnan(y).any(axis=1),
~np.isnan(x).any(axis=1))
y, x, weights = y[idx], x[idx], weights[idx]
if self.affine:
x = np.hstack((x, np.ones((x.shape[0], 1))))
if vectorize:
c0, c1 = 'nk,n,nh->nkh', 'nk,n,nk->nk'
n = weights
else:
c0, c1 = 'nk,n,nh->kh', 'nk,n,nk->k'
n = np.sum(weights)
yxT = np.einsum(c0, y, weights, x, optimize=True)
xxT = np.einsum(c0, x, weights, x, optimize=True)
yy = np.einsum(c1, y, weights, y, optimize=True)
return Stats([yxT, xxT, yy, n])
else:
func = partial(self.weighted_statistics, vectorize=vectorize)
stats = list(map(func, y, x, weights))
return stats if vectorize else reduce(add, stats)
def statistics(self, y, x):
if isinstance(y, np.ndarray) and isinstance(x, np.ndarray):
idx = np.logical_and(~np.isnan(y).any(axis=1),
~np.isnan(x).any(axis=1))
y, x = y[idx], x[idx]
if self.affine:
x = np.hstack((x, np.ones((x.shape[0], 1))))
yyT = y.T @ y
xxT = x.T @ x
xyT = x.T @ y
matnorm_stats = np.array([
self.lingauss.A @ self.matnorm.K, self.matnorm.K,
self.lingauss.A @ self.matnorm.K @ self.lingauss.A.T,
x.shape[1]
])
lingauss_stats = np.array([
0., 0., yyT - 2. * self.lingauss.A @ xyT +
self.lingauss.A @ xxT @ self.lingauss.A.T, x.shape[0]
])
stats = matnorm_stats + lingauss_stats
return Stats(stats)
def statistics(self, data):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
logx = np.log(data)
x = data
n = np.ones((self.data.shape[0], ))
return Stats([logx, n, x, n])
else:
return list(map(self.statistics, data))
def statistics(self, data):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
x = data
logdet_x = np.linalg.slogdet(data)[1]
n = np.ones((data.shape[0], ))
return Stats([x, n, logdet_x, n])
else:
return list(map(self.statistics, data))
def weighted_statistics(self, data, weights):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
weights = weights[idx]
logx = np.einsum('n,nk->nk', weights, np.log(data))
x = np.einsum('n,nk->nk', weights, data)
n = weights
return Stats([logx, n, x, n])
else:
return list(map(self.weighted_statistics, data, weights))
def weighted_statistics(self, data, weights):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
weights = weights[idx]
x = np.einsum('n,nkh->nkh', weights, data)
logdet_x = np.einsum('n,nkh->nkh', weights,
np.linalg.slogdet(data)[1])
n = weights
return Stats([x, n, logdet_x, n])
else:
return list(map(self.weighted_statistics, data, weights))
def std_to_nat(params):
# The definition of stats is slightly different
# from literatur to make posterior updates easy
# Assumed stats
# stats = [lmbda @ A,
# -0.5 * lmbda @ AAT,
# -0.5 * lmbda,
# 0.5 * logdet_lmbda]
M = params[0].dot(params[1])
K = params[1]
psi = invpd(params[2]) + params[0].dot(K).dot(params[0].T)
nu = params[3] - params[2].shape[0] - 1 + params[0].shape[-1]
return Stats([M, K, psi, nu])
def std_to_nat(params):
# The definition of stats is slightly different
# from literatur to make posterior updates easy
# Assumed stats
# stats = [lmbdas * x,
# -0.5 * lmbdas * xx,
# 0.5 * log_lmbdas
# -0.5 * lmbdas]
mu = params[1] * params[0]
kappas = params[1]
alphas = 2. * params[2] - 1.
betas = 2. * params[3] + params[1] * params[0]**2
return Stats([mu, kappas, alphas, betas])
def statistics(self, data, labels, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
labels = labels[idx]
stats = [
c.statistics(data[labels == idx, :], vectorize)
for idx, c in enumerate(self.components)
]
return Stats(stats)
else:
func = partial(self.statistics, vectorize=vectorize)
stats = list(map(func, data, labels))
return list(stats) if vectorize else reduce(add, stats)
def weighted_statistics(self, data, weights, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
weights = weights[idx]
stats = [
c.weighted_statistics(data, weights[:, idx], vectorize)
for idx, c in enumerate(self.components)
]
return Stats(stats)
else:
func = partial(self.weighted_statistics, vectorize=vectorize)
stats = map(func, data, weights)
return list(stats) if vectorize else reduce(add, stats)
def std_to_nat(params):
# The definition of stats is slightly different
# from literatur to make posterior updates easy
# Assumed stats
# stats = [lmbda @ x,
# -0.5 * lmbda @ xxT,
# -0.5 * lmbda,
# 0.5 * logdet_lmbda]
mu = params[1] * params[0]
kappa = params[1]
psi = invpd(params[2]) \
+ params[1] * np.outer(params[0], params[0])
nu = params[3] - params[2].shape[0]
return Stats([mu, kappa, psi, nu])
def statistics(self, data, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
x = data
xx = np.einsum('nk,nk->nk', data, data)
n = np.ones((data.shape[0], ))
if not vectorize:
x = np.sum(x, axis=0)
xx = np.sum(xx, axis=0)
n = np.sum(n, axis=0)
return Stats([x, n, n, xx])
else:
func = partial(self.statistics, vectorize=vectorize)
stats = list(map(func, data))
return stats if vectorize else reduce(add, stats)
def statistics(self, data, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
if vectorize:
c0, c1 = 'nk->nk', 'nk,nh->nkh'
n = np.ones((data.shape[0], ))
else:
c0, c1 = 'nk->k', 'nk,nh->kh'
n = data.shape[0]
x = np.einsum(c0, data, optimize=True)
xxT = np.einsum(c1, data, data, optimize=True)
return Stats([x, n, xxT, n])
else:
func = partial(self.statistics, vectorize=vectorize)
stats = list(map(func, data))
return stats if vectorize else reduce(add, stats)
def weighted_statistics(self, data, weights, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
weights = weights[idx]
x = np.einsum('n,nk->nk', weights, data)
xx = np.einsum('nk,n,nk->nk', data, weights, data)
n = np.repeat(weights[:, None], self.dim, axis=1)
if not vectorize:
x = np.sum(x, axis=0)
xx = np.sum(xx, axis=0)
n = np.sum(n, axis=0)
return Stats([x, n, n, xx])
else:
func = partial(self.weighted_statistics, vectorize=vectorize)
stats = list(map(func, data, weights))
return stats if vectorize else reduce(add, stats)
def weighted_statistics(self, data, weights, vectorize=False):
if isinstance(data, np.ndarray):
idx = ~np.isnan(data).any(axis=1)
data = data[idx]
weights = weights[idx]
if vectorize:
c0, c1 = 'n,nk->nk', 'nk,n,nh->nkh'
n = weights
else:
c0, c1 = 'n,nk->k', 'nk,n,nh->kh'
n = np.sum(weights)
x = np.einsum(c0, weights, data, optimize=True)
xxT = np.einsum(c1, data, weights, data, optimize=True)
return Stats([x, n, xxT, n])
else:
func = partial(self.weighted_statistics, vectorize=vectorize)
stats = list(map(func, data, weights))
return stats if vectorize else reduce(add, stats)
def nat_to_std(natparam):
sigma = - 0.5 * np.linalg.inv(natparam[1])
mu = - 0.5 * sigma @ natparam[0]
return Stats([mu, sigma])
def std_to_nat(params):
sigma = - 0.5 * np.linalg.inv(params[1])
mu = - 2. * sigma @ params[0]
return Stats([mu, sigma])
def std_to_nat(params):
alphas = params[0] - 1
betas = -params[1]
return Stats([alphas, betas])
def std_to_nat(params):
nat = [
NormalWishart.std_to_nat(_params)
for _params in zip(*extendlists(params))
]
return Stats(nat)
def statistics(self, A, lmbda):
# Stats corresponding to a diagonal Gamma prior on K
a = 0.5 * self.drow * np.ones((self.dcol, ))
b = -0.5 * np.einsum('kh,km,mh->h', A - self.matnorm.M, lmbda,
A - self.matnorm.M)
return Stats([a, b])
def nat_to_std(natparam):
mu = - 0.5 * natparam[1] @ natparam[0]
lmbda = - 0.5 * natparam[1]
return Stats([mu, lmbda])
def std_to_nat(params):
psi = -0.5 * params[0]
nu = -0.5 * (params[1] + psi.shape[0] + 1)
return Stats([psi, nu])
def nat_to_std(natparam):
sigmas = - 0.5 * (1. / natparam[1])
mu = - 0.5 * sigmas * natparam[0]
return Stats([mu, sigmas])
def std_to_nat(params):
mu = params[1] @ params[0]
lmbda = - 0.5 * params[1]
return Stats([mu, lmbda])
def std_to_nat(params):
M = params[0].dot(params[1])
K = params[1]
return Stats([M, K])
def std_to_nat(params):
sigmas = - 0.5 * (1. / params[1])
mu = - 2. * sigmas @ params[0]
return Stats([mu, sigmas])
def std_to_nat(params):
psi = -0.5 * np.linalg.inv(params[0])
nu = 0.5 * (params[1] - psi.shape[0] - 1)
return Stats([psi, nu])