def G4(positions, cell, numbers, elements, params):
cutoff_radius = params['cutoff_radius']
eta = params['eta']
zeta = params['zeta']
lbda = params['lbda']
cos, Rij, Rik, Rjk, i, jk = atomsAngle(positions, cell, cutoff_radius)
g4 = (1 + lbda * cos)**zeta * np.exp(
-eta * (Rij**2 + Rik**2 + Rjk**2) / cutoff_radius**2)
g4 = g4 * cutoff(cutoff_radius, Rij) * cutoff(cutoff_radius, Rik) * cutoff(
cutoff_radius, Rjk)
g4 *= 2**(1 - zeta)
atoms_mask = np.arange(len(positions))[:, None] == i[None, :]
# the shape of g4 will become (#atoms, len(g4)) and multiply atoms_mask to get the corresponding center atom's fingerprints
g4 = np.repeat(g4[None, :], len(positions), axis=0)
g4 *= atoms_mask
index = np.indices((len(elements), len(elements))).reshape(2, -1)
mask = index[1] >= index[0]
index = index[:, mask].T
pairs = np.repeat(np.sort(numbers[jk])[:, None], len(index), axis=1)
elements = np.sort(elements)[index]
pairs_mask = np.sum(pairs == elements, axis=2)
pairs_mask = np.where(pairs_mask == 2, 1, 0)
g4 = np.dot(g4, pairs_mask)
return g4
def estimates(self, log_p, ref):
n = ref.shape[0]
d = ref.shape[1]
if n % 2 == 1:
# make it even by removing the last row
ref = np.delete(ref, -1, axis=0)
n = n - 1
refOdd = ref[::2, :]
refEven = ref[1::2, :]
estimates = np.zeros((self.n_estimates(n)))
dlog_px = log_p.grad_log(ref)
Kxx = self.kernel.eval(ref, ref)
ddk = self.kernel.gradXY_sum(ref, ref)
mat2 = np.zeros((n, n))
mat3 = np.zeros((n, n))
mat1 = (np.matmul(dlog_px, dlog_px.T) * Kxx.T)
## TODO: Eigensum
for k in range(d):
dk_dX = self.kernel.gradX_Y(ref, ref, k)
dk_dY = self.kernel.gradY_X(ref, ref, k)
mat2 = mat2 + (np.repeat(dlog_px[:, k, np.newaxis], n, axis=1) *
dk_dY)
mat3 = mat3 + (np.repeat(dlog_px[:, k, np.newaxis], n, axis=1) *
dk_dX.T).T
mat4 = mat1 + mat2 + mat3 + ddk
e = 2 * np.array(range(self.n_estimates(n)))
o = 2 * np.array(range(self.n_estimates(n))) + 1
return mat4[e, o]
def periodic_kernel(x, xstar, hyp):
"""
Implements the periodic kernel function for Gaussian Process
x: input data with shape (N,d)
xstar: inpt data with data (Nstar,d)
hyp: (log(sigma_f),log(l1),log(l2),...,log(period)) with shape (d+2,)
returns:
a covariance matrix with shape (N,Nstar)
"""
sigma_f = np.exp(hyp[0])
N = x.shape[0]
Nstar = xstar.shape[0]
l = np.exp(hyp[1:-1]) #shape (d,)
l = np.repeat(np.repeat(l[np.newaxis, :], Nstar, axis=0)[np.newaxis, :],
N,
axis=0) #shape (N,Nstar,d)
period = np.exp(hyp[-1])
diff = np.sin(
np.pi * np.abs(np.expand_dims(x, 1) - np.expand_dims(xstar, 0)) /
period) / l #result of shape (N,Nstar,d)
K = sigma_f * np.exp(-2 *
(diff**2).sum(axis=2)) #should be of shape (N,Nstar)
return K
def index2d(channel, stride, kshape, xshape):
k_h, k_w = kshape
x_h, x_w = xshape
c_idx = np.repeat(np.arange(channel), k_h * k_w)
c_idx = c_idx.reshape(-1, 1)
res_h = int((x_h - k_h) / stride) + 1
res_w = int((x_w - k_w) / stride) + 1
size = channel * k_h * k_w
h_idx = np.tile(np.repeat(stride * np.arange(res_h), res_w), size)
h_idx = h_idx.reshape(size, -1)
h_off = np.tile(np.repeat(np.arange(k_h), k_w), channel)
h_off = h_off.reshape(size, -1)
h_idx = h_idx + h_off
w_idx = np.tile(np.tile(stride * np.arange(res_w), res_h), size)
w_idx = w_idx.reshape(size, -1)
w_off = np.tile(np.arange(k_w), channel * k_h)
w_off = w_off.reshape(size, -1)
w_idx = w_idx + w_off
return c_idx, h_idx, w_idx
def lstm_predict(params, inputs):
def update_lstm(input, hiddens, cells):
change = np.tanh(concat_and_multiply(params['change'], input, hiddens))
forget = sigmoid(concat_and_multiply(params['forget'], input, hiddens))
ingate = sigmoid(concat_and_multiply(params['ingate'], input, hiddens))
outgate = sigmoid(
concat_and_multiply(params['outgate'], input, hiddens))
cells = cells * forget + ingate * change
hiddens = outgate * np.tanh(cells)
return hiddens, cells
def hiddens_to_output_probs(hiddens):
output = concat_and_multiply(params['predict'], hiddens)
# Normalize log-probs.
return output - logsumexp(output, axis=1, keepdims=True)
num_sequences = inputs.shape[1]
hiddens = np.repeat(params['init hiddens'], num_sequences, axis=0)
cells = np.repeat(params['init cells'], num_sequences, axis=0)
output = [hiddens_to_output_probs(hiddens)]
for input in inputs: # Iterate over time steps.
hiddens, cells = update_lstm(input, hiddens, cells)
output.append(hiddens_to_output_probs(hiddens))
return output
def Bwham_NLL_eq(fi,Ni,Ml,Wil):
"""
Args:
fi: shape (S,)
Ni: Number of data counts in simulation i (S,)
Ml: Number of data in from simulation i=1,...,S in bin l (M,)
Wil: 0.5*k*beta*(n-nstar)**2 (S,M)
Returns:
the value of the negative likelihood function
"""
S = Wil.shape[0]
M = Wil.shape[1]
fi = fi - fi[-1]
first_term = -(Ni*fi).sum()
log_pl = nup.log(Ml) - \
alogsumexp(nup.repeat(fi[:,nup.newaxis],M,axis=1)-Wil,b=nup.repeat(Ni[:,nup.newaxis],M,axis=1),axis=0)
second_term = (Ml * log_pl).sum(axis=0)
return first_term - second_term
def differentiate(self):
"get gradient values using finite difference"
C = np.repeat(np.expand_dims(self.cost_fn.C, axis=0), [self.T, 1, 1])
F = np.repeat(np.expand_dims(self.dyn_model.F, axis=0), [self.T, 1, 1])
c = np.repeat(np.expand_dims(self.cost_fn.c, axis=0), (self.T, 1))
f = np.repeat(np.expand_dims(self.dyn_model.f, axis=0), (self.T, 1))
return C, F, c, f
def gp0(self, m, s):
"""
Compute joint predictions for MGP with uncertain inputs.
"""
assert hasattr(self, "hyp")
if not hasattr(self, "K"):
self.cache()
x = np.atleast_2d(self.inputs)
y = np.atleast_2d(self.targets)
n, D = x.shape
n, E = y.shape
X = self.hyp
iK = self.iK
beta = self.alpha
m = np.atleast_2d(m)
inp = x - m
# Compute the predicted mean and IO covariance.
iL = np.stack([np.diag(exp(-X[i, :D])) for i in range(E)])
iN = np.matmul(inp, iL)
B = iL @ s @ iL + np.eye(D)
t = np.stack([solve(B[i].T, iN[i].T).T for i in range(E)])
q = exp(-np.sum(iN * t, 2) / 2)
qb = q * beta.T
tiL = np.matmul(t, iL)
c = exp(2 * X[:, D]) / sqrt(det(B))
M = np.sum(qb, 1) * c
V = (np.transpose(tiL, [0, 2, 1]) @ np.expand_dims(qb, 2)).reshape(
E, D).T * c
k = 2 * X[:, D].reshape(E, 1) - np.sum(iN**2, 2) / 2
# Compute the predicted covariance.
inp = np.expand_dims(inp, 0) / np.expand_dims(exp(2 * X[:, :D]), 1)
ii = np.repeat(inp[:, newaxis, :, :], E, 1)
ij = np.repeat(inp[newaxis, :, :, :], E, 0)
iL = np.stack([np.diag(exp(-2 * X[i, :D])) for i in range(E)])
siL = np.expand_dims(iL, 0) + np.expand_dims(iL, 1)
R = np.matmul(s, siL) + np.eye(D)
t = 1 / sqrt(det(R))
iRs = np.stack(
[solve(R.reshape(-1, D, D)[i], s) for i in range(E * E)])
iRs = iRs.reshape(E, E, D, D)
Q = exp(k[:, newaxis, :, newaxis] + k[newaxis, :, newaxis, :] +
maha(ii, -ij, iRs / 2))
S = np.einsum('ji,iljk,kl->il', beta, Q, beta)
tr = np.hstack([np.sum(Q[i, i] * iK[i]) for i in range(E)])
S = (S - np.diag(tr)) * t + np.diag(exp(2 * X[:, D]))
S = S - np.matmul(M[:, newaxis], M[newaxis, :])
return M, S, V
def compute_path_params(eta, H, psi):
''' Compute the gaussian parameters for each path
H (list of nb_layers elements of shape (K_l x r_{l-1}, r_l)): Lambda
parameters for each layer
psi (list of nb_layers elements of shape (K_l x r_{l-1}, r_{l-1})): Psi
parameters for each layer
eta (list of nb_layers elements of shape (K_l x r_{l-1}, 1)): mu
parameters for each layer
------------------------------------------------------------------------------------------------
returns (tuple of len 2): The updated parameters mu_s and sigma for all s in Omega
'''
#=====================================================================
# Retrieving model parameters
#=====================================================================
L = len(H)
k = [len(h) for h in H]
k_aug = k + [
1
] # Integrating the number of components of the last layer i.e 1
r1 = H[0].shape[1]
r2_L = [h.shape[2] for h in H] # r[2:L]
r = [r1] + r2_L # r augmented
#=====================================================================
# Initiating the parameters for all layers
#=====================================================================
mu_s = [0 for i in range(L + 1)]
sigma_s = [0 for i in range(L + 1)]
# Initialization with the parameters of the last layer
mu_s[-1] = np.zeros((1, r[-1], 1)) # Inverser k et r plus tard
sigma_s[-1] = np.eye(r[-1])[n_axis]
#==================================================================================
# Compute Gaussian parameters from top to bottom for each path
#==================================================================================
for l in reversed(range(0, L)):
H_repeat = np.repeat(H[l], np.prod(k_aug[l + 1:]), axis=0)
eta_repeat = np.repeat(eta[l], np.prod(k_aug[l + 1:]), axis=0)
psi_repeat = np.repeat(psi[l], np.prod(k_aug[l + 1:]), axis=0)
mu_s[l] = eta_repeat + H_repeat @ np.tile(mu_s[l + 1], (k[l], 1, 1))
sigma_s[l] = H_repeat @ np.tile(sigma_s[l + 1], (k[l], 1, 1)) @ t(H_repeat, (0, 2, 1)) \
+ psi_repeat
return mu_s, sigma_s
def prep_opt(y_train, N, coeffs):
summedy_mat = np.sum(y_train, axis=0)
summedy = np.reshape(summedy_mat, [np.size(summedy_mat), -1])
a1 = np.reshape([np.repeat(coeffs.T[1], N)], [np.size(summedy), -1])
a0 = np.reshape([np.repeat(coeffs.T[0], N)], [np.size(summedy), -1])
a1y = np.multiply(a1, summedy)
a0y = np.multiply(a0, summedy)
consts = np.sum(gammaln(
y_train + scale)) - D * n_neurons * N * gammaln(scale) - np.sum(
coeffs.T[0] *
(D * scale * N)) - np.sum(a0y) - np.sum(summedy * np.log(scale))
return summedy, a1y, a0y, a1, consts
def getGRUTranstionDist(params, data):
try:
inputs = np.concatenate([data[k] for k in ['a', 'u']], axis=2)
except:
inputs = data['a']
def update_gru(input, hiddens):
update = sigmoid(
concat_and_multiply(params['transion']['update'], input, hiddens))
reset = sigmoid(
concat_and_multiply(params['transion']['reset'], input, hiddens))
hiddens = (1 - update) * hiddens + update * sigmoid(
concat_and_multiply(params['transion']['hiddenOut'], input,
hiddens * reset))
return hiddens
num_sequences = inputs.shape[1]
hiddens = np.repeat(params['transion']['init hiddens'],
num_sequences,
axis=0)
output = [(hiddens[:, :hiddens.shape[1] / 2],
hiddens[:, hiddens.shape[1] / 2:])]
for input in inputs: # Iterate over time steps.
hiddens = update_gru(input, hiddens)
output.append((hiddens[:, :hiddens.shape[1] / 2],
hiddens[:, hiddens.shape[1] / 2:]))
return zip(*output)
def get_k(stiffness, ke):
# Constructs a sparse stiffness matrix, k, for use in the displace function.
nely, nelx = stiffness.shape
# get position of the nodes of each element in the stiffness matrix
ely, elx = np.meshgrid(range(nely), range(nelx)) # x, y coords
ely, elx = ely.reshape(-1, 1), elx.reshape(-1, 1)
n1 = (nely + 1) * (elx + 0) + (ely + 0)
n2 = (nely + 1) * (elx + 1) + (ely + 0)
n3 = (nely + 1) * (elx + 1) + (ely + 1)
n4 = (nely + 1) * (elx + 0) + (ely + 1)
edof = np.array([
2 * n1, 2 * n1 + 1, 2 * n2, 2 * n2 + 1, 2 * n3, 2 * n3 + 1, 2 * n4,
2 * n4 + 1
])
edof = edof.T[0]
x_list = np.repeat(edof, 8) # flat list pointer of each node in an element
y_list = np.tile(edof,
8).flatten() # flat list pointer of each node in elem
# make the stiffness matrix
kd = stiffness.T.reshape(nelx * nely, 1, 1)
value_list = (kd * np.tile(ke, kd.shape)).flatten()
return value_list, y_list, x_list
def optimize(self, curb=None):
assert hasattr(self, "inputs")
assert hasattr(self, "targets")
x = np.atleast_2d(self.inputs)
y = np.atleast_2d(self.targets)
assert len(x) == len(y)
n, D = x.shape
n, E = y.shape
if curb is not None:
self.curb = curb
elif not hasattr(self, "curb"):
self.curb = Empty()
self.curb.snr = 500
self.curb.ls = 100
self.curb.std = std(x, 0)
if not hasattr(self, "hyp"):
self.hyp = np.zeros([E, D + 2])
self.hyp[:, :D] = np.repeat(log(std(x, 0)).reshape(1, D), E, 0)
self.hyp[:, D] = log(std(y, 0))
self.hyp[:, -1] = log(std(y, 0) / 10)
print("Train hyperparameters of full GP...")
try:
self.result = minimize(
value_and_grad(self.hyp_crub), self.hyp, jac=True)
except Exception:
self.result = minimize(
value_and_grad(self.hyp_crub), self.hyp, jac=True, method='CG')
self.hyp = self.result.get('x').reshape(E, -1)
self.cache()
def generate(si, theta, seed=0):
np.random.seed(seed)
n, p, r = len(si), 6, 5
X = np.random.normal(0, 1, n * p).reshape(n, p)
X_kar = np.kron(np.eye(r), X)
beta_star = np.random.uniform(0, 1, p * r).reshape(p * r, 1)
A = np.random.uniform(0, 1, 25).reshape(5, 5)
Gamma = PCA().fit(A).components_
Gamma1 = Gamma[:, :2]
Gamma0 = Gamma[:, 2:]
out1, out0 = list(), list()
for i in range(2):
out1.append([(-.9)**abs(i - j) for j in range(2)])
for i in range(3):
out0.append([(-.5)**abs(i - j) for j in range(3)])
Omega1 = np.array(out1)
Omega0 = np.array(out0)
Sigma = np.matmul(np.matmul(Gamma1, Omega1), Gamma1.T) + np.matmul(
np.matmul(Gamma0, Omega0), Gamma0.T)
if (theta[0] == 0) & (theta[1] == 0):
h = np.eye(len(si))
else:
h = np.array(rho(si, theta))
Sigma_kr = np.kron(Sigma, h)
Err_kr = np.random.multivariate_normal(np.repeat(0, n * r),
Sigma_kr).reshape(n * r, 1)
Y_kr = np.matmul(X_kar, beta_star) + np.array(Err_kr)
Y = Y_kr.reshape(n, r)
return (X, Y)
def log_py_zM_bin_j(lambda_bin_j, y_bin_j, zM, k, nj_bin_j):
''' Compute log p(y_j | zM, s1 = k1) of the jth
lambda_bin_j ( (r + 1) 1darray): Coefficients of the binomial distributions in the GLLVM layer
y_bin_j (numobs 1darray): The subset containing only the binary/count variables in the dataset
zM (M x r x k ndarray): M Monte Carlo copies of z for each component k1 of the mixture
k (int): The number of components of the mixture
nj_bin_j (int): The number of possible values/maximum values of the jth binary/count variable
--------------------------------------------------------------
returns (ndarray): p(y_j | zM, s1 = k1)
'''
M = zM.shape[0]
r = zM.shape[1]
numobs = len(y_bin_j)
yg = np.repeat(y_bin_j[np.newaxis], axis = 0, repeats = M)
yg = yg.astype(np.float)
nj_bin_j = np.float(nj_bin_j)
coeff_binom = binom(nj_bin_j, yg).reshape(M, 1, numobs)
eta = np.transpose(zM, (0, 2, 1)) @ lambda_bin_j[1:].reshape(1, r, 1)
eta = eta + lambda_bin_j[0].reshape(1, 1, 1) # Add the constant
den = nj_bin_j * log_1plusexp(eta)
num = eta @ y_bin_j[np.newaxis, np.newaxis]
log_p_y_z = num - den + np.log(coeff_binom)
return np.transpose(log_p_y_z, (0, 2, 1)).astype(np.float)
def draw_z2_z1s(chsi, rho, M, r):
''' Draw from f(z^{l+1} | z^{l}, s, Theta)
chsi (list of nd-arrays): The chsi parameters for all paths starting at each layer
rho (list of ndarrays): The rho parameters (covariance matrices) for
all paths starting at each layer
M (list of int): The number of MC to draw on each layer
r (list of int): The dimension of each layer
---------------------------------------------------------------------------
returns (list of nd-arrays): z^{l+1} | z^{l}, s, Theta for all (l,s)
'''
L = len(chsi)
S = [chsi[l].shape[0] for l in range(L)]
z2_z1s = []
for l in range(L):
z2_z1s_l = np.zeros((M[l + 1], M[l], S[l], r[l + 1]))
for s in range(S[l]):
z2_z1s_kl = multivariate_normal(size = M[l + 1], \
mean = rho[l][:,s].flatten(order = 'C'), \
cov = block_diag(*np.repeat(chsi[l][s][n_axis], M[l], axis = 0)))
z2_z1s_l[:, :, s] = z2_z1s_kl.reshape(M[l + 1],
M[l],
r[l + 1],
order='C')
z2_z1s_l = t(z2_z1s_l, (1, 0, 2, 3))
z2_z1s.append(z2_z1s_l)
return z2_z1s
def forward_step(params, X=None, cell_state_0=None, hid_state_0=None):
hid_state = np.repeat(hid_state_0,
X.shape[0] - hid_state_0.shape[0] + 1,
axis=0)
cell_state_1 = np.add(
np.multiply( # <-- forget old info
cell_state_0,
sigmoid(
c([X, hid_state]) @ params['forget']['w'] +
params['forget']['b']), # <-- forget gate
),
np.multiply( # <-- write new info
sigmoid(
c([X, hid_state]) @ params['ingate']['w'] +
params['ingate']['b']), # <-- input gate
np.tanh(
c([X, hid_state]) @ params['change']['w'] +
params['change']['b']), # <-- change gate
))
hid_state_1 = np.multiply(
sigmoid(c([X, hid_state]) @ params['outgate']['w']),
# 1,
np.tanh(cell_state_1))
return cell_state_1, hid_state_1
def get_states_and_transitions(self):
num_acts, num_states = self.num_acts, self.batch_size
if isinstance(self.env.observation_space, spaces.Discrete):
if num_states is None:
states = np.arange(self.env.observation_space.n)
else:
states = np.random.randint(0,
self.env.action_space.n,
size=(num_states, ))
else:
assert num_states is not None
state_low, state_high = self.env.observation_space.low, self.env.observation_space.high
states = np.random.uniform(state_low,
state_high,
size=(num_states, len(state_low)))
if isinstance(self.env.action_space, spaces.Discrete):
num_acts = self.env.action_space.n
actions = np.arange(num_acts)
else:
assert num_acts is not None
act_low, act_high = self.env.action_space.low, self.env.action_space.high
actions = np.random.uniform(act_low,
act_high,
size=(num_acts, len(act_low)))
states = np.tile(states.T, num_acts).T
actions = np.repeat(actions, num_states, axis=0)
self.env.vec_set_state(states)
next_states, rewards, dones, _ = self.env.vec_step(actions)
return states, next_states, rewards, dones
def draw_z_s(mu_s, sigma_s, eta, M):
''' Draw from f(z^{l} | s) for all s in Omega and return the centered and
non-centered draws
mu_s (list of nd-arrays): The means of the Gaussians starting at each layer
sigma_s (list of nd-arrays): The covariance matrices of the Gaussians
starting at each layer
eta (list of nb_layers elements of shape (K_l x r_{l-1}, 1)): mu parameters
for each layer
M (list of int): The number of MC to draw on each layer
-------------------------------------------------------------------------
returns (list of ndarrays): z^{l} | s for all s in Omega and all l in L
'''
L = len(mu_s) - 1
r = [mu_s[l].shape[1] for l in range(L + 1)]
S = [mu_s[l].shape[0] for l in range(L + 1)]
z_s = []
zc_s = [] # z centered (denoted c) or all l
for l in range(L + 1):
zl_s = multivariate_normal(size = (M[l], 1), \
mean = mu_s[l].flatten(order = 'C'), cov = block_diag(*sigma_s[l]))
zl_s = zl_s.reshape(M[l], S[l], r[l], order='C')
z_s.append(t(zl_s, (0, 2, 1)))
if l < L: # The last layer is already centered
eta_ = np.repeat(t(eta[l], (2, 0, 1)), S[l + 1], axis=1)
zc_s.append(zl_s - eta_)
return z_s, zc_s
def getGRUTranstionDist(params, data, latents):
inputs = np.concatenate(map(lambda x: np.expand_dims(x, axis=0), latents),
axis=0)
if ('a' in data and 'u' in data):
inputs = np.concatenate([data[k] for k in ['a', 'u']] + [inputs],
axis=2)
def update_gru(input, hiddens):
update = sigmoid(
concat_and_multiply(params['transion']['update'], input, hiddens))
reset = sigmoid(
concat_and_multiply(params['transion']['reset'], input, hiddens))
hiddens = (1 - update) * hiddens + update * sigmoid(
concat_and_multiply(params['transion']['hiddenOut'], input,
hiddens * reset))
return hiddens
num_sequences = inputs.shape[1]
hiddens = np.repeat(params['transion']['init hiddens'],
num_sequences,
axis=0)
output = []
for input in inputs: # Iterate over time steps.
hiddens = update_gru(input, hiddens)
output.append((hiddens[:, :hiddens.shape[1] / 2],
hiddens[:, hiddens.shape[1] / 2:]))
return zip(*output)
def compute_rho(eta, H, psi, mu_s, sigma_s, z_c, chsi):
''' Compute rho as defined in equation (8) of the DGMM paper
eta (list of nb_layers elements of shape (K_l x r_{l-1}, 1)): mu
parameters for each layer
H (list of nb_layers elements of shape (K_l x r_{l-1}, r_l)): Lambda
parameters for each layer
psi (list of nb_layers elements of shape (K_l x r_{l-1}, r_{l-1})): Psi
parameters for each layer
z_c (list of nd-arrays) z^{(l)} - eta^{(l)} for each layer.
chsi (list of nd-arrays): The chsi parameters for each layer
-----------------------------------------------------------------------
returns (list of ndarrays): The rho parameters (covariance matrices)
for all paths starting at each layer
'''
L = len(H)
rho = [0 for i in range(L)]
k = [len(h) for h in H]
k_aug = k + [1]
for l in range(0, L):
sigma_next_l = np.tile(sigma_s[l + 1], (k[l], 1, 1))
mu_next_l = np.tile(mu_s[l + 1], (k[l], 1, 1))
HxPsi_inv = t(H[l], (0, 2, 1)) @ pinv(psi[l])
HxPsi_inv = np.repeat(HxPsi_inv, np.prod(k_aug[l + 1: ]), axis = 0)
rho[l] = chsi[l][n_axis] @ (HxPsi_inv[n_axis] @ z_c[l][..., n_axis] \
+ (pinv(sigma_next_l) @ mu_next_l)[n_axis])
return rho
def get_causal_effect(params, do_A, w):
"to be called within experiment function."
np.random.seed(4)
random.seed(4)
al, bl = params
L = bl * bl * np.exp(-L0 / al / al / 2) + 1e-6 * EYEN
if nystr:
alpha = EYEN - eig_vec_K @ np.linalg.inv(
eig_vec_K.T @ L @ eig_vec_K / N2 + np.diag(1 / eig_val_K / N2)) @ eig_vec_K.T @ L / N2
alpha = alpha @ W_nystr @ Y * N2
else:
LWL_inv = chol_inv(L @ W @ L + L / N2 + JITTER * EYEN)
alpha = LWL_inv @ L @ W @ Y
# L_W_inv = chol_inv(W*N2+L_inv)
EYhat_do_A = []
for a in do_A:
a = np.repeat(a, [w.shape[0]]).reshape(-1, 1)
w = w.reshape(-1, 1)
aw = np.concatenate([a, w], axis=-1)
ate_L0 = _sqdist(aw, X)
ate_L = bl * bl * np.exp(-ate_L0 / al / al / 2)
h_out = ate_L @ alpha
mean_h = np.mean(h_out).reshape(-1, 1)
EYhat_do_A.append(mean_h)
print('a = {}, beta_a = {}'.format(np.mean(a), mean_h))
return np.concatenate(EYhat_do_A)
def compute_chsi(H, psi, mu_s, sigma_s):
''' Compute chsi as defined in equation (8) of the DGMM paper
H (list of nb_layers elements of shape (K_l x r_l-1, r_l)): Lambda
parameters for each layer
psi (list of nb_layers elements of shape (K_l x r_l-1, r_l-1)): Psi
parameters for each layer
mu_s (list of nd-arrays): The means of the Gaussians starting at each layer
sigma_s (list of nd-arrays): The covariance matrices of the Gaussians
starting at each layer
------------------------------------------------------------------------------------------------
returns (list of ndarray): The chsi parameters for all paths starting at each layer
'''
L = len(H)
k = [len(h) for h in H]
#=====================================================================
# Initiating the parameters for all layers
#=====================================================================
# Initialization with the parameters of the last layer
chsi = [0 for i in range(L)]
chsi[-1] = pinv(pinv(sigma_s[-1]) + t(H[-1], (0, 2, 1)) @ pinv(psi[-1]) @ H[-1])
#==================================================================================
# Compute chsi from top to bottom
#==================================================================================
for l in range(L - 1):
Ht_psi_H = t(H[l], (0, 2, 1)) @ pinv(psi[l]) @ H[l]
Ht_psi_H = np.repeat(Ht_psi_H, np.prod(k[l + 1:]), axis = 0)
sigma_next_l = np.tile(sigma_s[l + 1], (k[l], 1, 1))
chsi[l] = pinv(pinv(sigma_next_l) + Ht_psi_H)
return chsi
def _initialize_variational_params(self, data, input, mask, tag):
T = data.shape[0]
D = self.D
# Initialize the mean with the linear model, if applicable
ms = self.model.emissions.invert(data, input=input, mask=mask, tag=tag)
# Initialize with no covariance between adjacent time steps
# NOTE: it's important to initialize A and Q to be nonzero,
# otherwise the gradients wrt them are zero and they never
# change during optimization!
As = np.repeat(np.eye(D)[None, :, :], T-1, axis=0)
bs = np.zeros((T-1, D))
Qi_sqrts = np.repeat(np.eye(D)[None, :, :], T-1, axis=0)
Ri_sqrts = 1./np.sqrt(self.initial_variance) * np.repeat(np.eye(D)[None, :, :], T, axis=0)
return As, bs, Qi_sqrts, ms, Ri_sqrts
def _parameter_initialiser(self, x, c=None, n=None):
if (c is not None) & ((c == 0).all()):
x = np.repeat(x, n)
p = self._mom(x)
else:
p = 1., 1.
return p
def calc_result(self, x, y, fun_args, all_things, exp_kappa_int,
exp_kappa_bdy, grad_kappa_x, grad_kappa_y):
result = 0
A_1, A_2, A_3, B = self.__op_cache__.operators
A_1_bar, A_2_bar, A_3_bar, B_bar = self.__op_cache__.operators_bar
def printer(*args):
if self.__verbosity__ > 0:
print(*args)
for item in all_things:
try:
function = self.__op_cache__[item]
except Exception as ex:
printer('Failed to get {}'.format(item))
raise ex
new_mat = function(x, y, fun_args)
# unbarred
if A_1 in item:
printer('Transforming A_1')
multiplier = np.repeat(grad_kappa_x * exp_kappa_int,
y.shape[0], 1)
new_mat = multiplier * new_mat
elif A_2 in item:
printer('Transforming A_2')
multiplier = np.repeat(grad_kappa_y * exp_kappa_int,
y.shape[0], 1)
new_mat = multiplier * new_mat
elif A_3 in item:
printer('Transforming A_3')
multiplier = np.repeat(exp_kappa_int, y.shape[0], 1)
new_mat = multiplier * new_mat
# barred
if A_1_bar in item:
printer('Transforming A_1_bar')
new_mat = np.repeat(grad_kappa_x.T * exp_kappa_int.T,
x.shape[0], 0) * new_mat
elif A_2_bar in item:
printer('Transforming A_2_bar')
new_mat = np.repeat(grad_kappa_y.T * exp_kappa_int.T,
x.shape[0], 0) * new_mat
elif A_3_bar in item:
printer('Transforming A_3_bar')
new_mat = np.repeat(exp_kappa_int.T, x.shape[0], 0) * new_mat
# boundary
if B in item:
printer('Transforming B')
new_mat = np.repeat(exp_kappa_bdy, y.shape[0], 1) * new_mat
if B_bar in item:
printer('Transforming B_bar')
new_mat = np.repeat(exp_kappa_bdy.T, x.shape[0], 0) * new_mat
result += new_mat
return result
def getSigSeriesG(sts, nt, a, mu, sig):
# sts has shape T x M
# the rest are numbers
gaus = a*np.exp(-(np.arange(nt)-mu)**2/sig**2)
nper = np.int(nt/sts.shape[0])
stsRepeated = np.vstack([np.repeat(sts,nper,axis=0),np.zeros((nt-nper*6,sts.shape[1]))])
return (stsRepeated.T*gaus).T
def sample(self, n, mu, seed):
rstate = np.random.get_state()
np.random.seed(seed)
#x = 11 * np.random.random(200) - 6.0 # x lies in [-6,5]
x1 = np.random.normal(np.repeat(0, self.d), 1.0, size=n)
y1 = x1 + x1**2 + np.random.random(200)
#x = 2 * np.random.random(200) - 2.0 # x lies in [-2,0]
x2 = np.random.normal(np.repeat(mu, self.d), 1.0, size=n)
y2 = x2 + x2**2 + np.random.random(200)
return x1[:,
np.newaxis], x2[:,
np.newaxis], y1[:,
np.newaxis], y2[:,
np.newaxis]
def compute_log_prob(enc_w, dec_w, encode, decode_log_like, base_data,
conditional_data, samples_per_image, latent_dimensions,
rs):
(mus, log_sigs) = encode(enc_w, conditional_data)
sigs = np.exp(log_sigs)
noise = rs.randn(samples_per_image, conditional_data.shape[0],
latent_dimensions)
Z_samples = mus + sigs * noise
Z_samples = np.reshape(
Z_samples,
(conditional_data.shape[0] * samples_per_image, latent_dimensions),
order='F')
conditional_repeat = np.repeat(conditional_data, samples_per_image, axis=0)
base_repeat = np.repeat(base_data, samples_per_image, axis=0)
decoder_input = np.concatenate((Z_samples, base_repeat), axis=1)
mean_log_prob = decode_log_like(dec_w, decoder_input, conditional_repeat)
return mean_log_prob
def outputs(weights, inputs):
"""Goes from right to left, updating the state."""
forget_weights = parser.get(weights, 'forget')
change_weights = parser.get(weights, 'change')
ingate_weights = parser.get(weights, 'ingate')
outgate_weights = parser.get(weights, 'outgate')
predict_weights = parser.get(weights, 'predict')
num_sequences = inputs.shape[1]
hiddens = np.repeat(parser.get(weights, 'init_hiddens'), num_sequences, axis=0)
cells = np.repeat(parser.get(weights, 'init_cells'), num_sequences, axis=0)
output = []
for input in inputs: # Iterate over time steps.
hiddens, cells = update_lstm(input, hiddens, cells, forget_weights,
change_weights, ingate_weights, outgate_weights)
cur_output = activations(predict_weights, hiddens)
output.append(cur_output - logsumexp(cur_output))
return output # Output normalized log-probabilities.
def _compute_sigmas(self, data, input, mask, tag):
T, D = data.shape
sigma_init = np.exp(self.inv_sigma_init) * np.ones((self.lags, self.K, self.D))
sigma_ar = np.repeat(np.exp(self.inv_sigmas)[None, :, :], T-self.lags, axis=0)
sigmas = np.concatenate((sigma_init, sigma_ar))
assert sigmas.shape == (T, self.K, D)
return sigmas
def outputs(weights, inputs):
"""Outputs normalized log-probabilities of each character, plus an
extra one at the end."""
forget_weights = parser.get(weights, 'forget')
change_weights = parser.get(weights, 'change')
ingate_weights = parser.get(weights, 'ingate')
outgate_weights = parser.get(weights, 'outgate')
predict_weights = parser.get(weights, 'predict')
num_sequences = inputs.shape[1]
hiddens = np.repeat(parser.get(weights, 'init_hiddens'), num_sequences, axis=0)
cells = np.repeat(parser.get(weights, 'init_cells'), num_sequences, axis=0)
output = [hiddens_to_output_probs(predict_weights, hiddens)]
for input in inputs: # Iterate over time steps.
hiddens, cells = update_lstm(input, hiddens, cells, forget_weights,
change_weights, ingate_weights, outgate_weights)
output.append(hiddens_to_output_probs(predict_weights, hiddens))
return output
def calc_result(self, x, y, fun_args, all_things, exp_kappa_int, exp_kappa_bdy, grad_kappa_x, grad_kappa_y):
result = 0
A_1, A_2, A_3, B = self.__op_cache__.operators
A_1_bar, A_2_bar, A_3_bar, B_bar = self.__op_cache__.operators_bar
def printer(*args):
if self.__verbosity__ > 0:
print(*args)
for item in all_things:
try:
function = self.__op_cache__[item]
except Exception as ex:
printer('Failed to get {}'.format(item))
raise ex
new_mat = function(x, y, fun_args)
# unbarred
if A_1 in item:
printer('Transforming A_1')
multiplier = np.repeat(grad_kappa_x*exp_kappa_int, y.shape[0], 1)
new_mat = multiplier * new_mat
elif A_2 in item:
printer('Transforming A_2')
multiplier = np.repeat(grad_kappa_y*exp_kappa_int, y.shape[0], 1)
new_mat = multiplier * new_mat
elif A_3 in item:
printer('Transforming A_3')
multiplier = np.repeat(exp_kappa_int, y.shape[0], 1)
new_mat = multiplier * new_mat
# barred
if A_1_bar in item:
printer('Transforming A_1_bar')
new_mat = np.repeat(grad_kappa_x.T*exp_kappa_int.T,x.shape[0],0) * new_mat
elif A_2_bar in item:
printer('Transforming A_2_bar')
new_mat = np.repeat(grad_kappa_y.T*exp_kappa_int.T,x.shape[0],0) * new_mat
elif A_3_bar in item:
printer('Transforming A_3_bar')
new_mat = np.repeat(exp_kappa_int.T,x.shape[0],0) * new_mat
# boundary
if B in item:
printer('Transforming B')
new_mat = np.repeat(exp_kappa_bdy, y.shape[0], 1) * new_mat
if B_bar in item:
printer('Transforming B_bar')
new_mat = np.repeat(exp_kappa_bdy.T, x.shape[0], 0) * new_mat
result += new_mat
return result
def outputs(weights, inputs):
"""Goes from right to left, updating the state."""
num_sequences = inputs.shape[1]
hiddens = np.repeat(parser.get(weights, 'init_hiddens'), num_sequences, axis=0)
change_weights = parser.get(weights, 'change')
predict_weights = parser.get(weights, 'predict')
output = [hiddens_to_output_probs(predict_weights, hiddens)]
for input in inputs: # Iterate over time steps.
hiddens = update(input, hiddens, change_weights)
output.append(hiddens_to_output_probs(predict_weights, hiddens))
return output
def make_pinwheel_data(radial_std, tangential_std, num_classes, num_per_class, rate):
rads = np.linspace(0, 2*np.pi, num_classes, endpoint=False)
features = npr.randn(num_classes*num_per_class, 2) \
* np.array([radial_std, tangential_std])
features[:,0] += 1.
labels = np.repeat(np.arange(num_classes), num_per_class)
angles = rads[labels] + rate * np.exp(features[:,0])
rotations = np.stack([np.cos(angles), -np.sin(angles), np.sin(angles), np.cos(angles)])
rotations = np.reshape(rotations.T, (-1, 2, 2))
return 10*npr.permutation(np.einsum('ti,tij->tj', features, rotations))
def lstm_predict(params, inputs):
def update_lstm(input, hiddens, cells):
change = np.tanh(concat_and_multiply(params['change'], input, hiddens))
forget = sigmoid(concat_and_multiply(params['forget'], input, hiddens))
ingate = sigmoid(concat_and_multiply(params['ingate'], input, hiddens))
outgate = sigmoid(concat_and_multiply(params['outgate'], input, hiddens))
cells = cells * forget + ingate * change
hiddens = outgate * np.tanh(cells)
return hiddens, cells
def hiddens_to_output_probs(hiddens):
output = concat_and_multiply(params['predict'], hiddens)
return output - logsumexp(output, axis=1, keepdims=True) # Normalize log-probs.
num_sequences = inputs.shape[1]
hiddens = np.repeat(params['init hiddens'], num_sequences, axis=0)
cells = np.repeat(params['init cells'], num_sequences, axis=0)
output = [hiddens_to_output_probs(hiddens)]
for input in inputs: # Iterate over time steps.
hiddens, cells = update_lstm(input, hiddens, cells)
output.append(hiddens_to_output_probs(hiddens))
return output
def make_pinwheel(radial_std, tangential_std, num_classes, num_per_class, rate,
rs=npr.RandomState(0)):
"""Based on code by Ryan P. Adams."""
rads = np.linspace(0, 2*np.pi, num_classes, endpoint=False)
features = rs.randn(num_classes*num_per_class, 2) \
* np.array([radial_std, tangential_std])
features[:, 0] += 1
labels = np.repeat(np.arange(num_classes), num_per_class)
angles = rads[labels] + rate * np.exp(features[:,0])
rotations = np.stack([np.cos(angles), -np.sin(angles), np.sin(angles), np.cos(angles)])
rotations = np.reshape(rotations.T, (-1, 2, 2))
return np.einsum('ti,tij->tj', features, rotations)
def rnn_predict(params, inputs):
def update_rnn(input, hiddens):
return np.tanh(concat_and_multiply(params['change'], input, hiddens))
def hiddens_to_output_probs(hiddens):
output = concat_and_multiply(params['predict'], hiddens)
return output - logsumexp(output, axis=1, keepdims=True)
num_sequences = inputs.shape[1]
hiddens = np.repeat(params['init hiddens'], num_sequences, axis=0)
output = [hiddens_to_output_probs(hiddens)]
for input in inputs: # Iterate over time steps.
hiddens = update_rnn(input, hiddens)
output.append(hiddens_to_output_probs(hiddens))
return output
def process_one_batch(inputs, weights):
"""Process one batch of image sets
Recurrent Network process:
h1_out = H( W[x_h1]*X(t) + W[h2_h1]*h2_out + bias[h1] )
h2_out = H( W[h1_h2]*h1_out + bias[h2] )
output = H( W[h2_out]*h2_out + bias[out] )
"""
batch_size = inputs.shape[1]
w_in_2_h1 = parser.get(weights, "input_2_h1")
w_h1_2_h2 = parser.get(weights, "h1_2_h2")
w_h2_2_out = parser.get(weights, "h2_2_output")
h2_out = np.repeat(parser.get(weights, "pre_h2_out"), batch_size, axis=0)
outputs = []
for sub_input in inputs:
input_x = x_with_bias(np.concatenate((sub_input, h2_out), axis=1))
h1_in = w_act_on_x(input_x, w_in_2_h1)
h1_out = hidden_actfun(h1_in)
h2_in = w_act_on_x(x_with_bias(h1_out), w_h1_2_h2)
h2_out = hidden_actfun(h2_in)
output_in = w_act_on_x(x_with_bias(h2_out), w_h2_2_out)
output_out = output_actfun(output_in)
outputs.append(output_out)
return outputs
def fun(x): return to_scalar(np.repeat(x, 1, axis=0)) d_fun = lambda x : to_scalar(grad(fun)(x))
def _init_params(self, data, lengths=None, params='stmpaw'):
X = data['obs']
if self.n_lags == 0:
super(ARTHMM, self)._init_params(data, lengths, params)
else:
if 's' in params:
super(ARTHMM, self)._init_params(data, lengths, 's')
if 't' in params:
super(ARTHMM, self)._init_params(data, lengths, 't')
if 'm' in params or 'a' in params or 'p' in params:
kmmod = cluster.KMeans(
n_clusters=self.n_unique,
random_state=self.random_state).fit(X)
kmeans = kmmod.cluster_centers_
ar_mod = []
ar_alpha = []
ar_resid = []
if not self.shared_alpha:
for u in range(self.n_unique):
ar_mod.append(smapi.tsa.AR(X[kmmod.labels_ == \
u]).fit(self.n_lags))
ar_alpha.append(ar_mod[u].params[1:])
ar_resid.append(ar_mod[u].resid)
else:
# run one AR model on most part of time series
# that has most points assigned after clustering
mf = np.argmax(np.bincount(kmmod.labels_))
ar_mod.append(smapi.tsa.AR(X[kmmod.labels_ == \
mf]).fit(self.n_lags))
ar_alpha.append(ar_mod[0].params[1:])
ar_resid.append(ar_mod[0].resid)
if 'm' in params:
mu_init = np.zeros((self.n_unique, self.n_features))
for u in range(self.n_unique):
ar_idx = u
if self.shared_alpha:
ar_idx = 0
mu_init[u] = kmeans[u, 0] - np.dot(
np.repeat(kmeans[u, 0], self.n_lags),
ar_alpha[ar_idx])
self.mu_ = np.copy(mu_init)
if 'p' in params:
precision_init = np.zeros((self.n_unique, self.n_features))
for u in range(self.n_unique):
if not self.shared_alpha:
maxVar = np.max([np.var(ar_resid[i]) for i in
range(self.n_unique)])
else:
maxVar = np.var(ar_resid[0])
precision_init[u] = 1.0 / maxVar
self.precision_ = np.copy(precision_init)
if 'a' in params:
alpha_init = np.zeros((self.n_unique, self.n_lags))
for u in range(self.n_unique):
ar_idx = u
if self.shared_alpha:
ar_idx = 0
alpha_init[u, :] = ar_alpha[ar_idx]
self.alpha_ = alpha_init
def backward_pass(self, delta):
return np.repeat(delta[:, np.newaxis, :], 2, 1)
def _init_params(self, data, lengths=None, params='stmpaw'):
X = data['obs']
if self.n_lags == 0:
super(ARTHMM, self)._init_params(data, lengths, params)
else:
if 's' in params:
super(ARTHMM, self)._init_params(data, lengths, 's')
if 't' in params:
super(ARTHMM, self)._init_params(data, lengths, 't')
if 'm' in params or 'a' in params or 'p' in params:
kmmod = cluster.KMeans(
n_clusters=self.n_unique,
random_state=self.random_state).fit(X)
kmeans = kmmod.cluster_centers_
ar_mod = []
ar_alpha = []
ar_resid = []
if not self.shared_alpha:
count = 0
for u in range(self.n_unique):
for f in range(self.n_features):
ar_mod.append(smapi.tsa.AR(X[kmmod.labels_ == \
u,f]).fit(self.n_lags))
ar_alpha.append(ar_mod[count].params[1:])
ar_resid.append(ar_mod[count].resid)
count += 1
else:
# run one AR model on most part of time series
# that has most points assigned after clustering
mf = np.argmax(np.bincount(kmmod.labels_))
for f in range(self.n_features):
ar_mod.append(smapi.tsa.AR(X[kmmod.labels_ == \
mf,f]).fit(self.n_lags))
ar_alpha.append(ar_mod[f].params[1:])
ar_resid.append(ar_mod[f].resid)
if 'm' in params:
mu_init = np.zeros((self.n_unique, self.n_features))
for u in range(self.n_unique):
for f in range(self.n_features):
ar_idx = u
if self.shared_alpha:
ar_idx = 0
mu_init[u,f] = kmeans[u, f] - np.dot(
np.repeat(kmeans[u, f], self.n_lags), ar_alpha[ar_idx])
self.mu_ = np.copy(mu_init)
if 'p' in params:
precision_init = \
np.zeros((self.n_unique, self.n_features, self.n_features))
for u in range(self.n_unique):
if self.n_features == 1:
precision_init[u] = 1.0/(np.var(X[kmmod.labels_ == u]))
else:
precision_init[u] = np.linalg.inv\
(np.cov(np.transpose(X[kmmod.labels_ == u])))
# Alternative: Initialization using ar_resid
#for f in range(self.n_features):
# if not self.shared_alpha:
# precision_init[u,f,f] = 1./np.var(ar_resid[count])
# count += 1
# else:
# precision_init[u,f,f] = 1./np.var(ar_resid[f])'''
self.precision_ = np.copy(precision_init)
if 'a' in params:
if self.shared_alpha:
alpha_init = np.zeros((1, self.n_lags))
alpha_init = ar_alpha[0].reshape((1, self.n_lags))
else:
alpha_init = np.zeros((self.n_unique, self.n_lags))
for u in range(self.n_unique):
ar_idx = 0
alpha_init[u] = ar_alpha[ar_idx]
ar_idx += self.n_features
self.alpha_ = np.copy(alpha_init)
def get_pi(beta,X,alpha):
linear_pred = np.dot(X,beta[1:])
linear_pred = np.tile(linear_pred,len(alpha))
alpha = np.repeat(alpha,len(np.dot(X,beta[1:])))
return logistic(beta[0]+linear_pred+0*alpha)
def _compute_log_likelihood(self, data, from_=0, to_=-1):
ll = self._ll(self.mu_, self.precision_, data['obs'][from_:to_])
rep = self.n_chain
return np.repeat(ll, rep).reshape(-1, self.n_unique*rep)