def run():
# Create some data
N = 500
D = 2
# Initial state
x0 = np.array([0.5, -0.5])
# Dynamics (time varying)
A0 = np.array([[.9, -.4], [.4, .9]])
A1 = np.array([[.98, -.1], [.1, .98]])
l = np.linspace(0, 1, N - 1).reshape((-1, 1, 1))
A = (1 - l) * A0 + l * A1
# Innovation covariance matrix
V = np.identity(D)
# Observation noise covariance matrix
C = np.tile(np.identity(D), (N, 1, 1))
## C0 = 10*np.array([[1, 0], [0, 1]])
## C1 = 0.01*np.array([[1, 0], [0, 1]])
## C = (1-l)**2*C0 + l**2*C1
X = np.empty((N, D))
Y = np.empty((N, D))
# Simulate data
x = x0
X[0, :] = x
Y[0, :] = x + np.random.multivariate_normal(np.zeros(D), C[0, :, :])
for n in range(N - 1):
x = np.dot(A[n, :, :], x) + np.random.multivariate_normal(
np.zeros(D), V)
X[n + 1, :] = x
Y[n + 1, :] = x + np.random.multivariate_normal(
np.zeros(D), C[n + 1, :, :])
# Invert observation noise covariance to observation precision matrices
U = np.empty((N, D, D))
UY = np.empty((N, D))
for n in range(N):
U[n, :, :] = np.linalg.inv(C[n, :, :])
UY[n, :] = np.linalg.solve(C[n, :, :], Y[n, :])
# Construct VB model
Xh = GaussianMarkovChain(np.zeros(D), np.identity(D), A, np.ones(D), n=N)
Yh = Gaussian(Xh.as_gaussian(), np.identity(D), plates=(N, ))
Yh.observe(Y)
Xh.update()
xh = Xh.u[0]
varxh = utils.diagonal(Xh.u[1]) - xh**2
#err = 2 * np.sqrt(varxh)
plt.figure(1)
plt.clf()
for d in range(D):
plt.subplot(D, 1, d)
bpplt.errorplot(xh[:, d], error=2 * np.sqrt(varxh[:, d]))
plt.plot(X[:, d], 'r-')
plt.plot(Y[:, d], '.')
def run():
# Create some data
N = 500
D = 2
# Initial state
x0 = np.array([0.5, -0.5])
# Dynamics (time varying)
A0 = np.array([[.9, -.4], [.4, .9]])
A1 = np.array([[.98, -.1], [.1, .98]])
l = np.linspace(0, 1, N-1).reshape((-1,1,1))
A = (1-l)*A0 + l*A1
# Innovation covariance matrix
V = np.identity(D)
# Observation noise covariance matrix
C = np.tile(np.identity(D), (N, 1, 1))
## C0 = 10*np.array([[1, 0], [0, 1]])
## C1 = 0.01*np.array([[1, 0], [0, 1]])
## C = (1-l)**2*C0 + l**2*C1
X = np.empty((N,D))
Y = np.empty((N,D))
# Simulate data
x = x0
X[0,:] = x
Y[0,:] = x + np.random.multivariate_normal(np.zeros(D), C[0,:,:])
for n in range(N-1):
x = np.dot(A[n,:,:],x) + np.random.multivariate_normal(np.zeros(D), V)
X[n+1,:] = x
Y[n+1,:] = x + np.random.multivariate_normal(np.zeros(D), C[n+1,:,:])
# Invert observation noise covariance to observation precision matrices
U = np.empty((N,D,D))
UY = np.empty((N,D))
for n in range(N):
U[n,:,:] = np.linalg.inv(C[n,:,:])
UY[n,:] = np.linalg.solve(C[n,:,:], Y[n,:])
# Construct VB model
Xh = GaussianMarkovChain(np.zeros(D), np.identity(D), A, np.ones(D), n=N)
Yh = Gaussian(Xh.as_gaussian(), np.identity(D), plates=(N,))
Yh.observe(Y)
Xh.update()
xh = Xh.u[0]
varxh = utils.diagonal(Xh.u[1]) - xh**2
#err = 2 * np.sqrt(varxh)
plt.figure(1)
plt.clf()
for d in range(D):
plt.subplot(D,1,d)
bpplt.errorplot(xh[:,d], error=2*np.sqrt(varxh[:,d]))
plt.plot(X[:,d], 'r-')
plt.plot(Y[:,d], '.')
def run(maxiter=100):
seed = 496#np.random.randint(1000)
print("seed = ", seed)
np.random.seed(seed)
# Simulate some data
D = 3
M = 6
N = 200
c = np.random.randn(M,D)
w = 0.3
a = np.array([[np.cos(w), -np.sin(w), 0],
[np.sin(w), np.cos(w), 0],
[0, 0, 1]])
x = np.empty((N,D))
f = np.empty((M,N))
y = np.empty((M,N))
x[0] = 10*np.random.randn(D)
f[:,0] = np.dot(c,x[0])
y[:,0] = f[:,0] + 3*np.random.randn(M)
for n in range(N-1):
x[n+1] = np.dot(a,x[n]) + np.random.randn(D)
f[:,n+1] = np.dot(c,x[n+1])
y[:,n+1] = f[:,n+1] + 3*np.random.randn(M)
# Create the model
(Y, CX, X, tau, C, gamma, A, alpha) = linear_state_space_model(D, N, M)
# Add missing values randomly
mask = random.mask(M, N, p=0.3)
# Add missing values to a period of time
mask[:,30:80] = False
y[~mask] = np.nan # BayesPy doesn't require this. Just for plotting.
# Observe the data
Y.observe(y, mask=mask)
# Initialize nodes (must use some randomness for C)
C.initialize_from_random()
# Run inference
Q = VB(Y, X, C, gamma, A, alpha, tau)
#
# Run inference with rotations.
#
rotA = transformations.RotateGaussianARD(A, alpha)
rotX = transformations.RotateGaussianMarkovChain(X, A, rotA)
rotC = transformations.RotateGaussianARD(C, gamma)
R = transformations.RotationOptimizer(rotX, rotC, D)
#maxiter = 84
for ind in range(maxiter):
Q.update()
#print('C term', C.lower_bound_contribution())
R.rotate(maxiter=10,
check_gradient=True,
verbose=False,
check_bound=Q.compute_lowerbound,
#check_bound=None,
check_bound_terms=Q.compute_lowerbound_terms)
#check_bound_terms=None)
X_vb = X.u[0]
varX_vb = utils.diagonal(X.u[1] - X_vb[...,np.newaxis,:] * X_vb[...,:,np.newaxis])
u_CX = CX.get_moments()
CX_vb = u_CX[0]
varCX_vb = u_CX[1] - CX_vb**2
# Show results
plt.figure(3)
plt.clf()
for m in range(M):
plt.subplot(M,1,m+1)
plt.plot(y[m,:], 'r.')
plt.plot(f[m,:], 'b-')
bpplt.errorplot(y=CX_vb[m,:],
error=2*np.sqrt(varCX_vb[m,:]))
plt.figure()
Q.plot_iteration_by_nodes()
def run(maxiter=100):
seed = 496 #np.random.randint(1000)
print("seed = ", seed)
np.random.seed(seed)
# Simulate some data
D = 3
M = 6
N = 200
c = np.random.randn(M, D)
w = 0.3
a = np.array([[np.cos(w), -np.sin(w), 0], [np.sin(w),
np.cos(w), 0], [0, 0, 1]])
x = np.empty((N, D))
f = np.empty((M, N))
y = np.empty((M, N))
x[0] = 10 * np.random.randn(D)
f[:, 0] = np.dot(c, x[0])
y[:, 0] = f[:, 0] + 3 * np.random.randn(M)
for n in range(N - 1):
x[n + 1] = np.dot(a, x[n]) + np.random.randn(D)
f[:, n + 1] = np.dot(c, x[n + 1])
y[:, n + 1] = f[:, n + 1] + 3 * np.random.randn(M)
# Create the model
(Y, CX, X, tau, C, gamma, A, alpha) = linear_state_space_model(D, N, M)
# Add missing values randomly
mask = random.mask(M, N, p=0.3)
# Add missing values to a period of time
mask[:, 30:80] = False
y[~mask] = np.nan # BayesPy doesn't require this. Just for plotting.
# Observe the data
Y.observe(y, mask=mask)
# Initialize nodes (must use some randomness for C)
C.initialize_from_random()
# Run inference
Q = VB(Y, X, C, gamma, A, alpha, tau)
#
# Run inference with rotations.
#
rotA = transformations.RotateGaussianARD(A, alpha)
rotX = transformations.RotateGaussianMarkovChain(X, A, rotA)
rotC = transformations.RotateGaussianARD(C, gamma)
R = transformations.RotationOptimizer(rotX, rotC, D)
#maxiter = 84
for ind in range(maxiter):
Q.update()
#print('C term', C.lower_bound_contribution())
R.rotate(
maxiter=10,
check_gradient=True,
verbose=False,
check_bound=Q.compute_lowerbound,
#check_bound=None,
check_bound_terms=Q.compute_lowerbound_terms)
#check_bound_terms=None)
X_vb = X.u[0]
varX_vb = utils.diagonal(X.u[1] - X_vb[..., np.newaxis, :] *
X_vb[..., :, np.newaxis])
u_CX = CX.get_moments()
CX_vb = u_CX[0]
varCX_vb = u_CX[1] - CX_vb**2
# Show results
plt.figure(3)
plt.clf()
for m in range(M):
plt.subplot(M, 1, m + 1)
plt.plot(y[m, :], 'r.')
plt.plot(f[m, :], 'b-')
bpplt.errorplot(y=CX_vb[m, :], error=2 * np.sqrt(varCX_vb[m, :]))
plt.figure()
Q.plot_iteration_by_nodes()
