def initParam(prior, X, N, D, G, M, K, dir_param, prng):
""" initialize variational parameters with prior parameters
"""
[tpM, tpG, lb, ub] = [np.ones(M), np.ones(G), 10., 10.]
tpR = prng.rand(2*M)
[tau_a1, tau_a2, tau_b1, tau_b2, tau_v1, tau_v2] = \
[lb+(ub-lb)*tpR[0 : M], tpM,\
lb+(ub-lb)*tpR[M : 2*M], tpM, \
tpG, tpG]
mu_w = prng.randn(G,D,K)/np.sqrt(D)
sigma_w = np.ones(G*D*K) * 1e-3
mu_b = prng.randn(G, K)/np.sqrt(D)
sigma_b = np.ones(G*K) * 1e-3
phi = np.reshape(prng.dirichlet(np.ones(G)*dir_param, M), M*G)
mu_w = np.reshape(mu_w, G*D*K)
mu_b = np.reshape(mu_b, G*K)
param_init = np.concatenate((tau_a1, tau_a2, tau_b1, tau_b2, phi, tau_v1,\
tau_v2, mu_w, sigma_w, mu_b, sigma_b))
return param_init
def ye_limit(x, trackwidth):
k = TrackCurvature(x)
N = len(k)
lowlimit = -trackwidth/2 * np.ones(N)
highlimit = trackwidth/2 * np.ones(N)
# use a 5% margin so we can't actually hit the center of curvature
lowlimit[k < 0] = np.maximum(0.95/k[k < 0], -trackwidth/2)
highlimit[k > 0] = np.minimum(0.95/k[k > 0], trackwidth/2)
return lowlimit, highlimit
def init_params(D, rs=npr.RandomState(0), **kwargs):
init_mean = -1 * np.ones(D) + rs.randn(D) * .1
init_log_std = -5 * np.ones(D) + rs.randn(D) * .1
# u, w, b
norm_flow_params = [[rs.randn(D,1), rs.randn(D,1), rs.randn(1)] for x in range(k)]
return [init_mean, init_log_std, norm_flow_params]
def initParams(num):
mat = np.random.randn(m, m)
return dict({num + 'z': np.reshape(np.linspace(0.0, 1.0, num=m), (m, 1)),
num + 'u_mean': np.random.randn(m, 1),
num + 'u_cov_fac': mat @ mat.T,
num + 'h_mean': np.random.randn(n, 1),
num + 'h_cov_fac': np.random.randn(n, 1),
num + 'kernel_noise': np.ones((1, 1)),
num + 'kernel_lenscale': np.ones((1, 1)),
num + 'function_noise': np.ones((1, 1))})
def init_params(D, rs=npr.RandomState(0), **kwargs):
init_mean = -1 * np.ones(D) + rs.randn(D) * .1
init_log_std = -5 * np.ones(D) + rs.randn(D) * .1
# gauss_params = np.concatenate([init_mean, init_log_std])
u = rs.randn(D,1)
w = rs.randn(D,1)
b = rs.randn(1)
return [init_mean, init_log_std, u, w, b]
def compute_stats(Ex, ExxT, ExnxT, inhomog):
T = Ex.shape[-1]
E_init_stats = ExxT[:,:,0], Ex[:,0], 1., 1.
E_pair_stats = np.transpose(ExxT, (2, 0, 1))[:-1], \
ExnxT.T, np.transpose(ExxT, (2, 0, 1))[1:], np.ones(T-1)
E_node_stats = np.diagonal(ExxT.T, axis1=-1, axis2=-2), Ex.T, np.ones(T)
if not inhomog:
E_pair_stats = map(lambda x: np.sum(x, axis=0), E_pair_stats)
return E_init_stats, E_pair_stats, E_node_stats
def sinkhorn(w1, w2, M, reg, k):
"""Sinkhorn algorithm with fixed number of iteration (autograd)
"""
K = np.exp(-M / reg)
ui = np.ones((M.shape[0],))
vi = np.ones((M.shape[1],))
for i in range(k):
vi = w2 / (np.dot(K.T, ui))
ui = w1 / (np.dot(K, vi))
G = ui.reshape((M.shape[0], 1)) * K * vi.reshape((1, M.shape[1]))
return G
def get_Aopt(inX, iny):
X_train, y_train, X_test, y_test = ascdata.split_train_test(inX, iny)
X_train = np.concatenate((X_train, np.ones((X_train.shape[ 0 ], 1))), 1)
X_test = np.concatenate((X_test, np.ones((X_test.shape[ 0 ], 1))), 1)
X_train_less, s_train = ascdata.split_X_s(X_train)
X_test_less, s_test = ascdata.split_X_s(X_test)
s_train_phi = ascdata.generate_phi(s_train, d, A_phi, b_phi)
s_test_phi = ascdata.generate_phi(s_test, d, A_phi, b_phi)
nfeatures = X_train.shape[1] - 1
# Dimensions of phi(s)
nfeatures_phi = d
invT2 = 10
def logprob(inA, inX, iny, ins_phi):
RMS = 0
for i in range(len(iny)):
wi = np.dot(inA, inX[i])
RMS_current = (iny[i] - np.dot(wi, ins_phi[i]))**2
RMS += RMS_current
return -RMS
objective = lambda inA, t: -logprob(inA, X_train_less, y_train, s_train_phi)
LLHs = []
LLH_xs = []
def callback(params, t, g):
LLH = -objective(params, t)
LLHs.append(LLH)
LLH_xs.append(t)
print("Iteration {} log likelihood {}".format(t, LLH))
init_A = 0.00000000001*(np.ones((nfeatures_phi, nfeatures)))
# init_A = [[ -3.05236728e-04, -9.50015728e-04, -3.80139503e-04, 1.44010470e-04, -3.05236728e-04,
# -4.96117987e-04, -1.02736409e-04, -1.86416292e-04, -9.52628589e-04, -1.55023279e-03,
# 1.44717581e-04, 1.00000000e-11, -9.50028200e-04, -4.96117987e-04, 1.00000000e-11,
# -3.05236728e-04, 1.77416412e-06, -8.16665436e-06, 3.12622951e-05, -8.25700143e-04,
# 1.44627987e-04, 1.90211243e-05, -8.28273186e-04, -9.41349990e-04, -4.56671031e-04,
# 9.79097070e-03, -6.41866046e-04, -7.79274856e-05, 1.44539330e-04, -3.05236728e-04,
# -5.99188450e-04, -7.29470175e-04, -6.69558174e-04, -9.50028200e-04]]
init_A = np.array(init_A)
print("Optimizing network parameters...")
optimized_params = adam(grad(objective), init_A,
step_size=0.01, num_iters=1000, callback=callback)
Aopt = optimized_params
print "Aopt = ", Aopt
return Aopt, X_train_less, y_train, s_train, X_test_less, y_test, s_test, LLHs, LLH_xs
def get_KMM_ineq_constraints(num_train, B_max, eps):
G_gt_0 = -np.eye(num_train)
h_gt_0 = np.zeros(num_train)
G_lt_B_max = np.eye(num_train)
h_lt_B_max = np.ones(num_train) * B_max
G_B_sum_lt = np.ones(num_train, dtype=float)
h_B_sum_lt = (1+eps) * float(num_train) * np.ones(1)
G_B_sum_gt = -np.ones(num_train, dtype=float)
h_B_sum_gt = -(1-eps) * float(num_train) * np.ones(1)
G = np.vstack((G_gt_0,G_lt_B_max,G_B_sum_lt,G_B_sum_gt))
(h_gt_0,h_lt_B_max,h_B_sum_lt,h_B_sum_gt)
h = np.hstack((h_gt_0,h_lt_B_max,h_B_sum_lt,h_B_sum_gt))
return G,h
def update_K(self, k):
self.K = k
# reinitialize K related parameters
self.w = 1e-3 * np.ones((self.K + 1, self.K))
if not self.self_connect:
for i in xrange(self.K):
self.w[i + 1, i] = 1e-32
if self.extra_w:
tmp = 1e-10 * np.ones((self.K, self.K))
if not self.self_connect:
for i in xrange(self.K):
tmp[i, i] = 1e-32
self.w = np.concatenate([self.w, tmp], axis=0)
def optimize_and_lls(optfun):
num_iters = 200
elbos = []
def callback(params, t, g):
elbo_val = -objective(params, t)
elbos.append(elbo_val)
if t % 50 == 0:
print("Iteration {} lower bound {}".format(t, elbo_val))
init_mean = -1 * np.ones(D)
init_log_std = -5 * np.ones(D)
init_var_params = np.concatenate([init_mean, init_log_std])
variational_params = optfun(num_iters, init_var_params, callback)
return np.array(elbos)
def KL_two_gaussians(params):
mu = params[0:(len(params)-2)/2]
Sigma = np.exp(params[(len(params)-2)/2:-2])
d = len(mu)
muPrior = np.zeros(d)
sigmaPrior = np.ones(d)*50
return np.sum(np.log(sigmaPrior/Sigma)+(Sigma**2+(mu-muPrior)**2)/(2*(sigmaPrior**2))-1/2)
def init_params(D, rs=npr.RandomState(0), **kwargs):
init_mean = -1 * np.ones(D) + rs.randn(D) * .1
init_log_std = -5 * np.ones(D) + rs.randn(D) * .1
# gauss_params = np.concatenate([init_mean, init_log_std])
# u = rs.randn(D,1)
# w = rs.randn(D,1)
# b = rs.randn(1)
norm_flow_params = [[rs.randn(D,1), rs.randn(D,1), rs.randn(1)] for x in range(k)]
# norm_flow_params = np.array(norm_flow_params)
# print (norm_flow_params.shape)
# fadfsa
return [init_mean, init_log_std, norm_flow_params]
def add_data(self, S, F=None):
"""
Add a data set to the list of observations.
First, filter the data with the impulse response basis,
then instantiate a set of parents for this data set.
:param S: a TxK matrix of of event counts for each time bin
and each process.
"""
assert isinstance(S, np.ndarray) and S.ndim == 2 and S.shape[1] == self.K \
and np.amin(S) >= 0 and S.dtype == np.int, \
"Data must be a TxK array of event counts"
T = S.shape[0]
if F is None:
# Filter the data into a TxKxB array
Ftens = self.basis.convolve_with_basis(S)
# Flatten this into a T x (KxB) matrix
# [F00, F01, F02, F10, F11, ... F(K-1)0, F(K-1)(B-1)]
F = Ftens.reshape((T, self.K * self.B))
assert np.allclose(F[:,0], Ftens[:,0,0])
if self.B > 1:
assert np.allclose(F[:,1], Ftens[:,0,1])
if self.K > 1:
assert np.allclose(F[:,self.B], Ftens[:,1,0])
# Prepend a column of ones
F = np.hstack((np.ones((T,1)), F))
for k,node in enumerate(self.nodes):
node.add_data(F, S[:,k])
def expectedstats(natparam):
neghalfJ, h, _, _ = unpack_dense(natparam)
J = -2*neghalfJ
Ex = np.linalg.solve(J, h)
ExxT = np.linalg.inv(J) + Ex[...,None] * Ex[...,None,:]
En = np.ones(J.shape[0]) if J.ndim == 3 else 1.
return pack_dense(ExxT, Ex, En, En)
def main():
(parser, loss) = KLD(50)
print(parser)
print(parser.idxs_and_shapes)
datum = {}
datum['mu1']=np.zeros(50)
datum['mu2']=np.ones(50)
datum['sig1']=5
datum['sig2']=6
trial_vecs = []
for _ in range(5):
trial_vecs.append(np.random.rand(50))
value_and_grad_fun = value_and_grad(pairwise_distance)
value, grad = value_and_grad_fun(trial_vecs)
print(trial_vecs)
weights = parser.stack(datum)
value_and_grad_fun = value_and_grad(loss)
value, grad = value_and_grad_fun(weights)
print(value)
weights = weights - 10e-4*grad
value, grad = value_and_grad_fun(weights)
print(value)
pass
def prediction(params, X):
if len(X.shape)==1:
# Add columns of 1s (we assume params[0] is bias term)
N = X.shape[0]
X = np.c_[np.ones(N), X]
yhat = np.dot(X, params)
return yhat
def test_getter():
def fun(input_tuple):
A = np.sum(input_tuple[0])
B = np.sum(input_tuple[1])
C = np.sum(input_tuple[1])
return A + B + C
d_fun = grad(fun)
input_tuple = (npr.randn(5, 6),
npr.randn(4, 3),
npr.randn(2, 4))
result = d_fun(input_tuple)
assert np.allclose(result[0], np.ones((5, 6)))
assert np.allclose(result[1], 2 * np.ones((4, 3)))
assert np.allclose(result[2], np.zeros((2, 4)))
def test_getter():
def fun(input_dict):
A = np.sum(input_dict['item_1'])
B = np.sum(input_dict['item_2'])
C = np.sum(input_dict['item_2'])
return A + B + C
d_fun = grad(fun)
input_dict = {'item_1' : npr.randn(5, 6),
'item_2' : npr.randn(4, 3),
'item_X' : npr.randn(2, 4)}
result = d_fun(input_dict)
assert np.allclose(result['item_1'], np.ones((5, 6)))
assert np.allclose(result['item_2'], 2 * np.ones((4, 3)))
assert np.allclose(result['item_X'], np.zeros((2, 4)))
def test_getter():
def fun(input_list):
A = np.sum(input_list[0])
B = np.sum(input_list[1])
C = np.sum(input_list[1])
return A + B + C
d_fun = grad(fun)
input_list = [npr.randn(5, 6),
npr.randn(4, 3),
npr.randn(2, 4)]
result = d_fun(input_list)
print result
assert np.allclose(result[0], np.ones((5, 6)))
assert np.allclose(result[1], 2 * np.ones((4, 3)))
assert np.allclose(result[2], np.zeros((2, 4)))
def x_with_bias(x):
"""Add a row of vector which value=1 for the bias to the input X
x.shape=(batch_size, input_vector_length)
=> x_with_bias(x).shape=(batch_size, input_vector_length + 1)
"""
batch_size = x.shape[0]
return np.concatenate((x, np.ones([batch_size, 1])), axis=1)
def PlanePrior(siz):
D = np.ones(siz)
D[:siz[0]/2, :] *= 20
for i in range(siz[0]/2, siz[0]):
y = (i - siz[0]/2 + 1)
z = 20.0 / y
D[i, :] = z
return D
def PhotometricError(iref, inew, R, T, points, D):
# points is a tuple ([y], [x]); convert to homogeneous
siz = iref.shape
npoints = len(points[0])
f = siz[1] # focal length, FIXME
Xref = np.vstack(((points[1] - siz[1]*0.5) / f, # x
(siz[0]*0.5 - points[0]) / f, # y (left->right hand)
np.ones(npoints))) # z = 1
# this is confusingly written -- i am broadcasting the translation T to
# every column, but numpy broadcasting only works if it's rows, hence all
# the transposes
# print D * Xref
Xnew = (np.dot(so3.exp(R), (D * Xref)).T + T).T
# print Xnew
# right -> left hand projection
proj = Xnew[0:2] / Xnew[2]
p = (-proj[1]*f + siz[0]*0.5, proj[0]*f + siz[1]*0.5)
margin = 10 # int(siz[0] / 5)
inwindow_mask = ((p[0] >= margin) & (p[0] < siz[0]-margin-1) &
(p[1] >= margin) & (p[1] < siz[1]-margin-1))
npts_inw = sum(inwindow_mask)
if npts_inw < 10:
return 1e6, np.zeros(6 + npoints)
# todo: filter points which are now out of the window
oldpointidxs = (points[0][inwindow_mask],
points[1][inwindow_mask])
newpointidxs = (p[0][inwindow_mask], p[1][inwindow_mask])
origpointidxs = np.nonzero(inwindow_mask)[0]
E = InterpolatedValues(inew, newpointidxs) - iref[oldpointidxs]
# dE/dk ->
# d/dk r_p^2 = d/dk (Inew(w(r, T, D, p)) - Iref(p))^2
# = -2r_p dInew/dp dp/dw dw/dX dX/dk
# = -2r_p * g(w(r, T, D, p)) * dw(r, T, D, p)
# intensity gradients for each point
Ig = InterpolatedGradients(inew, newpointidxs)
# TODO: use tensors for this
# gradients for R, T, and D
gradient = np.zeros(6 + npoints)
for i in range(npts_inw):
# print 'newidx (y,x) = ', newpointidxs[0][i], newpointidxs[1][i]
# Jacobian of w
oi = origpointidxs[i]
Jw = dw(Xref[0][oi], Xref[1][oi], D[oi], R, T)
# scale back up into pixel space, right->left hand coords to get
# Jacobian of p
Jp = f * np.vstack((-Jw[1], Jw[0]))
# print origpointidxs[i], 'Xref', Xref[:, i], 'Ig', Ig[:, i], \
# 'dwdRz', Jw[:, 2], 'dpdRz', Jp[:, 2]
# full Jacobian = 2*E + Ig * Jp
J = np.sign(E[i]) * np.dot(Ig[:, i], Jp)
# print '2 E[i]', 2*E[i], 'Ig*Jp', np.dot(Ig[:, i], Jp)
gradient[:6] += J[:6]
# print J[:6]
gradient[6+origpointidxs[i]] += J[6]
print R, T, np.sum(np.abs(E)), npts_inw
# return ((0.2*(npoints - npts_inw) + np.dot(E, E)), gradient)
return np.sum(np.abs(E)) / (npts_inw), gradient / (npts_inw)
def expectedstats(natparam):
J, h = natparam[:2]
J = -2*J
Ex = np.linalg.solve(J, h)
ExxT = np.linalg.inv(J) + Ex[...,None] * Ex[...,None,:]
En = np.ones(J.shape[0]) if J.ndim == 3 else 1.
return ExxT, Ex, En, En
def evaluate_prior(all_params): # clean up code so we don't compute matrices twice
layer_params, x0, y0 = unpack_all_params(all_params)
log_prior = 0
for layer in xrange(n_layers):
#import pdb; pdb.set_trace()
mean, cov_params, noise_scale = unpack_kernel_params(layer_params[layer])
cov_y_y = covariance_function(cov_params, x0[layer], x0[layer]) + noise_scale * np.eye(len(y0[layer]))
log_prior += mvn.logpdf(y0[layer],np.ones(len(cov_y_y))*mean,cov_y_y+np.eye(len(cov_y_y))*10)
return log_prior
def main():
np.random.seed(1)
xtrain, ytrain, params_true = make_data_linreg_1d()
N = xtrain.shape[0]
Xtrain = np.c_[np.ones(N), xtrain] # add column of 1s
w_ols, loss_ols = LinregModel.ols_fit(Xtrain, ytrain)
expt_configs = make_expt_config(N)
nexpts = len(expt_configs)
print nexpts
nrows, ncols = nsubplots(nexpts)
#nrows, ncols = 4, 2
loss_trace_fig = plt.figure("loss trace fig")
param_trace_fig = plt.figure("param trace fig")
folder = 'figures'
for expt_num, config in enumerate(expt_configs):
logger = sgd.SGDLogger(print_freq=10)
np.random.seed(1)
batchifier = sgd.MiniBatcher(Xtrain, ytrain, config['batch_size'])
initial_params = np.zeros(2)
lr_fun = lambda(iter): sgd.get_learning_rate_exp_decay(iter,
config['init_lr'], config['lr_decay'])
ttl = config_to_str(config)
print '\nstarting experiment {}'.format(ttl)
print config
obj_fun = LinregModel.objective
#grad_fun = LinregModel.gradient
grad_fun = autograd.grad(obj_fun)
result = sgd.sgd_minimize(initial_params, obj_fun, grad_fun,
batchifier, config['n_steps'], lr_fun, config['momentum'],
callback=logger.update)
print result
plotnum = expt_num + 1
ax = loss_trace_fig.add_subplot(nrows, ncols, plotnum)
plot_loss_trace(logger.obj_trace, loss_ols, ax)
ax.set_title(ttl)
ax = param_trace_fig.add_subplot(nrows, ncols, plotnum)
loss_fun = lambda w0, w1: LinregModel.objective([w0, w1], xtrain, ytrain)
plot_error_surface(loss_fun, params_true, ax)
plot_param_trace(logger.param_trace, ax)
ax.set_title(ttl)
plt.figure("loss trace fig")
fname = os.path.join(folder, 'linreg_1d_sgd_loss_trace.png')
plt.savefig(fname)
plt.figure("param trace fig")
fname = os.path.join(folder, 'linreg_1d_sgd_param_trace.png')
plt.savefig(fname)
plt.show()
def rmsprop(grad, x, callback=None, num_iters=100, step_size=0.1, gamma=0.9, eps = 10**-8):
"""Root mean squared prop: See Adagrad paper for details."""
avg_sq_grad = np.ones(len(x))
for i in range(num_iters):
g = grad(x, i)
if callback: callback(x, i, g)
avg_sq_grad = avg_sq_grad * gamma + g**2 * (1 - gamma)
x -= step_size * g/(np.sqrt(avg_sq_grad) + eps)
return x
def _em_fit(self, init, free_vars_shape, fixed_vars, is_fixed_vars,
priors, max_nt=50, min_nt=0, gtol=1e-3, verbose=False, **kwargs):
# Check any arguments to be passed to the M-step optimisatio function
optim_opts = kwargs.pop('optim_opts', {})
# unpack the inital values
g, beta, mu_ivp = _var_mixer(init, free_vars_shape, fixed_vars, is_fixed_vars)
alpha = 1000.
# do some reshaping
beta = beta.reshape((self.dim.R+1, self.dim.D))
mu_ivp = mu_ivp.reshape((len(self._ifix),
len(self.Y_train_),
self.dim.K))
# initalise pi uniformly
pi = np.ones(len(self._ifix)) / len(self._ifix)
# get the initial responsibilities
r = self._get_responsibilities(pi, g, beta, mu_ivp, alpha)
free_vars = init.copy()
for nt in range(max_nt):
free_vars = self._M_step(free_vars, r, alpha,
free_vars_shape, fixed_vars, is_fixed_vars,
priors,
optim_opts=optim_opts,
**kwargs)
g_, beta, mu_ivp = _var_mixer(free_vars, free_vars_shape, fixed_vars, is_fixed_vars)
beta = beta.reshape((self.dim.R+1, self.dim.D))
mu_ivp = mu_ivp.reshape((len(self._ifix),
len(self.Y_train_),
self.dim.K))
pi = self._update_pi(r)
# check for convergence
dg = np.linalg.norm(g_ - g)
if verbose:
print('iter {}. Delta g: {}'.format(nt+1, dg))
if dg <= gtol and nt >= min_nt:
break
else:
g = g_
# E-step
r = self._get_responsibilities(pi, g, beta, mu_ivp, alpha)
self.g_ = g_
self.beta_ = beta
self.mu_ivp_ = mu_ivp
def init_pgm_param(K, N, alpha, niw_conc=10., random_scale=0.):
def init_niw_natparam(N):
nu, S, m, kappa = N+niw_conc, (N+niw_conc)*np.eye(N), np.zeros(N), niw_conc
m = m + random_scale * npr.randn(*m.shape)
return niw.standard_to_natural(S, m, kappa, nu)
dirichlet_natparam = alpha * (npr.rand(K) if random_scale else np.ones(K))
niw_natparam = np.stack([init_niw_natparam(N) for _ in range(K)])
return dirichlet_natparam, niw_natparam
def test_cast_to_int():
inds = np.ones(5)[:,None]
def fun(W):
W = np.concatenate((W, inds), axis=1)
W = W[:,:-1]
return W[np.int64(W[:,-1])].sum()
W = np.random.randn(5, 10)
check_grads(fun, W)
def draw_panel(self,ax,title,**kwargs):
# set viewing limits on contour plot
xvals = [self.w_hist[s][0] for s in range(len(self.w_hist))]
xvals.append(self.w_init[0])
yvals = [self.w_hist[s][1] for s in range(len(self.w_hist))]
yvals.append(self.w_init[1])
xmax = max(xvals)
xmin = min(xvals)
xgap = (xmax - xmin)*0.1
ymax = max(yvals)
ymin = min(yvals)
ygap = (ymax - ymin)*0.1
xmin -= xgap
xmax += xgap
ymin -= ygap
ymax += ygap
if 'xmin' in kwargs:
xmin = kwargs['xmin']
if 'xmax' in kwargs:
xmax = kwargs['xmax']
if 'ymin' in kwargs:
ymin = kwargs['ymin']
if 'ymax' in kwargs:
ymax = kwargs['ymax']
axes = False
if 'axes' in kwargs:
axes = kwargs['ymax']
pts = False
if 'pts' in kwargs:
pts = kwargs['pts']
pts = False
if 'pts' in kwargs:
pts = kwargs['pts']
linewidth = 2.5
if 'linewidth' in kwargs:
linewidth = kwargs['linewidth']
#### define input space for function and evaluate ####
w1 = np.linspace(xmin,xmax,400)
w2 = np.linspace(ymin,ymax,400)
w1_vals, w2_vals = np.meshgrid(w1,w2)
w1_vals.shape = (len(w1)**2,1)
w2_vals.shape = (len(w2)**2,1)
h = np.concatenate((w1_vals,w2_vals),axis=1)
func_vals = np.asarray([self.g(s) for s in h])
w1_vals.shape = (len(w1),len(w1))
w2_vals.shape = (len(w2),len(w2))
func_vals.shape = (len(w1),len(w2))
### make contour right plot - as well as horizontal and vertical axes ###
# set level ridges
num_contours = kwargs['num_contours']
levelmin = min(func_vals.flatten())
levelmax = max(func_vals.flatten())
cutoff = 0.5
cutoff = (levelmax - levelmin)*cutoff
numper = 3
levels1 = np.linspace(cutoff,levelmax,numper)
num_contours -= numper
levels2 = np.linspace(levelmin,cutoff,min(num_contours,numper))
levels = np.unique(np.append(levels1,levels2))
num_contours -= numper
while num_contours > 0:
cutoff = levels[1]
levels2 = np.linspace(levelmin,cutoff,min(num_contours,numper))
levels = np.unique(np.append(levels2,levels))
num_contours -= numper
a = ax.contour(w1_vals, w2_vals, func_vals,levels = levels,colors = 'k')
ax.contourf(w1_vals, w2_vals, func_vals,levels = levels,cmap = 'Blues')
if axes == True:
ax.axhline(linestyle = '--', color = 'k',linewidth = 1)
ax.axvline(linestyle = '--', color = 'k',linewidth = 1)
# colors for points
s = np.linspace(0,1,len(self.w_hist[:round(len(self.w_hist)/2)]))
s.shape = (len(s),1)
t = np.ones(len(self.w_hist[round(len(self.w_hist)/2):]))
t.shape = (len(t),1)
s = np.vstack((s,t))
colorspec = []
colorspec = np.concatenate((s,np.flipud(s)),1)
colorspec = np.concatenate((colorspec,np.zeros((len(s),1))),1)
### plot function decrease plot in right panel
for j in range(len(self.w_hist)):
w_val = self.w_hist[j]
g_val = self.g(w_val)
# plot in left panel
if pts == 'True':
ax.scatter(w_val[0],w_val[1],s = 30,c = colorspec[j],edgecolor = 'k',linewidth = 1.5*math.sqrt((1/(float(j) + 1))),zorder = 3)
# plot connector between points for visualization purposes
if j > 0:
w_old = self.w_hist[j-1]
w_new = self.w_hist[j]
ax.plot([w_old[0],w_new[0]],[w_old[1],w_new[1]],color = colorspec[j],linewidth = linewidth,alpha = 1,zorder = 2) # plot approx
ax.plot([w_old[0],w_new[0]],[w_old[1],w_new[1]],color = 'k',linewidth = linewidth + 0.4,alpha = 1,zorder = 1) # plot approx
# clean panel
ax.set_title(title,fontsize = 12)
ax.set_xlabel('$w_1$',fontsize = 12)
ax.set_ylabel('$w_2$',fontsize = 12,rotation = 0)
ax.axhline(y=0, color='k',zorder = 0,linewidth = 0.5)
ax.axvline(x=0, color='k',zorder = 0,linewidth = 0.5)
ax.set_xlim([xmin,xmax])
ax.set_ylim([ymin,ymax])
return const - 0.5 * np.dot(np.dot(z.T, pinv), z)
if __name__ == '__main__':
t0 = time.time()
rs = np.random.npr.RandomState(0)
num_samples = 500
num_steps = 32
num_sampler_optimization_steps = 400
sampler_learn_rate = 0.01
D = 2
init_mean = np.zeros(D)
init_log_stddevs = np.log(0.1*np.ones(D))
init_output_weights = 0.1*rs.randn(num_steps, D)
init_transform_weights = 0.1*rs.randn(num_steps, D)
init_biases = 0.1*rs.randn(num_steps)
logprob_mvn = build_logprob_mvn(mean=np.array([0.2,0.4]), cov=np.array([[1.0,0.9], [0.9,1.0]]))
flow_sample, parser = build_flow_sampler_with_inputs(D, num_steps)
parser.add_shape('mean', D)
parser.add_shape('log_stddev', D)
sampler_params = np.zeros(len(parser))
parser.put(sampler_params, 'mean', init_mean)
parser.put(sampler_params, 'log_stddev', init_log_stddevs)
parser.put(sampler_params, 'output weights', init_output_weights)
parser.put(sampler_params, 'transform weights', init_transform_weights)
parser.put(sampler_params, 'biases', init_biases)
def single_input_plot(self, g, weight_histories, cost_histories, **kwargs):
# adjust viewing range
wmin = -3.1
wmax = 3.1
if 'wmin' in kwargs:
wmin = kwargs['wmin']
if 'wmax' in kwargs:
wmax = kwargs['wmax']
onerun_perplot = False
if 'onerun_perplot' in kwargs:
onerun_perplot = kwargs['onerun_perplot']
### initialize figure
fig = plt.figure(figsize=(9, 4))
artist = fig
# remove whitespace from figure
#fig.subplots_adjust(left=0, right=1, bottom=0, top=1) # remove whitespace
#fig.subplots_adjust(wspace=0.01,hspace=0.01)
# create subplot with 2 panels, plot input function in center plot
gs = gridspec.GridSpec(1, 2, width_ratios=[1, 1])
ax1 = plt.subplot(gs[0])
ax2 = plt.subplot(gs[1])
### plot function in both panels
w_plot = np.linspace(wmin, wmax, 500)
g_plot = g(w_plot)
gmin = np.min(g_plot)
gmax = np.max(g_plot)
g_range = gmax - gmin
ggap = g_range * 0.1
gmin -= ggap
gmax += ggap
# plot function, axes lines
ax1.plot(w_plot, g_plot, color='k', zorder=2) # plot function
ax1.axhline(y=0, color='k', zorder=1, linewidth=0.25)
ax1.axvline(x=0, color='k', zorder=1, linewidth=0.25)
ax1.set_xlabel(r'$w$', fontsize=13)
ax1.set_ylabel(r'$g(w)$', fontsize=13, rotation=0, labelpad=25)
ax1.set_xlim(wmin, wmax)
ax1.set_ylim(gmin, gmax)
ax2.plot(w_plot, g_plot, color='k', zorder=2) # plot function
ax2.axhline(y=0, color='k', zorder=1, linewidth=0.25)
ax2.axvline(x=0, color='k', zorder=1, linewidth=0.25)
ax2.set_xlabel(r'$w$', fontsize=13)
ax2.set_ylabel(r'$g(w)$', fontsize=13, rotation=0, labelpad=25)
ax2.set_xlim(wmin, wmax)
ax2.set_ylim(gmin, gmax)
#### loop over histories and plot each
for j in range(len(weight_histories)):
w_hist = weight_histories[j]
c_hist = cost_histories[j]
# colors for points --> green as the algorithm begins, yellow as it converges, red at final point
s = np.linspace(0, 1, len(w_hist[:round(len(w_hist) / 2)]))
s.shape = (len(s), 1)
t = np.ones(len(w_hist[round(len(w_hist) / 2):]))
t.shape = (len(t), 1)
s = np.vstack((s, t))
self.colorspec = []
self.colorspec = np.concatenate((s, np.flipud(s)), 1)
self.colorspec = np.concatenate(
(self.colorspec, np.zeros((len(s), 1))), 1)
### plot all history points
ax = ax2
if onerun_perplot == True:
if j == 0:
ax = ax1
if j == 1:
ax = ax2
for k in range(len(w_hist)):
# pick out current weight and function value from history, then plot
w_val = w_hist[k]
g_val = c_hist[k]
ax.scatter(w_val,
g_val,
s=90,
c=self.colorspec[k],
edgecolor='k',
linewidth=0.5 * ((1 / (float(k) + 1)))**(0.4),
zorder=3,
marker='X') # evaluation on function
ax.scatter(w_val,
0,
s=90,
facecolor=self.colorspec[k],
edgecolor='k',
linewidth=0.5 * ((1 / (float(k) + 1)))**(0.4),
zorder=3)
return probe
if __name__ == '__main__':
# grid_delta = np.load('adhesin/phantom/grid_delta.npy')
# grid_beta = np.load('adhesin/phantom/grid_beta.npy')
# grid_delta = np.load('cone_256_foam/phantom/grid_delta.npy')
# grid_beta = np.load('cone_256_foam/phantom/grid_beta.npy')
grid_delta = dxchange.read_tiff(
'cone_256_foam/test0/intermediate/current.tiff')
grid_beta = np.load('cone_256_foam/phantom/grid_beta.npy')
grid_delta = np.reshape(grid_delta, [1, *grid_delta.shape])
grid_beta = np.reshape(grid_beta, [1, *grid_beta.shape])
probe_real = np.ones([*grid_delta.shape[1:3]])
probe_imag = np.zeros([*grid_delta.shape[1:3]])
# f = open('test/conv_ir_report.csv', 'a')
# f.write('kernel_size,time\n')
wavefield, probe_array, t = multislice_propagate_cnn(grid_delta,
grid_beta,
probe_real,
probe_imag,
5000, [1e-7] * 3,
kernel_size=17,
free_prop_cm=None,
debug=True)
dxchange.write_tiff(np.array(probe_array),
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
sp.random.seed(2)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1), np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.7, 0.3])
q0 = dist.mvnorm(np.ones(1) + 3, np.ones(1) * 2)
samps = q0.rvs(20)
lw = targd.logpdf(samps).flatten() - q0.logpdf(samps)
lw = lw - logsumexp(lw)
q1 = dist.mixt(1, [dist.mvnorm(mu, np.ones(1)) for mu in samps],
lw.flatten(),
comp_w_in_logspace=True)
fig, ax = plt.subplots(figsize=(6, 3))
ax.plot(x, exp(targd.logpdf(x)), label='target density', linewidth=2)
ax.plot(x, exp(q0.logpdf(x)), '-.', label='q0', linewidth=2)
ax.plot(x, exp(q1.logpdf(x)), '--', label='q1', linewidth=2)
ax.legend(loc='best')
ax.set_xticks([])
def sample(self, T, input=None, tag=None, prefix=None, with_noise=True):
N = self.N
K = self.K
D = (self.D, ) if isinstance(self.D, int) else self.D
M = (self.M, ) if isinstance(self.M, int) else self.M
assert isinstance(D, tuple)
assert isinstance(M, tuple)
# If prefix is given, pad the output with it
if prefix is None:
pad = 1
z = np.zeros(T + 1, dtype=int)
x = np.zeros((T + 1, ) + D)
# input = np.zeros((T+1,) + M) if input is None else input
input = np.zeros((T + 1, ) +
M) if input is None else np.concatenate(
(np.zeros((1, ) + M), input))
xmask = np.ones((T + 1, ) + D, dtype=bool)
# Sample the first state from the initial distribution
pi0 = self.init_state_distn.initial_state_distn
z[0] = npr.choice(self.K, p=pi0)
x[0] = self.dynamics.sample_x(z[0],
x[:0],
tag=tag,
with_noise=with_noise)
else:
zhist, xhist, yhist = prefix
pad = len(zhist)
assert zhist.dtype == int and zhist.min() >= 0 and zhist.max() < K
assert xhist.shape == (pad, D)
assert yhist.shape == (pad, N)
z = np.concatenate((zhist, np.zeros(T, dtype=int)))
x = np.concatenate((xhist, np.zeros((T, ) + D)))
# input = np.zeros((T+pad,) + M) if input is None else input
input = np.zeros((T + pad, ) +
M) if input is None else np.concatenate(
(np.zeros((pad, ) + M), input))
xmask = np.ones((T + pad, ) + D, dtype=bool)
# Sample z and x
for t in range(pad, T + pad):
Pt = np.exp(
self.transitions.log_transition_matrices(x[t - 1:t + 1],
input[t - 1:t + 1],
mask=xmask[t - 1:t +
1],
tag=tag))[0]
z[t] = npr.choice(self.K, p=Pt[z[t - 1]])
x[t] = self.dynamics.sample_x(z[t],
x[:t],
input=input[t],
tag=tag,
with_noise=with_noise)
# Sample observations given latent states
# TODO: sample in the loop above?
y = self.emissions.sample(z, x, input=input, tag=tag)
return z[pad:], x[pad:], y[pad:]
def __init__(self, N, K, D, M=0, single_subspace=True, **kwargs):
super(_StudentsTEmissionsMixin, self).__init__(N, K, D, M, single_subspace=single_subspace, **kwargs)
self.inv_etas = -4 + npr.randn(1, N) if single_subspace else npr.randn(K, N)
self.inv_nus = np.log(4) * np.ones(1, N) if single_subspace else np.log(4) * np.ones(K, N)
def fit(
self,
df,
duration_col=None,
event_col=None,
show_progress=False,
timeline=None,
weights_col=None,
robust=False,
initial_point=None,
):
"""
Fit the accelerated failure time model to a dataset.
Parameters
----------
df: DataFrame
a Pandas DataFrame with necessary columns `duration_col` and
`event_col` (see below), covariates columns, and special columns (weights).
`duration_col` refers to
the lifetimes of the subjects. `event_col` refers to whether
the 'death' events was observed: 1 if observed, 0 else (censored).
duration_col: string
the name of the column in DataFrame that contains the subjects'
lifetimes.
event_col: string, optional
the name of the column in DataFrame that contains the subjects' death
observation. If left as None, assume all individuals are uncensored.
show_progress: boolean, optional (default=False)
since the fitter is iterative, show convergence
diagnostics. Useful if convergence is failing.
timeline: array, optional
Specify a timeline that will be used for plotting and prediction
weights_col: string
the column in df that specifies weights per observation.
robust: boolean, optional (default=False)
Compute the robust errors using the Huber sandwich estimator.
initial_point: (d,) numpy array, optional
initialize the starting point of the iterative
algorithm. Default is the zero vector.
Returns
-------
self:
self with additional new properties: ``print_summary``, ``params_``, ``confidence_intervals_`` and more
Examples
--------
>>> N, d = 80000, 2
>>> # some numbers take from http://statwonk.com/parametric-survival.html
>>> breakpoints = (1, 31, 34, 62, 65)
>>> betas = np.array(
>>> [
>>> [1.0, -0.2, np.log(15)],
>>> [5.0, -0.4, np.log(333)],
>>> [9.0, -0.6, np.log(18)],
>>> [5.0, -0.8, np.log(500)],
>>> [2.0, -1.0, np.log(20)],
>>> [1.0, -1.2, np.log(500)],
>>> ]
>>> )
>>> X = 0.1 * np.random.exponential(size=(N, d))
>>> X = np.c_[X, np.ones(N)]
>>> T = np.empty(N)
>>> for i in range(N):
>>> lambdas = np.exp(-betas.dot(X[i, :]))
>>> T[i] = piecewise_exponential_survival_data(1, breakpoints, lambdas)[0]
>>> T_censor = np.minimum(
>>> T.mean() * np.random.exponential(size=N), 110
>>> ) # 110 is the end of observation, eg. current time.
>>> df = pd.DataFrame(X[:, :-1], columns=["var1", "var2"])
>>> df["T"] = np.round(np.maximum(np.minimum(T, T_censor), 0.1), 1)
>>> df["E"] = T <= T_censor
>>> pew = PiecewiseExponentialRegressionFitter(breakpoints=breakpoints, penalizer=0.0001).fit(df, "T", "E")
>>> pew.print_summary()
>>> pew.plot()
"""
if duration_col is None:
raise TypeError("duration_col cannot be None.")
self._time_fit_was_called = datetime.utcnow().strftime(
"%Y-%m-%d %H:%M:%S") + " UTC"
self.duration_col = duration_col
self.event_col = event_col
self.weights_col = weights_col
self._n_examples = df.shape[0]
self.timeline = timeline
self.robust = robust
df = df.copy()
T = pass_for_numeric_dtypes_or_raise_array(
df.pop(duration_col)).astype(float)
E = (pass_for_numeric_dtypes_or_raise_array(df.pop(self.event_col)) if
(self.event_col is not None) else pd.Series(np.ones(
self._n_examples, dtype=bool),
index=df.index,
name="E"))
weights = (pass_for_numeric_dtypes_or_raise_array(
df.pop(self.weights_col)).astype(float) if
(self.weights_col is not None) else pd.Series(
np.ones(self._n_examples, dtype=float),
index=df.index,
name="weights"))
# check to make sure their weights are okay
if self.weights_col:
if (weights.astype(int) != weights).any() and not self.robust:
warnings.warn(
dedent(
"""It appears your weights are not integers, possibly propensity or sampling scores then?
It's important to know that the naive variance estimates of the coefficients are biased. Instead a) set `robust=True` in the call to `fit`, or b) use Monte Carlo to
estimate the variances. See paper "Variance estimation when using inverse probability of treatment weighting (IPTW) with survival analysis"""
),
StatisticalWarning,
)
if (weights <= 0).any():
raise ValueError(
"values in weight column %s must be positive." %
self.weights_col)
df = df.astype(float)
self._check_values(df, T, E, self.event_col)
E = E.astype(bool)
self.durations = T.copy()
self.event_observed = E.copy()
self.weights = weights.copy()
if np.any(self.durations <= 0):
raise ValueError(
"This model does not allow for non-positive durations. Suggestion: add a small positive value to zero elements."
)
if self.fit_intercept:
assert "_intercept" not in df
df["_intercept"] = 1.0
self._LOOKUP_SLICE = self._create_slicer(len(df.columns))
_norm_std = df.std(0)
self._norm_mean = df.mean(0)
# if we included an intercept, we need to fix not divide by zero.
if self.fit_intercept:
_norm_std["_intercept"] = 1.0
else:
_norm_std[_norm_std < 1e-8] = 1.0
_index = pd.MultiIndex.from_tuples(
sum([[(name, c) for c in df.columns]
for name in self._fitted_parameter_names], []))
self._norm_std = pd.Series(np.concatenate([_norm_std.values] *
self.n_breakpoints),
index=_index)
_params, self._log_likelihood, self._hessian_ = self._fit_model(
T.values,
E.values,
weights.values,
normalize(df, 0, _norm_std).values,
show_progress=show_progress,
initial_point=initial_point,
)
self.params_ = _params / self._norm_std
self.variance_matrix_ = self._compute_variance_matrix()
self.standard_errors_ = self._compute_standard_errors(
T.values, E.values, weights.values, df.values)
self.confidence_intervals_ = self._compute_confidence_intervals()
self._predicted_cumulative_hazard_ = self.predict_cumulative_hazard(
df, times=[np.percentile(T, 75)]).T
return self
def fun(x):
return np.tensordot(x * np.ones((2, 2)), x * np.ones((2, 2)), 2)
print("restoring pickled initialization weights")
unpickled = np.load(picklefilename)
init_weights = unpickled['init_weights']
else:
# Build initialization objective
objective, init_gradient = build_init_objective(
L2_VAR_2, NUM_TRAIN, train_images, train_labels, C, D, L)
# Build callback for ADAM optimizer
def init_callback(params, t, g):
lik = -objective(params, t)
print("Initialization iteration {} log-likelihood {}".format(
t, lik))
# initialize weights
pre_init_weights = np.ones(L)
# optimize weights
print("Initializing weights...")
init_weights = adam(init_gradient,
pre_init_weights,
step_size=0.1,
num_iters=INIT_ITERS,
callback=init_callback)
# pickle processed data in /cache (if doesn't already exist)
if not os.path.exists('cache'):
print('creating cache folder')
os.makedirs('cache')
if not os.path.isfile(picklefilename):
print('saving pickled regression initalization data')
# Make an LDS with somewhat interesting dynamics parameters
true_lds = LDS(N, D, emissions="calcium", emission_kwargs={"bin_size":bin_size,"link":link_func})
A0 = .99 * random_rotation(D, theta=np.pi/40)
# S = (1 + 3 * npr.rand(D))
S = np.arange(1, D+1)
R = np.linalg.svd(npr.randn(D, D))[0] * S
A = R.dot(A0).dot(np.linalg.inv(R))
b = np.zeros(D)
true_lds.dynamics.As[0] = A
true_lds.dynamics.bs[0] = b
true_lds.dynamics.Sigmas = true_lds.dynamics.Sigmas / np.max(true_lds.dynamics.Sigmas[0]) * 0.5
# true_lds.dynamics.Sigmas = true_lds.dynamics.Sigmas
# true_lds.emissions.ds[0] = np.clip(npr.randn(N), -10, 0.1)
true_lds.emissions.ds[0] = 10.0 + 3.0 * npr.randn(N)
true_lds.emissions.As[0] = np.clip(0.85 + 0.05 * npr.randn(N), 0.8, 0.95)
true_lds.emissions.betas[0] = 1.0 * np.ones(N)
# set noise on correct scale
true_lds.emissions.inv_etas[0] = np.log(1e-2 * np.ones(N))
x, y = true_lds.sample(T)
smooth_y = true_lds.smooth(x, y)
plt.ion()
plt.figure()
plt.plot(x)
plt.figure()
for n in range(N):
plt.plot(y[:, n] + 10 * n, '-k')
# plt.plot(smooth_y[:, n] + 4 * n, 'r--')
num_samples = 50
num_langevin_steps = 15
num_sampler_optimization_steps = 100
sampler_learn_rate = 0.001
images_per_row = 10
layer_sizes = [784, 200, 100, 10]
L2_reg = 1.0
D = 784
init_init_stddev_scale = 0.2
init_langevin_stepsize = 0.0001
init_langevin_noise_size = 0.000001
init_gradient_power = 0.95
init_log_gradient_scales = np.log(np.ones((1, D)))
prior_relax = 0.05
prior_downscale = 0.1
# train_mnist_model() # Comment after running once.
with open('mnist_models.pkl') as f:
trained_weights, all_mean, all_cov = pickle.load(f)
# Regularize all_cov
all_cov = prior_downscale * (all_cov + prior_relax * np.eye(D))
N_weights, predict_fun, loss_fun, frac_err, nn_loglik = make_nn_funs(
layer_sizes, L2_reg)
from numpy import exp, log, sqrt
from scipy.misc import logsumexp
from autograd import grad, hessian
import distributions as dist
#import seaborn as sns
import matplotlib as mpl
import matplotlib.pyplot as plt
x = np.linspace(-2, 8, 1000)
sp.random.seed(5)
targd = dist.mixt(1, [
dist.mvnorm(np.ones(1) + 1, np.ones(1)),
dist.mvnorm(np.ones(1) + 3.8, np.ones(1))
], [0.8, 0.2])
qrw = dist.mvnorm(np.zeros(1), np.ones(1) * 0.4)
qind = dist.mvnorm(np.ones(1) * 2, np.ones(1) * 0.2)
fig, ax = plt.subplots(figsize=(4, 2))
ax.plot(x,
exp(targd.logpdf(x)) / exp(targd.logpdf(x)).max(),
label=r'$\pi$',
linewidth=2)
for i in range(3):
current = targd.rvs().flatten()
ax.plot(x,
exp(qrw.logpdf(x - current)) / exp(qrw.logpdf(x - current)).max() /
def read_image_data_knn():
print('Reading image data ...')
train_x = np.load('../../Data/data_train_knn.npy')
train_y = np.load('../../Data/train_labels_knn.npy')
test_x = np.load('../../Data/data_test.npy')
return (train_x, train_y, test_x)
############################################################################
train_x, train_y, test_x = read_image_data()
print('Train=', train_x.shape)
print('Test=', test_x.shape)
# Create dummy test output values to compute accuracy
test_y = np.ones(test_x.shape[0])
predicted_y = np.random.randint(0, 4, test_x.shape[0])
print('DUMMY Accuracy=%0.4f' % accuracy_score(test_y, predicted_y, normalize=True))
# Select the section to run by changing the associated boolean to True
# Code for 2b
run2 = False
# Code for 3b
run3 = False
# Code for 4a
run4 = False
# Code for 5a
run5a = True
# Code for 5b
run5b = True
def initialize_variational_params(self, data, input, mask, tag):
data = interpolate_data(data, mask)
q_mu = data.copy()
q_sigma_inv = -4 * np.ones((data.shape[0], self.D))
return q_mu, q_sigma_inv
def m_step(self, expectations, datas, inputs, masks, tags, **kwargs):
expected_joints = sum([np.sum(Ezzp1, axis=0) for _, Ezzp1, _ in expectations]) + 1e-16
expected_joints += self.kappa * np.eye(self.K) + (self.alpha-1) * np.ones((self.K, self.K))
P = (expected_joints / expected_joints.sum(axis=1, keepdims=True)) + 1e-16
assert np.all(P >= 0), "mode is well defined only when transition matrix entries are non-negative! Check alpha >= 1"
self.log_Ps = np.log(P)
def sample(self, T, prefix=None, input=None, tag=None, with_noise=True):
"""
Sample synthetic data from the model. Optionally, condition on a given
prefix (preceding discrete states and data).
Parameters
----------
T : int
number of time steps to sample
prefix : (zpre, xpre)
Optional prefix of discrete states (zpre) and continuous states (xpre)
zpre must be an array of integers taking values 0...num_states-1.
xpre must be an array of the same length that has preceding observations.
input : (T, input_dim) array_like
Optional inputs to specify for sampling
tag : object
Optional tag indicating which "type" of sampled data
with_noise : bool
Whether or not to sample data with noise.
Returns
-------
z_sample : array_like of type int
Sequence of sampled discrete states
x_sample : (T x observation_dim) array_like
Array of sampled data
"""
K = self.K
D = (self.D, ) if isinstance(self.D, int) else self.D
M = (self.M, ) if isinstance(self.M, int) else self.M
assert isinstance(D, tuple)
assert isinstance(M, tuple)
assert T > 0
# Check the inputs
if input is not None:
assert input.shape == (T, ) + M
# Get the type of the observations
dummy_data = self.observations.sample_x(0, np.empty(0, ) + D)
dtype = dummy_data.dtype
# Initialize the data array
if prefix is None:
# No prefix is given. Sample the initial state as the prefix.
pad = 1
z = np.zeros(T, dtype=int)
data = np.zeros((T, ) + D, dtype=dtype)
input = np.zeros((T, ) + M) if input is None else input
mask = np.ones((T, ) + D, dtype=bool)
# Sample the first state from the initial distribution
pi0 = self.init_state_distn.initial_state_distn
z[0] = npr.choice(self.K, p=pi0)
data[0] = self.observations.sample_x(z[0],
data[:0],
input=input[0],
with_noise=with_noise)
# We only need to sample T-1 datapoints now
T = T - 1
else:
# Check that the prefix is of the right type
zpre, xpre = prefix
pad = len(zpre)
assert zpre.dtype == int and zpre.min() >= 0 and zpre.max() < K
assert xpre.shape == (pad, ) + D
# Construct the states, data, inputs, and mask arrays
z = np.concatenate((zpre, np.zeros(T, dtype=int)))
data = np.concatenate((xpre, np.zeros((T, ) + D, dtype)))
input = np.zeros((T + pad, ) +
M) if input is None else np.concatenate(
(np.zeros((pad, ) + M), input))
mask = np.ones((T + pad, ) + D, dtype=bool)
# Convert the discrete states to the range (1, ..., K_total)
m = self.state_map
K_total = len(m)
_, starts = np.unique(m, return_index=True)
z = starts[z]
# Fill in the rest of the data
for t in range(pad, pad + T):
Pt = self.transitions.transition_matrices(data[t - 1:t + 1],
input[t - 1:t + 1],
mask=mask[t - 1:t + 1],
tag=tag)[0]
z[t] = npr.choice(K_total, p=Pt[z[t - 1]])
data[t] = self.observations.sample_x(m[z[t]],
data[:t],
input=input[t],
tag=tag,
with_noise=with_noise)
# Collapse the states
z = m[z]
# Return the whole data if no prefix is given.
# Otherwise, just return the simulated part.
if prefix is None:
return z, data
else:
return z[pad:], data[pad:]
def main():
### Setup
# autoencoder, encoder, decoder = load_autoencoder('models/12 17PM November 08 2017.h5')#models/2.7e-06.h5')
# def encode(q):
# return encoder.predict(numpy.array([q]))[0].astype(numpy.float64)
# def decode(z):
# return decoder.predict(numpy.array([z]))[0].astype(numpy.float64)
encode, decode = train_model()
# Constants
d = 2 # dimensions
I = numpy.identity(d)
B = numpy.concatenate((I, -I), axis=1) # Difference matrix
# Simulation Parameters
spring_const = 10.0 # Technically could vary per spring
h = 0.005
mass = 0.05
# Initial conditions
starting_stretch = 1 #0.6
starting_points = numpy.array([
[0, 1],
[0, 0],
[1, 1],
[1, 0],
[2, 1],
[2, 0],
[3, 1],
[3, 0],
[4, 1],
[4, 0],
]) * 0.1 + 0.3
n_points = len(starting_points) # Num points
q_initial = starting_points.flatten()
z_initial = encode(q_initial)
print("HIOIIIIII")
print(q_initial)
print(z_initial)
print(decode(z_initial))
pinned_points = numpy.array([0, 1])
q_mask = numpy.ones(n_points * d, dtype=bool)
q_mask[numpy.concatenate([pinned_points * d + i
for i in range(d)])] = False
springs = [
(0, 2),
(0, 3),
(2, 3),
(1, 2),
(1, 3),
(2, 4),
(2, 3),
(2, 5),
(3, 5),
(3, 4),
(4, 5),
(4, 6),
(4, 7),
(5, 6),
(5, 7),
(6, 7),
(6, 8),
(6, 9),
(7, 8),
(7, 9),
(8, 9),
]
n_springs = len(springs)
P_matrices = construct_P_matrices(springs, n_points, d)
all_spring_offsets = (B @ (P_matrices @ q_initial).T).T
rest_lens = numpy.linalg.norm(all_spring_offsets,
axis=1) * starting_stretch
mass_matrix = numpy.identity(len(q_initial)) * mass # Mass matrix
external_forces = numpy.array([0, -9.8] * n_points)
def kinetic_energy(q_k, q_k1):
""" Profile this to see if using numpy.dot is different from numpy.matmul (@)"""
d_q = q_k1 - q_k
energy = 1.0 / (2 * h**2) * d_q.T @ mass_matrix @ d_q
return energy
def potential_energy(q_k, q_k1):
q_tilde = 0.5 * (q_k + q_k1)
# sum = 0.0
# for i in range(len(rest_lens)): # TODO I might be able to do this simply with @ (see all_spring_offsets)
# P_i = P_matrices[i]
# l_i = rest_lens[i]
# d_q_tilde_i_sq = q_tilde.T @ P_i.T @ B.T @ B @ P_i @ q_tilde
# sum += (1.0 - 1.0 / l_i * numpy.sqrt(d_q_tilde_i_sq)) ** 2
# Optimized but ugly version
sum = numpy.sum((1.0 - (1.0 / rest_lens) * numpy.sqrt(
numpy.einsum('ij,ij->i', q_tilde.T @ P_matrices.transpose(
(0, 2, 1)) @ B.T, (B @ P_matrices @ q_tilde))))**2)
return 0.5 * spring_const * sum
def discrete_lagrangian(q_k, q_k1):
return kinetic_energy(q_k, q_k1) - potential_energy(q_k, q_k1)
D1_Ld = autograd.grad(discrete_lagrangian, 0) # (q_t, q_t+1) -> R^N*d
D2_Ld = autograd.grad(discrete_lagrangian, 1) # (q_t-1, q_t) -> R^N*d
# Want D1_Ld + D2_Ld = 0
# Do root finding
def DEL(new_q, cur_q, prev_q):
# SUPER hacky way of adding constrained points
for i in pinned_points:
new_q = numpy.insert(new_q, i * d, q_initial[i * d])
new_q = numpy.insert(new_q, i * d + 1, q_initial[i * d + 1])
res = D1_Ld(cur_q, new_q) + D2_Ld(
prev_q, cur_q) + mass_matrix @ external_forces
# SUPER hacky way of adding constrained points
return res[q_mask]
jac_DEL = autograd.jacobian(DEL, 0)
def latent_DEL(new_z, cur_q, prev_q):
new_q = decode(new_z)
res = D1_Ld(cur_q, new_q) + D2_Ld(
prev_q, cur_q) + mass_matrix @ external_forces
return res
def latent_DEL_objective(new_z, cur_q, prev_q):
res = latent_DEL(new_z, cur_q, prev_q)
return res.T @ res
### Simulation
q_history = []
save_freq = 1
current_frame = 0
output_path = 'pca_ae_configurations.pickle'
prev_q = q_initial
cur_q = q_initial
prev_z = z_initial
cur_z = z_initial
while True:
#sol = optimize.root(latent_DEL, cur_z, method='broyden1', args=(cur_q, prev_q))#, jac=jac_DEL) # Note numerical jacobian seems much faster
sol = optimize.minimize(latent_DEL_objective,
cur_z,
args=(cur_q, prev_q),
method='L-BFGS-B',
options={
'gtol': 1e-6,
'eps': 1e-06,
'disp': False
})
prev_z = cur_z
cur_z = sol.x
prev_q = cur_q
cur_q = decode(cur_z)
render(cur_q * 10, springs, save_frames=True)
if save_freq > 0:
current_frame += 1
q_history.append(cur_q)
if current_frame % save_freq == 0:
with open(output_path, 'wb') as f:
pickle.dump(q_history, f)
def activations(weights, *args):
cat_state = np.concatenate(args + (np.ones((args[0].shape[0],1)),), axis=1)
return np.dot(cat_state, weights)
import autograd.numpy as np
from qutip import qeye, sigmax, sigmay, tensor, fock
from tested.getCtrl import getCtrl, pltCtrl
from tested.getFid import getFid
from tested.minimize import minimize
a0 = np.ones([2, 6, 3])
T = np.pi
sx = np.array(sigmax().full())
sy = np.array(sigmay().full())
U0 = np.array(qeye(2).full())
Ugoal = sx
Hcs = [sx, sy]
def Hat(a, t):
c = getCtrl(a, t, T)
return sum([c[i] * Hcs[i] for i in range(len(Hcs))])
def goalFunc(U):
return 1 - getFid(U, Ugoal)
a = minimize(a0, U0, Hat, T, goalFunc)
pltCtrl(a, T)
(r[..., np.newaxis], g[..., np.newaxis], b[..., np.newaxis]),
axis=2))
ax.set_xticks([])
ax.set_yticks([])
plt.draw()
if render:
plt.savefig('step{0:03d}.png'.format(t), bbox_inches='tight')
plt.pause(0.001)
if __name__ == '__main__':
simulation_timesteps = 20
print("Loading initial and target states...")
init_vx = np.ones((rows, cols))
init_vy = np.zeros((rows, cols))
# Initialize the occlusion to be a block.
init_occlusion = -np.ones((rows, cols))
init_occlusion[15:25, 15:25] = 0.0
init_occlusion = init_occlusion.ravel()
def drag(vx):
return np.mean(init_vx - vx)
def lift(vy):
return np.mean(vy - init_vy)
def objective(params):
cur_occlusion = np.reshape(params, (rows, cols))
plt.tight_layout()
if save_figures:
plt.savefig("hmm_2.pdf")
# # Fit an HMM to this synthetic data
# In[7]:
N_iters = 50
hmm = ssm.HMM(K, D, observations="gaussian")
hmm_lls = hmm.fit(y, method="em", num_em_iters=N_iters)
plt.plot(hmm_lls, label="EM")
plt.plot([0, N_iters], true_ll * np.ones(2), ':k', label="True")
plt.xlabel("EM Iteration")
plt.ylabel("Log Probability")
plt.legend(loc="lower right")
# In[8]:
# Find a permutation of the states that best matches the true and inferred states
hmm.permute(find_permutation(z, hmm.most_likely_states(y)))
# In[11]:
# Plot the true and inferred discrete states
hmm_z = hmm.most_likely_states(y)
plt.figure(figsize=(8, 4))
def log_marginal_likelihood(params, x, y):
mean, cov_params, noise_scale = unpack_kernel_params(params)
cov_y_y = cov_func(cov_params, x, x) + noise_scale * np.eye(len(y))
prior_mean = mean * np.ones(len(y))
return mvn.logpdf(y, prior_mean, cov_y_y)
def plot_fit_and_feature_space(self,w,model,feat,**kwargs):
# construct figure
fig = plt.figure(figsize=(9,4))
# create subplot with 2 panels
gs = gridspec.GridSpec(1, 2, width_ratios=[1,1])
ax1 = plt.subplot(gs[0]);
ax2 = plt.subplot(gs[1]);
view = [20,20]
if 'view' in kwargs:
view = kwargs['view']
##### plot left panel in original space ####
# scatter points
xmin,xmax,ymin,ymax = self.scatter_pts_2d(self.x,ax1)
# clean up panel
ax1.set_xlim([xmin,xmax])
ax1.set_ylim([ymin,ymax])
# label axes
ax1.set_xlabel(r'$x$', fontsize = 16)
ax1.set_ylabel(r'$y$', rotation = 0,fontsize = 16,labelpad = 10)
# create fit
s = np.linspace(xmin,xmax,300)[np.newaxis,:]
normalizer = lambda a: a
if 'normalizer' in kwargs:
normalizer = kwargs['normalizer']
t = np.tanh(model(normalizer(s),w))
ax1.plot(s.flatten(),t.flatten(),linewidth = 2,c = 'lime')
#### plot fit in transformed feature space #####
# check if feature transform has internal parameters
x_transformed = 0
sig = signature(feat)
if len(sig.parameters) == 2:
if np.shape(w)[1] == 1:
x_transformed = feat(normalizer(self.x),w)
else:
x_transformed = feat(normalizer(self.x),w[0])
else:
x_transformed = feat(normalizer(self.x))
# two dimensional transformed feature space
if x_transformed.shape[0] == 1:
s = np.linspace(xmin,xmax,300)[np.newaxis,:]
# scatter points
xmin,xmax,ymin,ymax = self.scatter_pts_2d(x_transformed,ax2)
# produce plot
s2 = copy.deepcopy(s)
if len(sig.parameters) == 2:
if np.shape(w)[1] == 1:
s2 = feat(normalizer(s),w)
else:
s2 = feat(normalizer(s),w[0])
else:
s2 = feat(normalizer(s))
t = np.tanh(model(normalizer(s),w))
ax2.plot(s2.flatten(),t.flatten(),linewidth = 2,c = 'lime')
# label axes
ax2.set_xlabel(r'$f\left(x,\mathbf{w}^{\star}\right)$', fontsize = 16)
ax2.set_ylabel(r'$y$', rotation = 0,fontsize = 16,labelpad = 10)
# three dimensional transformed feature space
if x_transformed.shape[0] == 2:
# create panel
ax2 = plt.subplot(gs[1],projection = '3d');
s = np.linspace(xmin,xmax,100)[np.newaxis,:]
# plot data in 3d
xmin,xmax,xmin1,xmax1,ymin,ymax = self.scatter_3d_points(x_transformed,ax2)
# create and plot fit
s2 = copy.deepcopy(s)
if len(sig.parameters) == 2:
s2 = feat(normalizer(s),w[0])
else:
s2 = feat(normalizer(s))
# reshape for plotting
a = s2[0,:]
b = s2[1,:]
a = np.linspace(xmin,xmax,100)
b = np.linspace(xmin1,xmax1,100)
a,b = np.meshgrid(a,b)
# get firstem
a.shape = (1,np.size(s)**2)
f1 = feat(normalizer(a))[0,:]
# secondm
b.shape = (1,np.size(s)**2)
f2 = feat(normalizer(b))[1,:]
# tack a 1 onto the top of each input point all at once
c = np.vstack((a,b))
o = np.ones((1,np.shape(c)[1]))
c = np.vstack((o,c))
r = np.tanh(np.dot(c.T,w))
# various
a.shape = (np.size(s),np.size(s))
b.shape = (np.size(s),np.size(s))
r.shape = (np.size(s),np.size(s))
ax2.plot_surface(a,b,r,alpha = 0.1,color = 'lime',rstride=15, cstride=15,linewidth=0.5,edgecolor = 'k')
ax2.set_xlim([np.min(a),np.max(a)])
ax2.set_ylim([np.min(b),np.max(b)])
'''
a,b = np.meshgrid(t1,t2)
a.shape = (1,np.size(s)**2)
b.shape = (1,np.size(s)**2)
'''
'''
c = np.vstack((a,b))
o = np.ones((1,np.shape(c)[1]))
c = np.vstack((o,c))
# tack a 1 onto the top of each input point all at once
r = (np.dot(c.T,w))
a.shape = (np.size(s),np.size(s))
b.shape = (np.size(s),np.size(s))
r.shape = (np.size(s),np.size(s))
ax2.plot_surface(a,b,r,alpha = 0.1,color = 'lime',rstride=15, cstride=15,linewidth=0.5,edgecolor = 'k')
'''
# label axes
#self.move_axis_left(ax2)
ax2.set_xlabel(r'$f_1(x)$', fontsize = 12,labelpad = 5)
ax2.set_ylabel(r'$f_2(x)$', rotation = 0,fontsize = 12,labelpad = 5)
ax2.set_zlabel(r'$y$', rotation = 0,fontsize = 12,labelpad = 0)
self.move_axis_left(ax2)
ax2.xaxis.set_major_formatter(FormatStrFormatter('%.1f'))
ax2.yaxis.set_major_formatter(FormatStrFormatter('%.1f'))
ax2.view_init(view[0],view[1])
def test_lds_log_probability_perf(T=1000, D=10, N_iter=10):
"""
Compare performance of banded method vs message passing in pylds.
"""
print("Comparing methods for T={} D={}".format(T, D))
from pylds.lds_messages_interface import kalman_info_filter, kalman_filter
# Convert LDS parameters into info form for pylds
As, bs, Qi_sqrts, ms, Ri_sqrts = make_lds_parameters(T, D)
Qis = np.matmul(Qi_sqrts, np.swapaxes(Qi_sqrts, -1, -2))
Ris = np.matmul(Ri_sqrts, np.swapaxes(Ri_sqrts, -1, -2))
x = npr.randn(T, D)
print("Timing banded method")
start = time.time()
for itr in range(N_iter):
lds_log_probability(x, As, bs, Qi_sqrts, ms, Ri_sqrts)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))
# Compare to Kalman Filter
mu_init = np.zeros(D)
sigma_init = np.eye(D)
Bs = np.ones((D, 1))
sigma_states = np.linalg.inv(Qis)
Cs = np.eye(D)
Ds = np.zeros((D, 1))
sigma_obs = np.linalg.inv(Ris)
inputs = bs
data = ms
print("Timing PyLDS message passing (kalman_filter)")
start = time.time()
for itr in range(N_iter):
kalman_filter(mu_init, sigma_init,
np.concatenate([As, np.eye(D)[None, :, :]]), Bs,
np.concatenate([sigma_states,
np.eye(D)[None, :, :]]), Cs, Ds,
sigma_obs, inputs, data)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))
# Info form comparison
J_init = np.zeros((D, D))
h_init = np.zeros(D)
log_Z_init = 0
J_diag, J_lower_diag, h = convert_lds_to_block_tridiag(
As, bs, Qi_sqrts, ms, Ri_sqrts)
J_pair_21 = J_lower_diag
J_pair_22 = J_diag[1:]
J_pair_11 = J_diag[:-1]
J_pair_11[1:] = 0
h_pair_2 = h[1:]
h_pair_1 = h[:-1]
h_pair_1[1:] = 0
log_Z_pair = 0
J_node = np.zeros((T, D, D))
h_node = np.zeros((T, D))
log_Z_node = 0
print("Timing PyLDS message passing (kalman_info_filter)")
start = time.time()
for itr in range(N_iter):
kalman_info_filter(J_init, h_init, log_Z_init, J_pair_11, J_pair_21,
J_pair_22, h_pair_1, h_pair_2, log_Z_pair, J_node,
h_node, log_Z_node)
stop = time.time()
print("Time per iter: {:.4f}".format((stop - start) / N_iter))
def fprop(params):
"""
Forward pass of the NTM.
"""
W = params # aliasing for brevity
xs, hs, ys, ps, ts, os = {}, {}, {}, {}, {}, {}
def l():
"""
Silly utility function that should be called in init.
"""
return [{} for _ in xrange(self.heads)]
rs = l()
k_rs, beta_rs, g_rs, s_rs, gamma_rs = l(),l(),l(),l(),l()
k_ws, beta_ws, g_ws, s_ws, gamma_ws = l(),l(),l(),l(),l()
adds, erases = l(),l()
w_ws, w_rs = l(),l() # read weights and write weights
for idx in range(self.heads):
rs[idx][-1] = self.W['rsInit' + str(idx)] # stores values read from memory
w_ws[idx][-1] = softmax(self.W['w_wsInit' + str(idx)])
w_rs[idx][-1] = softmax(self.W['w_rsInit' + str(idx)])
mems = {} # the state of the memory at every timestep
mems[-1] = self.W['memsInit']
loss = 0
for t in xrange(len(inputs)):
xs[t] = np.reshape(np.array(inputs[t]),inputs[t].shape[::-1])
rsum = 0
for idx in range(self.heads):
rsum = rsum + np.dot(W['rh' + str(idx)], np.reshape(rs[idx][t-1],(self.M,1)))
hs[t] = np.tanh(np.dot(W['xh'], xs[t]) + rsum + W['bh'])
os[t] = np.tanh(np.dot(W['ho'], hs[t]) + W['bo'])
for idx in range(self.heads):
# parameters to the read head
k_rs[idx][t] = np.tanh(np.dot(W['ok_r' + str(idx)],os[t]) + W['bk_r' + str(idx)])
beta_rs[idx][t] = softplus(np.dot(W['obeta_r' + str(idx)],os[t])
+ W['bbeta_r' + str(idx)])
g_rs[idx][t] = sigmoid(np.dot(W['og_r' + str(idx)],os[t]) + W['bg_r' + str(idx)])
s_rs[idx][t] = softmax(np.dot(W['os_r' + str(idx)],os[t]) + W['bs_r' + str(idx)])
gamma_rs[idx][t] = 1 + sigmoid(np.dot(W['ogamma_r' + str(idx)], os[t])
+ W['bgamma_r' + str(idx)])
# parameters to the write head
k_ws[idx][t] = np.tanh(np.dot(W['ok_w' + str(idx)],os[t]) + W['bk_w' + str(idx)])
beta_ws[idx][t] = softplus(np.dot(W['obeta_w' + str(idx)], os[t])
+ W['bbeta_w' + str(idx)])
g_ws[idx][t] = sigmoid(np.dot(W['og_w' + str(idx)],os[t]) + W['bg_w' + str(idx)])
s_ws[idx][t] = softmax(np.dot(W['os_w' + str(idx)],os[t]) + W['bs_w' + str(idx)])
gamma_ws[idx][t] = 1 + sigmoid(np.dot(W['ogamma_w' + str(idx)], os[t])
+ W['bgamma_w' + str(idx)])
# the erase and add vectors
# these are also parameters to the write head
# but they describe "what" is to be written rather than "where"
adds[idx][t] = np.tanh(np.dot(W['oadds' + str(idx)], os[t]) + W['badds' + str(idx)])
erases[idx][t] = sigmoid(np.dot(W['oerases' + str(idx)], os[t]) + W['erases' + str(idx)])
w_ws[idx][t] = addressing.create_weights( k_ws[idx][t]
, beta_ws[idx][t]
, g_ws[idx][t]
, s_ws[idx][t]
, gamma_ws[idx][t]
, w_ws[idx][t-1]
, mems[t-1])
w_rs[idx][t] = addressing.create_weights( k_rs[idx][t]
, beta_rs[idx][t]
, g_rs[idx][t]
, s_rs[idx][t]
, gamma_rs[idx][t]
, w_rs[idx][t-1]
, mems[t-1])
ys[t] = np.dot(W['oy'], os[t]) + W['by']
ps[t] = sigmoid(ys[t])
one = np.ones(ps[t].shape)
ts[t] = np.reshape(np.array(targets[t]),(self.out_size,1))
epsilon = 2**-23 # to prevent log(0)
a = np.multiply(ts[t] , np.log2(ps[t] + epsilon))
b = np.multiply(one - ts[t], np.log2(one-ps[t] + epsilon))
loss = loss - (a + b)
for idx in range(self.heads):
# read from the memory
rs[idx][t] = memory.read(mems[t-1],w_rs[idx][t])
# write into the memory
mems[t] = memory.write(mems[t-1],w_ws[idx][t],erases[idx][t],adds[idx][t])
self.stats = [loss, ps, w_rs, w_ws, adds, erases]
return np.sum(loss)
true_rarhmm = rARHMM(nb_states=3, dm_obs=2, trans_type='neural')
# trajectory lengths
T = [1250, 1150, 1025]
true_z, x = true_rarhmm.sample(horizon=T)
true_ll = true_rarhmm.log_norm(x)
rarhmm = rARHMM(nb_states=3, dm_obs=2, trans_type='neural')
rarhmm.initialize(x)
lls = rarhmm.em(x, nb_iter=100, prec=0., verbose=True)
print("true_ll=", true_ll, "hmm_ll=", lls[-1])
plt.figure(figsize=(5, 5))
plt.plot(np.ones(len(lls)) * true_ll, '-r')
plt.plot(lls)
plt.show()
_, rarhmm_z = rarhmm.viterbi(x)
_seq = npr.choice(len(x))
rarhmm.permute(permutation(true_z[_seq], rarhmm_z[_seq], K1=3, K2=3))
_, rarhmm_z = rarhmm.viterbi(x[_seq])
plt.figure(figsize=(8, 4))
plt.subplot(211)
plt.imshow(true_z[_seq][None, :], aspect="auto", cmap=cmap, vmin=0, vmax=len(colors) - 1)
plt.xlim(0, len(x[_seq]))
plt.ylabel("$z_{\\mathrm{true}}$")
plt.yticks([])
def init_var_params(layer_sizes, scale=-5, scale_mean=1):
_, num_weights = shapes_and_num(layer_sizes)
return rs.randn(num_weights) * scale_mean, np.ones(
num_weights) * scale # mean, log_std
def _add_intercept(self, X):
if self.fit_intercept:
return np.c_[np.ones(len(X)), X]
# wDc = np.array([1.0]) wDc = np.array([-5.5]) w = np.concatenate((wDc, wfilt, wfilt2)) # Generate simulated dataset # Xmat = np.hstack((np.ones((T,1)), npr.randn(T, D_in))) Cov = np.array([[1.0, 0.4], [0.4, 1.0]]) L = np.linalg.cholesky(Cov) Xstim = (L @ npr.randn(2, T * 2)).T # split in halfs from scipy.linalg import hankel Xmat1 = hankel(Xstim[:, 0], Xstim[:, 0][-19:]) Xmat2 = hankel(Xstim[:, 1], Xstim[:, 1][-19:]) Xmat = np.hstack((np.ones((T * 2, 1)), Xmat1, Xmat2)) # import ssm # from ssm import LDS # from ssm.util import random_rotation # true_lds = LDS(2, D_in, emissions="gaussian") # A0 = .95 * random_rotation(D_in, theta=np.pi/40) # S = np.arange(1, D_in+1) # R = np.linalg.svd(npr.randn(D_in, D_in))[0] * S # A = R.dot(A0).dot(np.linalg.inv(R)) # b = np.zeros(D_in) # true_lds.dynamics.As[0] = A # true_lds.dynamics.bs[0] = b # true_lds.dynamics.Sigmas = true_lds.dynamics.Sigmas / np.max(true_lds.dynamics.Sigmas[0]) * 0.5 # x, y = true_lds.sample(T) # x = x / np.max(x) * 5.0
