def plot_y_vs_u(xs_train, ys_train, P, xs_test=None, ys_test=None, xlim=None, ylim=None):
s = 0.75
alpha = 0.8
us_train = np.dot(xs_train, P)
if P.shape[1] == 1:
fig, ax = plt.subplots()
ax.scatter(us_train[:,0], ys_train, color='r', label='train', s=s, alpha=alpha)
if not ys_test is None:
us_test = np.dot(xs_test, P)
ax.scatter(us_test[:,0], ys_test, color='b', label='test', s=s, alpha=alpha)
ax.legend()
ax.set_xlabel('u0')
ax.set_ylabel('y')
ax.set_title('y vs projected features')
basic.display_fig_inline(fig)
elif P.shape[1] == 2:
fig = plt.figure()
ax = fig.add_subplot(111, projection='3d')
ax.scatter(us_train[:,0], us_train[:,1],ys_train, color='r', label='train', s=s, alpha=alpha)
if not ys_test is None:
us_test = np.dot(xs_test, P)
ax.scatter(us_test[:,0], us_test[:,1],ys_test, color='b', label='test', s=s, alpha=alpha)
ax.set_xlabel('u0')
ax.set_ylabel('u1')
ax.set_zlabel('y')
ax.set_title('y vs projected features')
basic.display_fig_inline(fig)
def standard_to_natural(nu, S, M, K):
Kinv = np.linalg.inv(K)
A = Kinv
B = np.dot(Kinv, M.T)
C = S + np.dot(M, B)
d = nu
return (A, B, C, d)
def get_KMM_ws_given_P(xs_train, xs_test, get_K, B_max, eps, P):
# project data
us_train = np.dot(xs_train, P)
us_test = np.dot(xs_test, P)
return get_KMM_ws(B_max, eps, get_K, us_train, us_test)
def normalizing_flows(z_0, norm_flow_params):
'''
z_0: [n_samples, D]
u: [D,1]
w: [D,1]
b: [1]
'''
current_z = z_0
all_zs = []
all_zs.append(z_0)
for params_k in norm_flow_params:
u = params_k[0]
w = params_k[1]
b = params_k[2]
# Appendix equations
m_x = -1. + np.log(1.+np.exp(np.dot(w.T,u)))
u_k = u + (-1. + np.log(1.+np.exp(np.dot(w.T,u))) - np.dot(w.T,u)) * (w/np.linalg.norm(w))
# u_k = u
# [D,1]
term1 = np.tanh(np.dot(current_z,w)+b)
# [n_samples, D]
term1 = np.dot(term1,u_k.T)
# [n_samples, D]
current_z = current_z + term1
all_zs.append(current_z)
return current_z, all_zs
def get_predictions(Aopt, inX, s_bp):
s_bp_phi = ascdata.generate_phi(s_bp, d, A_phi, b_phi)
y_pred = []
for i in range(inX.shape[0]):
wi = np.dot(Aopt, inX[i])
y_pred.append(np.dot(wi.T, s_bp_phi[i]))
return y_pred
def mvt_logpdf(x, mu, Li, df):
dim = Li.shape[0]
Ki = np.dot(Li.T, Li)
#determinant is just multiplication of diagonal elements of cholesky
logdet = 2*log(1./np.diag(Li)).sum()
lpdf_const = (gammaln((df + dim) / 2)
-(gammaln(df/2)
+ (log(df)+log(np.pi)) * dim*0.5
+ logdet * 0.5)
)
x = np.atleast_2d(x)
if x.shape[1] != mu.size:
x = x.T
assert(x.shape[1] == mu.size
or x.shape[0] == mu.size)
d = (x - mu.reshape((1 ,mu.size))).T
Ki_d_scal = np.dot(Ki, d) /df #vector
d_Ki_d_scal_1 = diag_dot(d.T, Ki_d_scal) + 1. #scalar
res_pdf = (lpdf_const
- 0.5 * (df + dim) * np.log(d_Ki_d_scal_1)).flatten()
if res_pdf.size == 1:
res_pdf = np.float(res_pdf)
return res_pdf
def _cumulative_hazard(self, params, T, *Xs):
alpha_params = params[self._LOOKUP_SLICE["alpha_"]]
alpha_ = np.exp(np.dot(Xs[0], alpha_params))
beta_params = params[self._LOOKUP_SLICE["beta_"]]
beta_ = np.exp(np.dot(Xs[1], beta_params))
return np.log1p((T / alpha_) ** beta_)
def natural_condition_on(J, h, y, Jxx, Jxy, Jyy=None, logZ=None):
# NOTE: assumes Jxy is *negative* definite, usually h - np.dot(Jxy, y.T).T
J_cond, h_cond = J + Jxx, h + np.dot(Jxy, y.T).T
if Jyy is None or logZ is None:
return J_cond, h_cond
return (J_cond, h_cond), logZ + np.dot(y, np.dot(Jyy, y.T))
def ns_loss_a(Wsub):
h = Wsub[0, :N]
vwo = Wsub[1, N:]
vwi_negs = Wsub[2:, N:]
vwo_h = npa.dot(vwo, h)
vwi_negs_h = npa.dot(vwi_negs, h)
return -npa.log(siga(vwo_h)) - npa.sum(npa.log(siga(-vwi_negs_h)))
def backward_pass(self, delta):
if len(delta.shape) == 2:
delta = delta[:, np.newaxis, :]
n_samples, n_timesteps, input_shape = delta.shape
p = self._params
# Temporal gradient arrays
grad = {k: np.zeros_like(p[k]) for k in p.keys()}
dh_next = np.zeros((n_samples, input_shape))
output = np.zeros((n_samples, n_timesteps, self.input_dim))
# Backpropagation through time
for i in reversed(range(n_timesteps)):
dhi = self.activation_d(self.states[:, i, :]) * (delta[:, i, :] + dh_next)
grad['W'] += np.dot(self.last_input[:, i, :].T, dhi)
grad['b'] += delta[:, i, :].sum(axis=0)
grad['U'] += np.dot(self.states[:, i - 1, :].T, dhi)
dh_next = np.dot(dhi, p['U'].T)
d = np.dot(delta[:, i, :], p['U'].T)
output[:, i, :] = np.dot(d, p['W'].T)
# Change actual gradient arrays
for k in grad.keys():
self._params.update_grad(k, grad[k])
return output
def cost(usv):
delta = .5
u = usv[0]
s = usv[1]
vt = usv[2]
X = np.dot(np.dot(u, np.diag(s)), vt)
return np.sum(np.sqrt((X - A)**2 + delta**2) - delta)
def mean(self, test_points, g=None):
if g is None:
g = np.concatenate([val for _, val in self.__obs])
L, Lbar = calc_side_matrices(self.__operators, self.__operators_bar, self.__obs, test_points, self.__op_cache, self.__fun_args)
mu_multiplier = np.dot(Lbar, self.__LLbar_inv)
return np.dot(mu_multiplier, g)
def magcal_residual(X, a, mb):
""" residual from all observations given magnetometer eccentricity, bias,
gyro bias, and gyro scale"""
# (x-c)T A^T A (x-c) = 1
# x^T Ax - 2x^T Ac + c^T Ac = 1
# a b c | x' = ax + by + cz
# 0 d e | y' = dy + ez
# 0 0 f | z' = fz
# z = 1/f z'
# y = 1/d (y' - e/f z')
# x = 1/a (x' - b/d(y' - e/f z') - c/f z')
# = 1/a (x' - b/d y' - (be/df - c/f) z')
# (x-c) A^T A (x-c)
# [(A x) - (A c)]^2 - 1 = 0
# y = A(x-c)
# y /= ||y||
# q(x; A, c) = (A^-1 (y+c) - x)^2
Y = np.dot(X - mb, Ainv(a)).T
Y /= np.linalg.norm(Y, axis=0)
# Y /= np.sqrt(np.sum(np.square(Y), axis=0))
Y = np.dot(Y.T, Amatrix(a)) + mb
return np.mean(np.sum(np.square(X - Y), axis=1))
def scalar_log_lik(theta_1, theta_2, x):
arg = (x - theta_1)
lik1 = 1.0 / np.sqrt(2 * SIGMA_x ** 2 * np.pi) * np.exp(- np.dot(arg, arg) / (2 * SIGMA_x ** 2))
arg = (x - theta_1 - theta_2)
lik2 = 1.0 / np.sqrt(2 * SIGMA_x ** 2 * np.pi) * np.exp(- np.dot(arg, arg) / (2 * SIGMA_x ** 2))
return np.log(0.5 * lik1 + 0.5 * lik2)
def get_obj(use_yu, obj_from_ws_and_Ks, xs_train, xs_test, Ky, y, KMM_get_K, SDR_get_K, cvxopt_solver, A, b, P, B=None):
# wrapper
us_train = np.dot(xs_train, P)
us_test = np.dot(xs_test, P)
# pdb.set_trace()
Ku, kappau = get_KMM_params(us_train, us_test, KMM_get_K)
# pdb.set_trace()
wsopt = cvxopt_solver(Ku, kappau, A, b)
SDR_Ku = SDR_get_K(us_train, us_train)
if B is None:
if not use_yu:
return obj_from_ws_and_Ks((Ky, SDR_Ku), wsopt)
else:
try:
return obj_from_ws_and_Ks((Ky, SDR_Ku), (y, us_train), wsopt)
except Exception as e:
print e
pdb.set_trace()
else:
if not use_yu:
return obj_from_ws_and_Ks((Ky, SDR_Ku), wsopt, B) # NEW!
else:
return obj_from_ws_and_Ks((Ky, SDR_Ku), (y, us_train), wsopt, B)
def variational_log_density(params, samples):
'''
samples: [n_samples, D]
u: [D,1]
w: [D,1]
b: [1]
Returns: [num_samples]
'''
n_samples = len(samples)
mean = params[0]
log_std = params[1]
u = params[2]
w = params[3]
b = params[4]
# print (samples.shape)
# samples = sample_diag_gaussian(mean, log_std, num_samples, rs)
z_k = normalizing_flows(samples, u, w, b)
logp_zk = logprob(z_k)
logp_zk = np.reshape(logp_zk, [n_samples, 1])
logq_z0 = diag_gaussian_log_density(samples, mean, log_std)
logq_z0 = np.reshape(logq_z0, [n_samples, 1])
# [n_samples, D]
phi = np.dot((1.-np.tanh(np.dot(samples,w)+b)**2), w.T)
# [n_samples, 1]
sum_nf = np.log(abs(1+np.dot(phi, u)))
# return logq_z0 - sum_nf
return np.reshape(logq_z0 - sum_nf, [n_samples])
def get_dobj_dP(use_yu, xs_train, xs_test, Ky, y, SDR_get_K, KMM_get_K, dobj_dP_thru_Ku, lin_solver, cvxopt_solver, df_dws, d_dP_df_dws, d_dws_df_dws, dobj_dwsopt, A, b, P, B=None):
# wrapper
# calculate intermediate stuff
us_train = np.dot(xs_train, P)
us_test = np.dot(xs_test, P)
KMM_Ku, kappau = get_KMM_params(us_train, us_test, KMM_get_K)
wsopt = cvxopt_solver(KMM_Ku, kappau, A, b)
# gradient thru wsopt
SDR_Ku = SDR_get_K(us_train, us_train)
if B is None:
if not use_yu:
dobj_dP_thru_wsopt_val = get_dL_dp_thru_xopt(lin_solver, df_dws, d_dP_df_dws, d_dws_df_dws, dobj_dwsopt, A, b, wsopt, P, L_args=(Ky, SDR_Ku)) # L_args is the 2nd argument to dobj_dwsopt
else:
dobj_dP_thru_wsopt_val = get_dL_dp_thru_xopt(lin_solver, df_dws, d_dP_df_dws, d_dws_df_dws, dobj_dwsopt, A, b, wsopt, P, L_args=(Ky, SDR_Ku, y, us_train))
else:
if not use_yu:
dobj_dP_thru_wsopt_val = get_dL_dp_thru_xopt(lin_solver, df_dws, d_dP_df_dws, d_dws_df_dws, dobj_dwsopt, A, b, wsopt, P, L_args=(Ky, SDR_Ku, B)) # NEW! means dobj_dwsopt will accept h in 2nd argument
else:
dobj_dP_thru_wsopt_val = get_dL_dp_thru_xopt(lin_solver, df_dws, d_dP_df_dws, d_dws_df_dws, dobj_dwsopt, A, b, wsopt, P, L_args=(Ky, SDR_Ku, y, us_train, B))
# gradient thru Ku
if B is None:
dobj_dP_thru_Ku_val = dobj_dP_thru_Ku(P, wsopt)
else:
dobj_dP_thru_Ku_val = dobj_dP_thru_Ku(P, wsopt, B) # NEW!
return dobj_dP_thru_wsopt_val + dobj_dP_thru_Ku_val
def vjp(g):
vjps = []
q_vjp = solve_sylvester(anp.transpose(a), anp.transpose(b), g)
if 0 in argnums: vjps.append(-anp.dot(q_vjp, anp.transpose(ans)))
if 1 in argnums: vjps.append(-anp.dot(anp.transpose(ans), q_vjp))
if 2 in argnums: vjps.append(q_vjp)
return tuple(vjps)
def setUp(self):
self.m = m = 5
self.n = n = 2
self.k = k = 1
self.man = Grassmann(m, n, k=k)
self.proj = lambda x, u: u - npa.dot(x, npa.dot(x.T, u))
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
def setUp(self):
self.m = m = 20
self.n = n = 2
self.k = k = 1
self.man = Stiefel(m, n, k=k)
self.proj = lambda x, u: u - npa.dot(x, npa.dot(x.T, u) +
npa.dot(u.T, x)) / 2
def natural_predict_grad(g, ans, belief, J11, J12, J22, logZ):
J, h = belief
(g_J_predict, g_h_predict), g_lognorm = g
# re-run forward pass (need to pass these things back here!)
L, v, v2, temp, h, lognorm = natural_predict_forward_temps(J, J11, J12, h)
J12 = -J12
# run the backward pass
# NEEDS: L, v, v2, temp
# ALSO USES: h, lognorm
g_temp = np.dot(temp, (g_J_predict + g_J_predict.T)/2.)
g_L_1 = solve_triangular_grad_arg0(g_temp, temp, L, J12, 'N')
g_a = -np.dot(J12, g_h_predict)
g_L_2 = solve_triangular_grad_arg0(g_a, v2, L, v, 'T')
g_v_1 = solve_triangular_grad_arg1(g_a, v2, L, v, 'T')
g_L_3 = lognorm_grad_arg0(g_lognorm, lognorm, L, v)
g_v_2 = lognorm_grad_arg1(g_lognorm, lognorm, L, v)
g_L_4 = solve_triangular_grad_arg0(g_v_1 + g_v_2, v, L, h, 'N')
# print 'high-level: {}'.format((g_v_1 + g_v_2, v, L))
g_h = solve_triangular_grad_arg1(g_v_1 + g_v_2, v, L, h, 'N')
# print 'high_level: {}'.format(g_h)
g_J = cholesky_grad(L, g_L_1 + g_L_2 + g_L_3 + g_L_4)
return (-2*g_J, g_h)
def predict(self, x): if self.prob_func_ == "sigmoid": prob = (1.0 / (1.0 + np.exp(-np.dot(x, self.coef_) - self.intercept_)))[:,np.newaxis] prob = np.concatenate((1.0-prob, prob), axis=1) else: # self.prob_func_ == "softmax" prob = np.exp(np.dot(x, self.coef_.T) + self.intercept_) prob /= np.sum(prob, axis=1)[:,np.newaxis] return np.array([self.classes_[i] for i in np.argmax(prob, axis=1)])
def ortho(P):
ans = np.zeros(P.shape)
x_dim, z_dim = P.shape
for j in xrange(z_dim):
temp = P[:,j] - np.dot(ans, np.dot(ans.T, P[:,j]))
temp = temp / np.linalg.norm(temp)
ans[:,j] = temp
return ans
def backward_pass(self, delta):
dW = np.dot(self.last_input.T, delta)
db = np.sum(delta, axis=0)
# Update gradient values
self._params.update_grad('W', dW)
self._params.update_grad('b', db)
return np.dot(delta, self._params['W'].T)
def _cumulative_hazard(self, params, T, *Xs):
mu_params = params[self._LOOKUP_SLICE["mu_"]]
mu_ = np.dot(Xs[0], mu_params)
sigma_params = params[self._LOOKUP_SLICE["sigma_"]]
sigma_ = np.exp(np.dot(Xs[1], sigma_params))
Z = (np.log(T) - mu_) / sigma_
return -logsf(Z)
def natural_to_standard(natparam):
A, B, C, d = natparam
nu = d
Kinv = A
K = symmetrize(np.linalg.inv(Kinv))
M = np.dot(K, B).T
S = C - np.dot(M, B)
return nu, S, M, K
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 neural_net_predict(params, inputs):
"""Params is a list of (weights, bias) tuples.
inputs is an (N x D) matrix."""
for W, b in params[:-1]:
outputs = batch_normalize(np.dot(inputs, W) + b)
inputs = relu(outputs)
outW, outb = params[-1]
outputs = np.dot(inputs, outW) + outb
return outputs
def eval_log_properly(self, x): det = np.linalg.det(self.Sigma) const = (self.size/2.0)*np.log(2*np.pi) const = -0.5*np.log(det) - const prec = np.linalg.inv(self.Sigma) t = np.subtract(x, self.Mu) v = np.dot(np.transpose(t), prec) v = -0.5*np.dot(v, t) return const + v
def fun(A):
rng = np.random.RandomState(0)
z = np.dot(np.linalg.cholesky(A), rng.randn(A.shape[0]))
return np.linalg.norm(z)
def rand_psd(D):
mat = npr.randn(D,D)
return np.dot(mat, mat.T)
def model(self, x, w):
a = w[0] + np.dot(x.T, w[1:])
return a.T
def log_gaussian_density(x, mu, sigma):
b, log_det_sigma = solve_posdef(sigma, x - mu)
const = x.shape[0] * np.log(2 * np.pi) # Can remove if needed
return -0.5 * (np.dot(x - mu, b) + log_det_sigma + const)
def loss(W_vect, X, T):
log_prior = -L2_reg * np.dot(W_vect.T, W_vect)
log_lik = np.sum(predictions(W_vect, X) * T)
return -log_prior - log_lik
def test_hessian_vector_product():
fun = lambda a: np.sum(np.sin(a))
a = npr.randn(5)
v = npr.randn(5)
H = hessian(fun)(a)
check_equivalent(np.dot(H, v), hessian_vector_product(fun)(a, v))
def outputs(weights,
input_set,
fence_set,
output_set=None,
return_pred_set=False):
update_x_weights = parser.get(weights, 'update_x_weights')
update_h_weights = parser.get(weights, 'update_h_weights')
reset_x_weights = parser.get(weights, 'reset_x_weights')
reset_h_weights = parser.get(weights, 'reset_h_weights')
thidden_x_weights = parser.get(weights, 'thidden_x_weights')
thidden_h_weights = parser.get(weights, 'thidden_h_weights')
output_h_weights = parser.get(weights, 'output_h_weights')
data_count = len(fence_set) - 1
feat_count = input_set.shape[0]
ll = 0.0
n_i_track = -1
fence_base = fence_set[0]
interval = fence_set[1] - fence_set[0]
pred_set = None
if return_pred_set:
pred_set = np.zeros(
(output_count, int(input_set.shape[1] / interval)))
print('Prediction set sized ', pred_set.shape)
# loop through sequences and time steps
for data_iter in range(data_count):
# print('Executing iteration %d'%data_iter)
hiddens = copy(parser.get(weights, 'init_hiddens'))
fence_post_1 = fence_set[data_iter] - fence_base
fence_post_2 = fence_set[data_iter + 1] - fence_base
time_count = fence_post_2 - fence_post_1
curr_input = input_set[:, fence_post_1:fence_post_2]
for time_iter in range(time_count):
hiddens = update(
np.expand_dims(np.hstack((curr_input[:, time_iter], 1)),
axis=0), hiddens, update_x_weights,
update_h_weights, reset_x_weights, reset_h_weights,
thidden_x_weights, thidden_h_weights)
n_i_track += 1
if output_set is not None:
# subtract a small number so -1
out_proba = softmax_sigmoid(np.dot(hiddens, output_h_weights))
out_lproba = safe_log(out_proba)
ll += np.sum(output_set[:, n_i_track] * out_lproba)
else:
out_proba = softmax_sigmoid(np.dot(hiddens, output_h_weights))
out_lproba = safe_log(out_proba)
if return_pred_set:
agm = np.argmax(out_lproba[0])
pred_set[agm, n_i_track] = int(1)
return ll, pred_set
testx = np.copy(test['x']) test_dict = pecmy.rewrap_y(testx) test_dict["theta_m"] # 07/23/2019 # originally feeding wrong war values to Lagrangian, checking everything again w/ equality constraints # compare war vals to rcvs and make sure everything looks right # still fails with equality constraints, trying with lower bounds on multipliers but epsilon ball around 0 in dGm_ji # still returns nonsense after 230 minutes war_diffs = np.array([-1, 1, 0]) np.where(war_diffs < 0, 0, war_diffs) pecmy.rewrap_y(test['x']) np.dot(np.array([1, 2, 3]), np.array([1, 2, 3])) test1 = pecmy.rewrap_y(test['x']) pecmy.rewrap_m(test1['m']) # CLAIMS 'INEQUALITY CONSTRAINTS INCOMPATIBLE' after 8923 function evaluations, ~40 minutes of running # only 14 jacobian evaluations # attempting with equality constraints # here we get 'Singular matrix C in LSQ subproblem' in first Jacobian evaluation, refers to constraint qualification problem, study up on this # Might be due to starting at zero multipliers, or because derivative wrt own policy is linear combination of other derivatives when gamma = 1 # removing derivative wrt own allocation doesn't seem to help though # problem seems to be that we weren't selecting self.M[j], rather selecting whole vector # fixing this lets everything run, but gamma shrinks to zero and everything goes to shit # got objective value down to 56 w/o gamma but hit same error at minute 111, not clear why here, estimates were pretty stable generally. SSE seemed to be monotonically decreasing in c_hat for most of estimation routine. # try starting at zero lambda vector # problem is that equality constraint jacobian inversion fails for weird trial paramters, try with upper and lower constraints?
def forward_pass(self, inputs, param_vector):
params = self.parser.get(param_vector, 'params')
biases = self.parser.get(param_vector, 'biases')
if inputs.ndim > 2:
inputs = inputs.reshape((inputs.shape[0], np.prod(inputs.shape[1:])))
return self.nonlinearity(np.dot(inputs[:, :], params) + biases)
def vector_product(x, v):
return np.sin(np.dot(v, df(x)))
def PNLL(self, W_vect, X, Y, N=None):
'''Penalized negative log likelihood.'''
self.num_obj_fun_calls += 1
log_prior = -self.L2_reg * np.dot(W_vect, W_vect)
log_lik = -self.NLL(W_vect, X, Y, N)
return -(log_lik + log_prior)
def loss_jacobian(self, packed_coef_inter, X_batch, y_batch):
y_pred = np.dot(X_batch, packed_coef_inter) # svm decision function
idx = np.argwhere(np.abs(y_pred - y_batch) > self.epsilon).ravel()
return np.dot(y_batch[idx] - y_pred[idx], X_batch[idx])
def propose(self, theta):
theta = np.atleast_1d(theta)
if self.L.shape[1] != theta.shape[0]:
raise ParameterError("theta and L have incompatible shapes")
xi = np.random.normal(size=theta.shape)
return theta + np.dot(self.L, xi), 0.0
def squared_loss(y, y_hat):
return np.dot((y - y_hat), (y - y_hat))
def prior_kl(global_natparam, prior_natparam):
expected_stats = flat(prior_expectedstats(global_natparam))
natparam_difference = flat(global_natparam) - flat(prior_natparam)
logZ_difference = prior_logZ(global_natparam) - prior_logZ(prior_natparam)
return np.dot(natparam_difference, expected_stats) - logZ_difference
def predictions(W_vect, inputs):
for W, b in unpack_layers(W_vect):
outputs = np.dot(inputs, W) + b
inputs = np.tanh(outputs)
return outputs - logsumexp(outputs, axis=1, keepdims=True)
def logistic_predictions(weights, inputs):
return sigmoid(np.dot(inputs, weights))
def RKF45_Integrator(t_start, t_stop, h0, x0, A):
# An integrator using a 4(5) RKF method
T_0 = time.time()
"""
x0 = initial conditions
t_start = start time
t_stop = end time
n_step = number of steps
A = A(t) matrix function
"""
Ndim = x0.size
x_ = np.zeros((1, Ndim)) # set up the array of x values
t_ = np.zeros(1) # set up the array of t values
t_[0] = t_start
x_[0,:] = x0
h = h0
h_min = h0*(10**(-2))
h_max = 5*h0
n = 0
t = t_start
#
S = 0.98 # safety factor
#
while t <= t_stop:
x_n = x_[n,:].reshape(Ndim, 1)
Err_small = False
h_new = h
while Err_small == False:
# compute the predictions using 4th and 5th order RK methods
test_M = np.matrix([[1, 2], [1, 2]])
k1 = np.dot(test_M,x_n)
k1 = np.dot(h*A(t),x_n)
k2 = h*A(t + 0.25*h) @ (x_n + 0.25*k1)
k3 = h*A(t + (3/8)*h) @ (x_n + (3/32)*k1 + (9/32)*k2)
k4 = h*A(t + (12/13)*h) @ (x_n + (1932/2197)*k1 - (7200/2197)*k2 + (7296/2197)*k3)
k5 = h*A(t + h) @ (x_n + (439/216)*k1 - 8*k2 + (3680/513)*k3 - (845/4104)*k4)
k6 = h*A(t + 0.5*h) @ (x_n - (8/27)*k1 + 2*k2 - (3544/2565)*k3 + (1859/4104)*k4 - (11/40)*k5)
y_np1 = x_n + (25/216)*k1 + (1408/2565)*k3 + (2197/4101)*k4 - (11/40)*k5
z_np1 = x_n + (16/135)*k1 + (6656/12825)*k3 + (28561/56430)*k4 - (9/50)*k5 + (2/55)*k6
#
Err = ferr(y_np1, z_np1)
"""
Err_max = ε(rtol*|z_np1| + atol)
"""
Err_max = epsilon_RK*(rtol_RK*np.abs(z_np1) + atol_RK)
Err_ratio = np.asscalar(np.mean(Err / Err_max))
#
if Err_ratio <= 1:
h_new = h*S*np.power(Err_ratio, -1.0/5)
#Delta = max(np.asscalar(max(Err)), epsilon_RK*0.1)
#h_new = h*(epsilon_RK*h/Delta)**(1/4)
if h_new > 10*h: # limit how fast the step size can increase
h_new = 10*h
if h_new > h_max: # limit the maximum step size
h_new = h_max
Err_small = True # break loop
elif Err_ratio > 1:
h_new = h*S*np.power(np.abs(Err_ratio), -1.0/4)
#h_new = h*(epsilon_RK*h/np.asscalar(max(Err)))**(1/4)
if h_new < 0.2*h: # limit how fast the step size decreases
h_new = 0.2*h
if h_new < h_min: # limit the minimum step size
h_new = h_min
Err_small = True # break loop
elif h_new >= h_min:
h = h_new
t = t + h
x_ = np.vstack((x_,z_np1.reshape(1, Ndim))) # add x_n+1 to the array of x values
t_ = np.append(t_, t) # add t_n+1 to the array of t values
n = n + 1
h = h_new
if True: #np.round(((t-t_start)/(t_stop-t_start))*100000) % 1000 == 0:
print("\r" + "integrated {:.1%}".format((t-t_start)/(t_stop-t_start)), end='')
T = time.time() - T_0
print(" done in {:.5g}s".format(T))
return (t_, x_, T)
def fun(x):
return np.dot(np.dot(x, H), x)
def conv_function(self,tensor_window):
tensor_window = np.reshape(tensor_window,(np.shape(tensor_window)[0],np.shape(tensor_window)[1]*np.shape(tensor_window)[2]))
t = np.dot(self.kernels,tensor_window.T)
return t
def neural_network(x, theta):
w1, b1, w2, b2 = theta
return np.tanh(np.dot((np.tanh(np.dot(x, w1) + b1)), w2) + b2)
def fun(x):
return np.sin(np.dot(x, randv))
def predict(self, X):
X = check_array(X, estimator=self, dtype=FLOAT_DTYPES)
check_is_fitted(self, ["coefs_"])
return np.dot(X, self.coefs_)
def training_loss(weights):
diff = np.abs(np.dot(X, weights) - y)
if self.relative:
diff = diff / y
return np.mean(deadzone(diff))
def rayleigh_quotient(self, vec):
hv_val = self.hess_dot_vec(self.params_flat, vec)
rq = np.dot(hv_val, vec) / np.dot(vec, vec)
return rq
def outputs(weights,
input_set,
fence_set,
output_set=None,
return_pred_set=False):
update_x_weights = parser.get(weights, 'update_x_weights')
update_h_weights = parser.get(weights, 'update_h_weights')
reset_x_weights = parser.get(weights, 'reset_x_weights')
reset_h_weights = parser.get(weights, 'reset_h_weights')
thidden_x_weights = parser.get(weights, 'thidden_x_weights')
thidden_h_weights = parser.get(weights, 'thidden_h_weights')
output_h_weights = parser.get(weights, 'output_h_weights')
data_count = len(fence_set) - 1
feat_count = input_set.shape[0]
ll = 0.0
n_i_track = 0
fence_base = fence_set[0]
pred_set = None
if return_pred_set:
pred_set = np.zeros((output_count, input_set.shape[1]))
# loop through sequences and time steps
for data_iter in range(data_count):
hiddens = copy(parser.get(weights, 'init_hiddens'))
fence_post_1 = fence_set[data_iter] - fence_base
fence_post_2 = fence_set[data_iter + 1] - fence_base
time_count = fence_post_2 - fence_post_1
curr_input = input_set[:, fence_post_1:fence_post_2]
for time_iter in range(time_count):
hiddens = update(
np.expand_dims(np.hstack((curr_input[:, time_iter], 1)),
axis=0), hiddens, update_x_weights,
update_h_weights, reset_x_weights, reset_h_weights,
thidden_x_weights, thidden_h_weights)
# IF WE WANT PREDICTION, WE HAVE TO TURN SIGMOID TO LINEAR
if output_set is not None:
# subtract a small number so -1
out_proba = sigmoid(
np.sign(output_set[:, n_i_track] - 1e-3) *
np.dot(hiddens, output_h_weights))
out_lproba = safe_log(out_proba)
ll += np.sum(out_lproba)
else:
out_proba = sigmoid(np.dot(hiddens, output_h_weights))
out_lproba = safe_log(out_proba)
# if output_set is not None:
# # subtract a small number so -1
# out_proba = linear(np.sign(output_set[:, n_i_track] - 1e-3) *
# np.dot(hiddens, output_h_weights))
# out_lproba = safe_log(out_proba)
# ll += np.sum(out_lproba)
# else:
# out_proba = linear(np.dot(hiddens, output_h_weights))
# out_lproba = safe_log(out_proba)
if return_pred_set:
pred_set[:, n_i_track] = out_lproba[0]
n_i_track += 1
return ll, pred_set
def test(self, InpsAndTargsFunc, testdelay=0, **kwargs):
p = self.p
'''
Function that tests a trained network. Relevant parameters in p start with 'test'
Inputs:
InpsAndTargsFunc: function used to generate time series (same as in train)
testdelay: Amount of time to wait between plots (useful for debugging)
**kwargs: arguments passed to InpsAndTargsFunc
'''
self.initialize_act()
print('Initializing', end="")
for i in range(p['test_init_trials']):
print('.', end="")
inps_and_targs = InpsAndTargsFunc(dt=p['dt'], **kwargs)
self.run(inps_and_targs['inps'])
print('')
inps_and_targs = InpsAndTargsFunc(dt=p['dt'], **kwargs)
inp = inps_and_targs['inps']
targ = inps_and_targs['targs']
test_fig = plt.figure()
ax = test_fig.add_subplot(1, 1, 1)
tvec = np.expand_dims(np.arange(0, len(inp)) * p['dt'], axis=1)
line_inp = plt.Line2D(np.repeat(tvec, inp.shape[1], axis=1).T,
inp.T,
linestyle='--',
color='g')
line_targ = plt.Line2D(np.repeat(tvec, targ.shape[1], axis=1).T,
targ.T,
linestyle='--',
color='r')
line_out = plt.Line2D(np.repeat(tvec, targ.shape[1], axis=1).T,
targ.T,
color='b')
ax.add_line(line_inp)
ax.add_line(line_targ)
ax.add_line(line_out)
ax.legend([line_inp, line_targ, line_out],
['Input', 'Target', 'Output'],
loc=1)
ax.set_title('RNN Testing: Wait')
ax.set_xlim([0, p['dt'] * len(inp)])
ax.set_ylim([-1.2, 1.2])
ax.set_xlabel('Time (s)')
test_fig.canvas.draw()
E_out = 0 # Running squared error
V_targ = 0 # Running variance of target
print('Testing: %g trials' % p['test_trials'])
for idx in range(p['test_trials']):
print('.', end="")
inps_and_targs = InpsAndTargsFunc(dt=p['dt'], **kwargs)
inp = inps_and_targs['inps']
targ = inps_and_targs['targs']
targ_idx = inps_and_targs['targ_idx']
tvec = np.expand_dims(np.arange(0, len(inp)) * p['dt'], axis=1)
ax.set_xlim([0, p['dt'] * len(inp)])
line_inp.set_xdata(np.repeat(tvec, inp.shape[1], axis=1).T)
line_inp.set_ydata(inp.T)
line_targ.set_xdata(np.repeat(tvec, targ.shape[1], axis=1).T)
line_targ.set_ydata(targ.T)
out = self.run(inp)[0]
line_out.set_xdata(np.repeat(tvec, out.shape[1], axis=1).T)
line_out.set_ydata(out.T)
ax.set_title('RNN Testing, trial %g' % (idx + 1))
test_fig.canvas.draw()
E_out = E_out + np.trace(
np.dot(
np.transpose(out[targ_idx] - targ[targ_idx]),
out[targ_idx] - targ[targ_idx])) / targ[targ_idx].shape[1]
V_targ = V_targ + np.trace(
np.dot(np.transpose(targ[targ_idx]),
targ[targ_idx])) / targ[targ_idx].shape[1]
time.sleep(testdelay)
print('')
E_norm = E_out / V_targ
print('Normalized error: %g' % E_norm)
return E_norm
def test_inv():
def fun(x): return np.linalg.inv(x)
D = 8
mat = npr.randn(D, D)
mat = np.dot(mat, mat) + 1.0 * np.eye(D)
check_grads(fun)(mat)
def loss_jacobian(self, packed_coef_inter, X_batch, y_batch):
y_pred = np.dot(X_batch, packed_coef_inter) # svm decision function
idx = np.argwhere(y_batch * y_pred < 1.).ravel()
return np.dot(y_batch[idx], X_batch[idx])
def penalty_term(coefficients): return n.sum(((n.dot(p, c.flatten())**2).sum() for p,c in zip(penalties, coefficients)))