def get_projected(self, data, params):
(X1, X2) = data
(Phi1, Phi2) = params
# Get empirical covariance matrices
zmuvX1 = get_zm_uv(X1)
zmuvX2 = get_zm_uv(X2)
# Get projected data
XPhi1 = np.dot(zmuvX1, Phi1)
XPhi2 = np.dot(zmuvX2, Phi2)
# Get gram matrices
S1 = np.dot(XPhi1.T, XPhi1)
S2 = np.dot(XPhi2.T, XPhi2)
# Get normalizers
inv_srqt1 = get_svd_power(S1, -0.5)
inv_srqt2 = get_svd_power(S2, -0.5)
# Get normalized
normed1 = np.dot(Phi1, inv_sqrt1)
normed2 = np.dot(Phi2, inv_sqrt2)
return (normed1, normed2)
def _update_Phi(self):
pre_sqrt = np.dot(self.X_unn_Phi.T, self.X_unn_Phi)
pre_sqrt_norm = np.thelineg.norm(pre_sqrt)
normalizer = get_svd_power(pre_sqrt, -0.5)
self.Phi = np.dot(self.unn_Phi, normalizer)
def __init__(self,
dynamics,
W,
Psi,
mu,
Z,
lazy=True):
self.dynamics = dynamics
self.W = W
self.Psi = Psi
self.mu = mu
self.Z = Z
self.lazy = lazy
self.d = self.W.shape[0]
(self.k, self.num_data) = self.Z.shape
(lam, self.Q) = np.linalg.eig(dynamics)
self.lam = lam[:,np.newaxis]
QW = np.dot(self.Q, self.W)
self.mean = np.dot(QW, Z) + self.mu
for t in range(Z.shape[0]):
self.mean[:,t:] *= self.lam
self.mean = np.dot(self.Q.H, self.mean)
self.sd = get_svd_power(self.Psi, 0.5)
self.data = None
if not self.lazy:
self._set_data()
def get_woodbury_inversion(H, rho):
(m, d) = H.shape
I_m = np.identity(m)
I_d = np.identity(d)
to_invert = rho*I_m + np.dot(H, H.T)
inversion = get_svd_power(to_invert, -1)
quad = gq(H, inversion)
unscaled = I_d - quad
return rho**(-1) * unscaled
def get_rotation(angle, P, P_inv=None):
if P_inv is None:
P_inv = get_svd_power(P, -1)
A = np.eye(P.shape[0])
A[0, 0] = np.cos(angle)
A[1, 1] = np.cos(angle)
A[0, 1] = -np.sin(angle)
A[1, 0] = np.sin(angle)
return get_multi_dot([P_inv, A, P])
def get_SPC_SCCAPMLs(num_data, k, ds, rho=0.8, seed=None, lazy=True):
loader = GL(num_data, k)
Y = loader.get_data().T
Psi_z = get_spc(k, rho=rho)
sqrt_Psi_z = get_svd_power(Psi_z, 0.5)
Z = np.dot(sqrt_Psi_z, Y)
Psi_inits = [np.random.randn(d * 2, d) for d in ds]
Psis = [np.dot(Pi.T, Pi) for Pi in Psi_inits]
Ws = [np.random.randn(d, k) for d in ds]
mus = [np.random.randn(d, 1) for d in ds]
zipped = zip(Ws, Psis, mus)
SCCAPML = StaticCCAProbabilisticModelLoader
return [SCCAPML(W, Psi, mu, Z, lazy=lazy) for (W, Psi, mu) in zipped]
def _get_primal(self, dual_update):
if self.lower is not None:
dus = dual_update.shape
if len(dus) == 2 and not 1 in set(dus):
(U, s, V) = np.linalg.svd(dual_update)
sparse_s = get_st(s, lower=self.lower)
dual_update = get_multiplied_svd(U, s, V)
else:
dual_update = get_st(dual_update, lower=self.lower)
H_inv = get_svd_power(self.H, -1)
return np.dot(H_inv, dual_update)
def get_update(self, parameters, gradient, eta):
self.num_rounds += 1
if self.G is None:
self.G = np.dot(gradient, gradient.T)
self.d = gradient.shape[0]
else:
self.G += np.dot(gradient, gradient.T)
self.S = get_svd_power(self.G, 0.5)
self.H = self.S + np.eye(self.d) * self.delta
return get_mu(parameters, eta, gradient, self._get_dual,
self._get_primal)
def __init__(self, W, Psi, mu, Z, lazy=True):
self.W = W
self.Psi = Psi
self.mu = mu
self.Z = Z
self.lazy = lazy
self.d = self.W.shape[0]
(self.k, self.num_data) = self.Z.shape
self.mean = np.dot(self.W, Z) + self.mu
self.sd = get_svd_power(self.Psi, 0.5)
self.data = None
if not self.lazy:
self._set_data()
def get_data(self):
# Calculate current means
scale = get_svd_power(self.rate, self.num_rounds)
current_mean = np.dot(self.mean, scale)
# Get batch
batch = _get_batch(self.bs,
self.p,
self.k,
current_mean,
unit_norm=self.unit_norm)
# Update global state variable
self.num_rounds += 1
return batch
def run(self):
theta = None
if len(self.d) == 1 or self.d[1] == 1:
theta = np.zeros((self.d, 1))
else:
theta = np.zeros(self.d)
w_t = None
for t in range(self.max_rounds):
# Update parameter estimate
w_t = self.drdw_inv(theta)
# Sample search direction
sphere_sample = None
if len(self.d) == 1 or self.d[1] == 1:
normal_sample = np.random.randn(d, 1)
sphere_sample = normal_sample / np.linalg.norm(normal_sample)
else:
normal_sample = np.random.randn(*d)
quad = np.dot(normal_sample.T, normal_sample)
normalizer = get_svd_power(quad, -0.5)
shere_sample = np.dot(normal_sample, normalizer)
# Compute one-dimensional finite difference approximation
delta_t = self.delta_scheduler.get_stepsize()
delta_plus = self.get_objective(w_t + delta_t * sphere_sample)
delta_minus = self.get_objective(w_t - delta_t * sphere_sample)
# Compute gradient scale and gradient
grad_scale = 0.5 * delta_t**(-1) * self.d * (delta_plus -
delta_minus)
grad_approx = grad_scale * sphere_sample
# Update theta
theta -= self.eta * grad_approx
self.w = w_t
def get_gram_normed(unnormed, S):
basis_quad = get_quad(unnormed, S)
normalizer = get_svd_power(basis_quad, -0.5)
return np.dot(unnormed, normalizer)
def get_cca_vecs(X1, X2, n_components=1, num_nonzero=None):
(n1, p1) = X1.shape
(n2, p2) = X2.shape
n = None
if not n1 == n2:
raise ValueError(
'X1 and X2 must have same 1st dimension.')
else:
n = n1
# Get means, zero-mean, normed vars
mu1 = np.nanmean(X1, axis=0)
mu2 = np.nanmean(X2, axis=0)
normalizer = n**(0.5)
zm_X1 = (X1 - mu1) / normalizer
zm_X2 = (X2 - mu2) / normalizer
# Get sample covariance matrices
CX1 = np.dot(zm_X1.T, zm_X1)
CX2 = np.dot(zm_X2.T, zm_X2)
CX12 = np.dot(zm_X1.T, zm_X2)
# Get inverse sqrts and normed sample cross-covariance
CX1_inv_sqrt = get_svd_power(CX1, -0.5)
CX2_inv_sqrt = get_svd_power(CX2, -0.5)
Omega = get_multi_dot([
CX1_inv_sqrt,
CX12,
CX2_inv_sqrt])
(Phi1, Phi2) = [None] * 2
if num_nonzero is None:
(U, s, V) = np.linalg.svd(Omega)
unnormed_Phi1 = U[:,:n_components]
unnormed_Phi2 = V[:,:n_components]
Phi1 = np.dot(CX1_inv_sqrt, unnormed_Phi1)
Phi2 = np.dot(CX2_inv_sqrt, unnormed_Phi2)
else:
x_project = spancca.projections.setup_sparse(
nnz=num_nonzero)
y_project = spancca.projections.setup_sparse(
nnz=num_nonzero)
rank = min([
num_nonzero * 2 + 1,
min(Omega.shape) - 1])
(Phi1, Phi2) = spancca.cca(
Omega,
rank,
n,
x_project,
y_project,
verbose=False)
projected1 = np.dot(X1 - mu1, Phi1)
projected2 = np.dot(X2 - mu2, Phi2)
cc = np.sum(
projected1 * projected2,
axis=1)[:,np.newaxis] / n_components
return (Phi1, Phi2, cc)
