def ppca(Y, Q, iterations=100):
"""
EM implementation for probabilistic pca.
:param array-like Y: Observed Data
:param int Q: Dimensionality for reduced array
:param int iterations: number of iterations for EM
"""
from numpy.ma import dot as madot
N, D = Y.shape
# Initialise W randomly
W = np.random.randn(D, Q) * 1e-3
Y = np.ma.masked_invalid(Y, copy=0)
mu = Y.mean(0)
Ycentered = Y - mu
try:
for _ in range(iterations):
exp_x = np.asarray_chkfinite(
np.linalg.solve(W.T.dot(W), madot(W.T, Ycentered.T))).T
W = np.asarray_chkfinite(
np.linalg.solve(exp_x.T.dot(exp_x), madot(exp_x.T,
Ycentered))).T
except np.linalg.linalg.LinAlgError:
#"converged"
pass
return np.asarray_chkfinite(exp_x), np.asarray_chkfinite(W)
def ppca(Y, Q, iterations=100):
"""
EM implementation for probabilistic pca.
:param array-like Y: Observed Data
:param int Q: Dimensionality for reduced array
:param int iterations: number of iterations for EM
"""
from numpy.ma import dot as madot
N, D = Y.shape
# Initialise W randomly
W = np.random.randn(D, Q) * 1e-3
Y = np.ma.masked_invalid(Y, copy=0)
mu = Y.mean(0)
Ycentered = Y - mu
try:
for _ in range(iterations):
exp_x = np.asarray_chkfinite(np.linalg.solve(W.T.dot(W), madot(W.T, Ycentered.T))).T
W = np.asarray_chkfinite(np.linalg.solve(exp_x.T.dot(exp_x), madot(exp_x.T, Ycentered))).T
except np.linalg.linalg.LinAlgError:
#"converged"
pass
return np.asarray_chkfinite(exp_x), np.asarray_chkfinite(W)
def ppca_missing_data_at_random(Y, Q, iters=100):
"""
EM implementation of Probabilistic pca for when there is missing data.
Taken from <SheffieldML, https://github.com/SheffieldML>
.. math:
\\mathbf{Y} = \mathbf{XW} + \\epsilon \\text{, where}
\\epsilon = \\mathcal{N}(0, \\sigma^2 \mathbf{I})
:returns: X, W, sigma^2
"""
from numpy.ma import dot as madot
import diag
from GPy.util.subarray_and_sorting import common_subarrays
import time
debug = 1
# Initialise W randomly
N, D = Y.shape
W = np.random.randn(Q, D) * 1e-3
Y = np.ma.masked_invalid(Y, copy=1)
nu = 1.
#num_obs_i = 1./Y.count()
Ycentered = Y - Y.mean(0)
X = np.zeros((N, Q))
cs = common_subarrays(Y.mask)
cr = common_subarrays(Y.mask, 1)
Sigma = np.zeros((N, Q, Q))
Sigma2 = np.zeros((N, Q, Q))
mu = np.zeros(D)
if debug:
import matplotlib.pyplot as pylab
fig = pylab.figure("FIT MISSING DATA")
ax = fig.gca()
ax.cla()
lines = pylab.plot(np.zeros((N, Q)).dot(W))
W2 = np.zeros((Q, D))
for i in range(iters):
# Sigma = np.linalg.solve(diag.add(madot(W,W.T), nu), diag.times(np.eye(Q),nu))
# exp_x = madot(madot(Ycentered, W.T),Sigma)/nu
# Ycentered = (Y - exp_x.dot(W).mean(0))
# #import ipdb;ipdb.set_trace()
# #Ycentered = mu
# W = np.linalg.solve(madot(exp_x.T,exp_x) + Sigma, madot(exp_x.T, Ycentered))
# nu = (((Ycentered - madot(exp_x, W))**2).sum(0) + madot(W.T,madot(Sigma,W)).sum(0)).sum()/N
for csi, (mask, index) in enumerate(cs.iteritems()):
mask = ~np.array(mask)
Sigma2[index, :, :] = nu * np.linalg.inv(
diag.add(W2[:, mask].dot(W2[:, mask].T), nu))
#X[index,:] = madot((Sigma[csi]/nu),madot(W,Ycentered[index].T))[:,0]
X2 = ((Sigma2 / nu) *
(madot(Ycentered, W2.T).base)[:, :, None]).sum(-1)
mu2 = (Y - X.dot(W)).mean(0)
for n in range(N):
Sigma[n] = nu * np.linalg.inv(
diag.add(W[:, ~Y.mask[n]].dot(W[:, ~Y.mask[n]].T), nu))
X[n, :] = (Sigma[n] / nu).dot(W[:, ~Y.mask[n]].dot(
Ycentered[n, ~Y.mask[n]].T))
for d in range(D):
mu[d] = (Y[~Y.mask[:, d], d] -
X[~Y.mask[:, d]].dot(W[:, d])).mean()
Ycentered = (Y - mu)
nu3 = 0.
for cri, (mask, index) in enumerate(cr.iteritems()):
mask = ~np.array(mask)
W2[:, index] = np.linalg.solve(
X[mask].T.dot(X[mask]) + Sigma[mask].sum(0),
madot(X[mask].T, Ycentered[mask, index]))[:, None]
W2[:, index] = np.linalg.solve(
X.T.dot(X) + Sigma.sum(0), madot(X.T, Ycentered[:, index]))
#nu += (((Ycentered[mask,index] - X[mask].dot(W[:,index]))**2).sum(0) + W[:,index].T.dot(Sigma[mask].sum(0).dot(W[:,index])).sum(0)).sum()
nu3 += (
((Ycentered[index] - X.dot(W[:, index]))**2).sum(0) +
W[:, index].T.dot(Sigma.sum(0).dot(W[:, index])).sum(0)).sum()
nu3 /= N
nu = 0.
nu2 = 0.
W = np.zeros((Q, D))
for j in range(D):
W[:, j] = np.linalg.solve(
X[~Y.mask[:, j]].T.dot(X[~Y.mask[:, j]]) +
Sigma[~Y.mask[:, j]].sum(0),
madot(X[~Y.mask[:, j]].T, Ycentered[~Y.mask[:, j], j]))
nu2f = np.tensordot(W[:, j].T, Sigma[~Y.mask[:, j], :, :],
[0, 1]).dot(W[:, j])
nu2s = W[:, j].T.dot(Sigma[~Y.mask[:, j], :, :].sum(0).dot(W[:,
j]))
nu2 += (((Ycentered[~Y.mask[:, j], j] -
X[~Y.mask[:, j], :].dot(W[:, j]))**2) + nu2f).sum()
for i in range(N):
if not Y.mask[i, j]:
nu += ((Ycentered[i, j] - X[i, :].dot(W[:, j]))**
2) + W[:, j].T.dot(Sigma[i, :, :].dot(W[:, j]))
nu /= N
nu2 /= N
nu4 = (((Ycentered - X.dot(W))**2).sum(0) +
W.T.dot(Sigma.sum(0).dot(W)).sum(0)).sum() / N
import ipdb
ipdb.set_trace()
if debug:
#print Sigma[0]
print "nu:", nu, "sum(X):", X.sum()
pred_y = X.dot(W)
for x, l in zip(pred_y.T, lines):
l.set_ydata(x)
ax.autoscale_view()
ax.set_ylim(pred_y.min(), pred_y.max())
fig.canvas.draw()
time.sleep(.3)
return np.asarray_chkfinite(X), np.asarray_chkfinite(W), nu
def ppca_missing_data_at_random(Y, Q, iters=100):
"""
EM implementation of Probabilistic pca for when there is missing data.
Taken from <SheffieldML, https://github.com/SheffieldML>
.. math:
\\mathbf{Y} = \mathbf{XW} + \\epsilon \\text{, where}
\\epsilon = \\mathcal{N}(0, \\sigma^2 \mathbf{I})
:returns: X, W, sigma^2
"""
from numpy.ma import dot as madot
import diag
from GPy.util.subarray_and_sorting import common_subarrays
import time
debug = 1
# Initialise W randomly
N, D = Y.shape
W = np.random.randn(Q, D) * 1e-3
Y = np.ma.masked_invalid(Y, copy=1)
nu = 1.
#num_obs_i = 1./Y.count()
Ycentered = Y - Y.mean(0)
X = np.zeros((N,Q))
cs = common_subarrays(Y.mask)
cr = common_subarrays(Y.mask, 1)
Sigma = np.zeros((N, Q, Q))
Sigma2 = np.zeros((N, Q, Q))
mu = np.zeros(D)
"""
if debug:
import matplotlib.pyplot as pylab
fig = pylab.figure("FIT MISSING DATA");
ax = fig.gca()
ax.cla()
lines = pylab.plot(np.zeros((N,Q)).dot(W))
"""
W2 = np.zeros((Q,D))
for i in range(iters):
# Sigma = np.linalg.solve(diag.add(madot(W,W.T), nu), diag.times(np.eye(Q),nu))
# exp_x = madot(madot(Ycentered, W.T),Sigma)/nu
# Ycentered = (Y - exp_x.dot(W).mean(0))
# #import ipdb;ipdb.set_trace()
# #Ycentered = mu
# W = np.linalg.solve(madot(exp_x.T,exp_x) + Sigma, madot(exp_x.T, Ycentered))
# nu = (((Ycentered - madot(exp_x, W))**2).sum(0) + madot(W.T,madot(Sigma,W)).sum(0)).sum()/N
for csi, (mask, index) in enumerate(cs.iteritems()):
mask = ~np.array(mask)
Sigma2[index, :, :] = nu * np.linalg.inv(diag.add(W2[:,mask].dot(W2[:,mask].T), nu))
#X[index,:] = madot((Sigma[csi]/nu),madot(W,Ycentered[index].T))[:,0]
X2 = ((Sigma2/nu) * (madot(Ycentered,W2.T).base)[:,:,None]).sum(-1)
mu2 = (Y - X.dot(W)).mean(0)
for n in range(N):
Sigma[n] = nu * np.linalg.inv(diag.add(W[:,~Y.mask[n]].dot(W[:,~Y.mask[n]].T), nu))
X[n, :] = (Sigma[n]/nu).dot(W[:,~Y.mask[n]].dot(Ycentered[n,~Y.mask[n]].T))
for d in range(D):
mu[d] = (Y[~Y.mask[:,d], d] - X[~Y.mask[:,d]].dot(W[:, d])).mean()
Ycentered = (Y - mu)
nu3 = 0.
for cri, (mask, index) in enumerate(cr.iteritems()):
mask = ~np.array(mask)
W2[:,index] = np.linalg.solve(X[mask].T.dot(X[mask]) + Sigma[mask].sum(0), madot(X[mask].T, Ycentered[mask,index]))[:,None]
W2[:,index] = np.linalg.solve(X.T.dot(X) + Sigma.sum(0), madot(X.T, Ycentered[:,index]))
#nu += (((Ycentered[mask,index] - X[mask].dot(W[:,index]))**2).sum(0) + W[:,index].T.dot(Sigma[mask].sum(0).dot(W[:,index])).sum(0)).sum()
nu3 += (((Ycentered[index] - X.dot(W[:,index]))**2).sum(0) + W[:,index].T.dot(Sigma.sum(0).dot(W[:,index])).sum(0)).sum()
nu3 /= N
nu = 0.
nu2 = 0.
W = np.zeros((Q,D))
for j in range(D):
W[:,j] = np.linalg.solve(X[~Y.mask[:,j]].T.dot(X[~Y.mask[:,j]]) + Sigma[~Y.mask[:,j]].sum(0), madot(X[~Y.mask[:,j]].T, Ycentered[~Y.mask[:,j],j]))
nu2f = np.tensordot(W[:,j].T, Sigma[~Y.mask[:,j],:,:], [0,1]).dot(W[:,j])
nu2s = W[:,j].T.dot(Sigma[~Y.mask[:,j],:,:].sum(0).dot(W[:,j]))
nu2 += (((Ycentered[~Y.mask[:,j],j] - X[~Y.mask[:,j],:].dot(W[:,j]))**2) + nu2f).sum()
for i in range(N):
if not Y.mask[i,j]:
nu += ((Ycentered[i,j] - X[i,:].dot(W[:,j]))**2) + W[:,j].T.dot(Sigma[i,:,:].dot(W[:,j]))
nu /= N
nu2 /= N
nu4 = (((Ycentered - X.dot(W))**2).sum(0) + W.T.dot(Sigma.sum(0).dot(W)).sum(0)).sum()/N
import ipdb;ipdb.set_trace()
"""
if debug:
#print Sigma[0]
print "nu:", nu, "sum(X):", X.sum()
pred_y = X.dot(W)
for x, l in zip(pred_y.T, lines):
l.set_ydata(x)
ax.autoscale_view()
ax.set_ylim(pred_y.min(), pred_y.max())
fig.canvas.draw()
time.sleep(.3)
"""
return np.asarray_chkfinite(X), np.asarray_chkfinite(W), nu
