def valid(loghyper,
covfunc,
X,
id,
y,
X_val,
y_val,
R_tr,
w,
R_tr_val,
R_val,
trafo=None):
'''Do validation on validation dataset
tuning weight parameter of SUM of
parameterized cov **function** AND cov **martix**. '''
## TRAINING the parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y, R_tr, w)
## GET self covariances for the test cases (needed in covMatrix)
d = diag(R_val).transpose()
R_tr_val = vstack((R_tr_val, d))
## PREDICTION
[MU, S2] = gpr.gp_pred(logtheta, covfunc, X, y, X_val, R_tr, w, R_tr_val)
## VALIDATION for predictions on validation dataset
## DO NOT resacle predictions - rescaling is done in valid_fig if needed!!!
M = valid_fig(y_val, MU, trafo=trafo)
print w
print M
return hstack((M, logtheta))
def gp_correct_poses(gt_poses_train,
poses_train,
state_train,
poses_test,
state_test,
logtheta=None):
print "using gp poses"
pose_error = calc_pose_error(gt_poses_train, poses_train)
n_test = len(poses_test)
n_task_vars = 6
MU = np.empty((n_test, n_task_vars))
S2 = np.empty((n_test, n_task_vars))
for i_task_var in range(n_task_vars):
## data from a noisy GP
X = state_train
## DEFINE parameterized covariance funcrion
covfunc = ['kernels.covSum', ['kernels.covSEiso', 'kernels.covNoise']]
#print 'hyperparameters: ', np.exp(logtheta)
### sample observations from the GP
y = np.array([pose_error[:, i_task_var]]).reshape((-1, 1))
### TEST POINTS
Xstar = state_test
## LEARN hyperparameters if not provided
if logtheta == None:
# ***UNCOMMENT THE FOLLOWING LINES TO DO TRAINING OF HYPERPARAMETERS***
### TRAINING GP
print
print 'GP: ...training'
### INITIALIZE (hyper)parameters by -1
d = X.shape[1]
init = -1.0 * np.ones((d, 1))
loghyper = np.array([[-1.0], [-1.0]])
loghyper = np.vstack((init, loghyper))[:, 0]
print 'initial hyperparameters: ', np.exp(loghyper)
### TRAINING of (hyper)parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y)
print 'trained hyperparameters: ', np.exp(logtheta)
## PREDICTION
print 'GP: ...prediction'
results = gpr.gp_pred(logtheta, covfunc, X, y,
Xstar) # get predictions for unlabeled data ONLY
MU[:, i_task_var] = results[0][:, 0]
S2[:, i_task_var:i_task_var + 1] = results[1]
est_gt_poses_test = apply_pose_error(poses_test, MU)
return est_gt_poses_test
def gp_correct_poses(gt_poses_train, poses_train, state_train, poses_test, state_test, logtheta=None):
print "using gp poses"
pose_error = calc_pose_error(gt_poses_train, poses_train)
n_test = len(poses_test)
n_task_vars = 6
MU = np.empty((n_test, n_task_vars))
S2 = np.empty((n_test, n_task_vars))
for i_task_var in range(n_task_vars):
## data from a noisy GP
X = state_train
## DEFINE parameterized covariance funcrion
covfunc = ['kernels.covSum', ['kernels.covSEiso','kernels.covNoise']]
#print 'hyperparameters: ', np.exp(logtheta)
### sample observations from the GP
y = np.array([pose_error[:,i_task_var]]).reshape((-1,1))
### TEST POINTS
Xstar = state_test
## LEARN hyperparameters if not provided
if logtheta == None:
# ***UNCOMMENT THE FOLLOWING LINES TO DO TRAINING OF HYPERPARAMETERS***
### TRAINING GP
print
print 'GP: ...training'
### INITIALIZE (hyper)parameters by -1
d = X.shape[1]
init = -1.0*np.ones((d,1))
loghyper = np.array([[-1.0], [-1.0]])
loghyper = np.vstack((init, loghyper))[:,0]
print 'initial hyperparameters: ', np.exp(loghyper)
### TRAINING of (hyper)parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y)
print 'trained hyperparameters: ',np.exp(logtheta)
## PREDICTION
print 'GP: ...prediction'
results = gpr.gp_pred(logtheta, covfunc, X, y, Xstar) # get predictions for unlabeled data ONLY
MU[:,i_task_var] = results[0][:,0]
S2[:,i_task_var:i_task_var+1] = results[1]
est_gt_poses_test = apply_pose_error(poses_test, MU)
return est_gt_poses_test
def valid(loghyper, covfunc, X, id, y, X_val, y_val, R_tr, w, R_tr_val, R_val, trafo=None):
'''Do validation on validation dataset
tuning weight parameter of SUM of
parameterized cov **function** AND cov **martix**. '''
## TRAINING the parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y, R_tr, w)
## GET self covariances for the test cases (needed in covMatrix)
d = diag(R_val).transpose()
R_tr_val = vstack((R_tr_val, d))
## PREDICTION
[MU, S2] = gpr.gp_pred(logtheta, covfunc, X, y, X_val, R_tr, w, R_tr_val)
## VALIDATION for predictions on validation dataset
## DO NOT resacle predictions - rescaling is done in valid_fig if needed!!!
M = valid_fig(y_val, MU, trafo=trafo)
print w
print M
return hstack((M, logtheta))
def gp_correct_poses(gt_poses_train, poses_train, state_train, poses_test, state_test, hy_params=None): pose_error = calc_pose_error(gt_poses_train, poses_train) n_test = len(poses_test) n_task_vars = 6 MU = np.empty((n_test, n_task_vars)) S2 = np.empty((n_test, n_task_vars)) for i_task_var in range(n_task_vars): X = state_train ## DEFINE parameterized covariance funcrion covfunc = ['kernels.covSum', ['kernels.covSEiso','kernels.covNoise']] ## SET (hyper)parameters if hy_params==None: logtheta = np.array([np.log(0.1), np.log(1), np.log(np.sqrt(0.5))]) else: logtheta = hy_params[i_task_var,:] #print 'hyperparameters: ', np.exp(logtheta) ### sample observations from the GP y = pose_error[:,i_task_var] ### TEST POINTS Xstar = state_test ## PREDICTION print 'GP: ...prediction' results = gpr.gp_pred(logtheta, covfunc, X, y, Xstar) # get predictions for unlabeled data ONLY MU[:,i_task_var] = results[0] S2[:,i_task_var:i_task_var+1] = results[1] est_gt_poses_test = [pose_to_tf(pose_diff).dot(pose) for (pose_diff, pose) in zip(MU, poses_test)] return est_gt_poses_test
def k_fold_cv(k, loghyper, covfunc, X, id, y, R, w, trafo=None):
'''Do k-fold cross validation for
tuning weight parameter of SUM of
parameterized cov **function** AND cov **martix**. '''
## TRAINING the parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y, R, w)
#print exp(logtheta)
MU = zeros((y.shape))
S2 = zeros((y.shape))
n = id.shape[0]
s = floor(n/k)
for j in range(0,k):
# prepare X, y and R according to fold
if j==0: # first fold
X_tr = X[s:n,:]
y_tr = y[s:n,:]
id_tr = id[s:n,:]
X_val = X[0:s,:]
id_val = id[0:s,:]
elif 0<j<k-1:
X_tr = X[0:j*s,:]
X_tr = vstack((X_tr,X[j*s+s:n,:]))
y_tr = y[0:j*s,:]
y_tr = vstack((y_tr,y[j*s+s:n,:]))
id_tr = id[0:j*s,:]
id_tr = vstack((id_tr,id[j*s+s:n,:]))
X_val = X[j*s:j*s+s,:]
id_val = id[j*s:j*s+s,:]
else: # last fold
s1 = s+fmod(n,k)
X_tr = X[0:n-s1,:]
y_tr = y[0:n-s1,:]
id_tr = id[0:n-s1,:]
X_val = X[n-s1:n,:]
id_val = id[n-s1:n,:]
loc_tr = general.get_index_vec(id_tr[:,0], id[:,0])
R_tr = R.take(loc_tr.astype(int),axis=0).take(loc_tr.astype(int),axis=1)
loc_val = general.get_index_vec(id_val[:,0], id[:,0])
R_tr_val = R.take(loc_tr.astype(int),axis=0).take(loc_val.astype(int),axis=1)
## GET self covariances for the test cases (needed in covMatrix)
R_val = R.take(loc_val.astype(int),axis=0).take(loc_val.astype(int),axis=1)
d = diag(R_val).transpose()
R_tr_val = vstack((R_tr_val, d))
## PREDICTION
[MU_temp, S2_temp] = gpr.gp_pred(logtheta, covfunc, X_tr, y_tr, X_val, R_tr, w, R_tr_val)
if j==0: # first fold
MU[0:s,:] = MU_temp
S2[0:s,:] = S2_temp
elif 0<j<k-1:
MU[j*s:j*s+s,:] = MU_temp
S2[j*s:j*s+s,:] = S2_temp
else: # last fold
MU[n-s1:n,:] = MU_temp
S2[n-s1:n,:] = S2_temp
## VALIDATION for predictions on validation dataset
## DO NOT resacle predictions - rescaling is done in valid_fig if needed!!!
M = valid_fig(y, MU, trafo=trafo)
print w
print M
return hstack((M, logtheta))
#d = X.shape[1]
#init = -1*ones((d,1))
#loghyper = array([[-1], [-1]])
#loghyper = vstack((init, loghyper))[:,0]
#print 'initial hyperparameters: ', exp(loghyper)
### TRAINING of (hyper)parameters
#logtheta = gpr.gp_train(loghyper, covfunc, X, y)
#print 'trained hyperparameters: ',exp(logtheta)
## to GET prior covariance of Standard GP use:
#[Kss, Kstar] = general.feval(covfunc, logtheta, X, Xstar) # Kss = self covariances of test cases,
# # Kstar = cov between train and test cases
## PREDICTION
print 'GP: ...prediction'
results = gpr.gp_pred(logtheta, covfunc, X, y, Xstar) # get predictions for unlabeled data ONLY
MU = results[0]
S2 = results[1]
#print MU
## plot results
pyplot.suptitle('logtheta:', fontsize=12)
pyplot.title(logtheta)
pyplot.plot(Xstar,MU, 'g^', X,y, 'ro')
pyplot.show()
# loghyper = array([[-1], [-1]])
# loghyper = vstack((init, loghyper))[:,0]
# print 'initial hyperparameters: ', exp(loghyper)
#
# w = array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]) # set vector for grid search
# M = zeros((size(w),3+size(loghyper))) # matrix to collect[r_sq_B, RMSE_B, MAE_B] for all weights w(i)
# print 'XGP: ...training (PT)'
# print 'XGP: ...tune weight parameter w (via CV)'
# for i in range(0,size(w)):
# M[i,:] = validation.k_fold_cv(3, loghyper, covfunc, X, id_lab, y.copy(), A, w[i])
#
## SELECT weight and corresponding hyperparameters according to highest R_sq value
# loc = M[:,0].argmax(0)
# w_used = w[loc]
# print 'selected weight: '+str(w_used)
# logtheta = array(M[loc,3:])
# XGP PREDICTION
print "XGP: ...prediction (PT)"
[MU, S2] = gpr.gp_pred(logtheta, covfunc, X, y, Xstar, A, w_used, B)
# print MU
## plot results
pyplot.suptitle("logtheta:", fontsize=12)
pyplot.title(logtheta)
pyplot.plot(Xstar, MU, "g^", X, y, "ro")
pyplot.show()
#loghyper = vstack((init, loghyper))[:,0]
#print 'initial hyperparameters: ', exp(loghyper)
#
#w = array([0, 0.1, 0.2, 0.3, 0.4, 0.5, 0.6, 0.7, 0.8, 0.9, 1]) # set vector for grid search
#M = zeros((size(w),3+size(loghyper))) # matrix to collect[r_sq_B, RMSE_B, MAE_B] for all weights w(i)
#print 'XGP: ...training (PT)'
#print 'XGP: ...tune weight parameter w (via CV)'
#for i in range(0,size(w)):
# M[i,:] = validation.k_fold_cv(3, loghyper, covfunc, X, id_lab, y.copy(), A, w[i])
#
## SELECT weight and corresponding hyperparameters according to highest R_sq value
#loc = M[:,0].argmax(0)
#w_used = w[loc]
#print 'selected weight: '+str(w_used)
#logtheta = array(M[loc,3:])
# XGP PREDICTION
print 'XGP: ...prediction (PT)'
[MU, S2] = gpr.gp_pred(logtheta, covfunc, X, y, Xstar, A, w_used, B)
#print MU
## plot results
pyplot.suptitle('logtheta:', fontsize=12)
pyplot.title(logtheta)
pyplot.plot(Xstar,MU, 'g^', X,y, 'ro')
pyplot.show()
def predict_2(self, X, y, x_star):
prediction = gpr.gp_pred(self.logtheta, self.covfunc, X, y, x_star)
return prediction
def k_fold_cv(k, loghyper, covfunc, X, id, y, R, w, trafo=None):
'''Do k-fold cross validation for
tuning weight parameter of SUM of
parameterized cov **function** AND cov **martix**. '''
## TRAINING the parameters
logtheta = gpr.gp_train(loghyper, covfunc, X, y, R, w)
#print exp(logtheta)
MU = zeros((y.shape))
S2 = zeros((y.shape))
n = id.shape[0]
s = floor(n / k)
for j in range(0, k):
# prepare X, y and R according to fold
if j == 0: # first fold
X_tr = X[s:n, :]
y_tr = y[s:n, :]
id_tr = id[s:n, :]
X_val = X[0:s, :]
id_val = id[0:s, :]
elif 0 < j < k - 1:
X_tr = X[0:j * s, :]
X_tr = vstack((X_tr, X[j * s + s:n, :]))
y_tr = y[0:j * s, :]
y_tr = vstack((y_tr, y[j * s + s:n, :]))
id_tr = id[0:j * s, :]
id_tr = vstack((id_tr, id[j * s + s:n, :]))
X_val = X[j * s:j * s + s, :]
id_val = id[j * s:j * s + s, :]
else: # last fold
s1 = s + fmod(n, k)
X_tr = X[0:n - s1, :]
y_tr = y[0:n - s1, :]
id_tr = id[0:n - s1, :]
X_val = X[n - s1:n, :]
id_val = id[n - s1:n, :]
loc_tr = general.get_index_vec(id_tr[:, 0], id[:, 0])
R_tr = R.take(loc_tr.astype(int), axis=0).take(loc_tr.astype(int),
axis=1)
loc_val = general.get_index_vec(id_val[:, 0], id[:, 0])
R_tr_val = R.take(loc_tr.astype(int), axis=0).take(loc_val.astype(int),
axis=1)
## GET self covariances for the test cases (needed in covMatrix)
R_val = R.take(loc_val.astype(int), axis=0).take(loc_val.astype(int),
axis=1)
d = diag(R_val).transpose()
R_tr_val = vstack((R_tr_val, d))
## PREDICTION
[MU_temp, S2_temp] = gpr.gp_pred(logtheta, covfunc, X_tr, y_tr, X_val,
R_tr, w, R_tr_val)
if j == 0: # first fold
MU[0:s, :] = MU_temp
S2[0:s, :] = S2_temp
elif 0 < j < k - 1:
MU[j * s:j * s + s, :] = MU_temp
S2[j * s:j * s + s, :] = S2_temp
else: # last fold
MU[n - s1:n, :] = MU_temp
S2[n - s1:n, :] = S2_temp
## VALIDATION for predictions on validation dataset
## DO NOT resacle predictions - rescaling is done in valid_fig if needed!!!
M = valid_fig(y, MU, trafo=trafo)
print w
print M
return hstack((M, logtheta))
#print 'GP: ...training'
### INITIALIZE (hyper)parameters by -1
#d = X.shape[1]
#init = -1*ones((d,1))
#loghyper = array([[-1], [-1]])
#loghyper = vstack((init, loghyper))[:,0]
#print 'initial hyperparameters: ', exp(loghyper)
### TRAINING of (hyper)parameters
#logtheta = gpr.gp_train(loghyper, covfunc, X, y)
#print 'trained hyperparameters: ',exp(logtheta)
## to GET prior covariance of Standard GP use:
#[Kss, Kstar] = general.feval(covfunc, logtheta, X, Xstar) # Kss = self covariances of test cases,
# # Kstar = cov between train and test cases
## PREDICTION
print 'GP: ...prediction'
results = gpr.gp_pred(logtheta, covfunc, X, y,
Xstar) # get predictions for unlabeled data ONLY
MU = results[0]
S2 = results[1]
#print MU
## plot results
pyplot.suptitle('logtheta:', fontsize=12)
pyplot.title(logtheta)
pyplot.plot(Xstar, MU, 'g^', X, y, 'ro')
pyplot.show()