def __CV_Leave_One_Curve(self, x0, candidate_h, ker_fun, binning, dtype,
**kwargs):
"""
input variable:
"""
grid_shape = np.array(x0.shape[:-1])
d = x0.shape[-1]
sse = np.ones(candidate_h.shape[0])
bin_width = np.ptp(x0.reshape(-1, d), 0) / (grid_shape - 1)
if binning == True:
bin_data = kwargs['bin_data']
test_bin_data = kwargs['test_bin_data']
for i in range(candidate_h.shape[0]):
h = candidate_h.take(i, 0)
for test_data in test_bin_data:
train_bin_data = bin_data - test_data
fit_y = lpr.Lpr_For_Bin(train_bin_data, bin_width, h,
ker_fun, dtype)
if np.any(np.isnan(fit_y)):
sse[i] = np.nan
break
nozero = (test_data.take(1, 0) != 0).flatten()
test_bin_data_nozero = np.compress(
nozero, test_data.reshape(2, -1), 1)
sse[i] += (((test_bin_data_nozero.take(0, 0) - np.compress(
nozero, fit_y) * test_bin_data_nozero.take(1, 0))**2) /
test_bin_data_nozero.take(1, 0)).sum()
else:
x, y = kwargs['x'], kwargs['y']
if self.__num_fun > 100:
test_index = np.random.random_integers(0, self.__num_fun - 1,
100)
else:
test_index = range(self.__num_fun)
for i in range(candidate_h.shape[0]):
h = candidate_h.take(i, 0)
print(i)
for j in test_index:
print(j)
fit_y = lpr.Lpr(np.vstack(x[-j]),
np.hstack(y[-j]),
x[j],
h.take(i, 0),
binning=binning,
ker_fun=ker_fun)
if np.any(np.isnan(fit_y)):
sse[i] = np.nan
break
sse[i] += ((y[j] - fit_y)**2).sum()
opt_h = candidate_h.take(np.nanargmin(sse), 0)
return (opt_h)
def __Fit_Cov(self, x, y, x0, candidate_h, binning, ker_fun):
self.cov_bw, xx_p, yy = self.__CV_Cov_Leave_One_Out(
x, y, x0, candidate_h, ker_fun)
bin_xx = np.bincount(xx_p.reshape(-1),
minlength=np.prod(self.__grid_shape)**2)
bin_yy = np.bincount(xx_p.reshape(-1),
yy.reshape(-1),
minlength=np.prod(self.__grid_shape)**2)
fit_yy = lpr.Lpr_For_Bin([
bin_yy.reshape(np.tile(self.__grid_shape, 2)),
bin_xx.reshape(np.tile(self.__grid_shape, 2))
],
np.tile(self.__bin_width, 2),
h=self.cov_bw,
ker_fun=ker_fun)
self.cov_fun = fit_yy.reshape(np.repeat(np.prod(
self.__grid_shape), 2)) - np.outer(self.mean_fun, self.mean_fun)
def __BW_Partition(self, x0, candidate_h, ker_fun, binning, dtype,
**kwargs):
"""
input variable:
"""
grid_shape = np.asarray(x0.shape[:-1])
n_h, d = candidate_h.shape
bin_width = np.ptp(x0.reshape(-1, d), 0) / (grid_shape - 1)
ssq = np.zeros(n_h)
if binning == True:
train_bin_data = kwargs['train_bin_data']
test_bin_data = kwargs['test_bin_data']
for i in range(n_h):
fit_y = lpr.Lpr_For_Bin(train_bin_data, bin_width,
candidate_h.take(i, 0), ker_fun,
dtype).reshape(x0.shape[:-1])
if np.isnan(fit_y).any():
ssq[i] = np.nan
continue
nozero = (test_bin_data.take(1, 0) != 0).flatten()
test_bin_data_nozero = np.compress(
nozero, test_bin_data.reshape(2, -1), 1)
ssq[i] = (((test_bin_data_nozero.take(0, 0) -
np.compress(nozero, fit_y.flatten()) *
test_bin_data_nozero.take(1, 0))**2) /
test_bin_data_nozero.take(1, 0)).sum()
else:
x, y = kwargs['x'], kwargs['y']
combined = list(zip(x, y))
random.shuffle(combined)
train_data, test_data = combined[:self.__n_train], combined[
self.__n_train:]
train_x, train_y = list(zip(*train_data))
test_x, test_y = list(zip(*test_data))
for i in range(n_h):
fit_y = lpr.Lpr(np.vstack(train_x),
np.hstack(train_y),
np.vstack(test_x),
candidate_h.take(i, 0),
binning=binning,
ker_fun=ker_fun)
ssq[i] = ((test_y - fit_y)**2).sum()
h_opt = candidate_h.take(np.nanargmin(ssq), 0)
return (h_opt)
def __CV_Cov_Partition(self, x, y, x0, h, ker_fun):
grid_shape, d = np.asarray(x0.shape[:-1]), x0.shape[-1]
n_grid = np.prod(self.__grid_shape)
x_displacement = (
(x - x0.reshape(-1, d).min(axis=0)) / self.__bin_width +
np.ones(self.__d) / 2).astype(np.int32)
x_p = np.sum(x_displacement *
np.append(grid_shape[::-1].cumprod()[-2::-1], 1),
axis=2)
xx_p = (x_p.repeat(x_p.shape[1], 1) * n_grid +
np.tile(x_p, x_p.shape[1]))
xx_p = np.delete(xx_p, np.arange(0, self.__num_pt**2,
self.__num_pt + 1), 1)
yy = np.einsum('ij,ik->ijk', y, y).reshape(self.__num_fun, -1)
yy = np.delete(yy, np.arange(0, self.__num_pt**2, self.__num_pt + 1),
1)
non_nan_value = ~np.isnan(yy).reshape(-1)
n_real_val = non_nan_value.sum()
xx_p = np.compress(non_nan_value, xx_p.reshape(-1))
yy = np.compress(non_nan_value, yy.reshape(-1))
n_train = lpr.Partition_Data_Size(n_real_val)
random_order = np.random.permutation(n_real_val)
train_xx, test_xx = np.split(
xx_p.reshape(-1).take(random_order), [n_train])
train_yy, test_yy = np.split(
yy.reshape(-1).take(random_order), [n_train])
bin_xx = np.bincount(train_xx, minlength=n_grid**2)
bin_yy = np.bincount(train_xx, train_yy, minlength=n_grid**2)
bin_xx = bin_xx.reshape(np.tile(self.__grid_shape, 2))
bin_yy = bin_yy.reshape(np.tile(self.__grid_shape, 2))
ssq = np.zeros(h.shape[0])
for i in range(h.shape[0]):
fit_y = lpr.Lpr_For_Bin([bin_yy, bin_xx],
np.tile(self.__bin_width, 2),
h.take(i, 0),
ker_fun=ker_fun)
ssq[i] = ((test_yy - fit_y[test_xx])**2).sum()
if np.isnan(fit_y).any():
ssq[i] = np.nan
h_opt = h.take(np.nanargmin(ssq), 0)
return ([h_opt, xx_p, yy])
def __Fit_Cov(self, x, y, x0, candidate_h, binning, ker_fun, bw_select):
if bw_select is 'Partition':
self.cov_bw, xx_p, yy = self.__CV_Cov_Partition(
x, y, x0, candidate_h, ker_fun)
elif bw_select is 'LeaveOneOut':
self.cov_bw, xx_p, yy = self.__CV_Cov_Leave_One_Out(
x, y, x0, candidate_h, ker_fun)
bin_xx = np.bincount(xx_p.reshape(-1),
minlength=np.prod(self.__grid_shape)**2)
bin_yy = np.bincount(xx_p.reshape(-1),
yy.reshape(-1),
minlength=np.prod(self.__grid_shape)**2)
fit_yy = lpr.Lpr_For_Bin([
bin_yy.reshape(np.tile(self.__grid_shape, 2)),
bin_xx.reshape(np.tile(self.__grid_shape, 2))
],
np.tile(self.__bin_width, 2),
h=self.cov_bw,
ker_fun=ker_fun).reshape(
np.tile(np.prod(self.__grid_shape), 2))
fit_yy = (fit_yy.T + fit_yy) / 2
self.cov_fun = fit_yy - np.outer(self.mean_fun, self.mean_fun)
def __Fit_Sigma2(self, x, y, x0, candidate_h, binning, bin_weight, ker_fun,
bw_select, dtype):
yy = [yi**2 for yi in y]
if binning == True:
cov_diag_bin_data = np.asarray(
list(
map(lambda xy: lpr.Bin_Data(xy[0], xy[1], x0, bin_weight),
zip(x, yy))))
if bw_select == 'Partition':
rand_index = np.random.permutation(self.__num_fun)
train_bin_data, test_bin_data = np.split(
cov_diag_bin_data.take(rand_index, 0), [self.__n_train])
self.cov_diag_bw = self.__BW_Partition(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
train_bin_data=train_bin_data.sum(0),
test_bin_data=test_bin_data.sum(0))
elif bw_select == 'LeaveOneOut':
if self.__num_fun > 100:
test_index = np.random.random_integers(
0, self.__num_fun - 1, 100)
else:
test_index = range(self.__num_fun)
test_bin_data = cov_diag_bin_data.take(test_index, 0)
self.cov_diag_bw = self.__CV_Leave_One_Curve(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
bin_data=cov_diag_bin_data.sum(0),
test_bin_data=test_bin_data)
self.cov_dia_fun = lpr.Lpr_For_Bin(
bin_data=cov_diag_bin_data.sum(0),
bin_width=self.__bin_width,
h=self.cov_diag_bw,
ker_fun=ker_fun,
dtype=dtype) - self.mean_fun**2
else:
if bw_select == 'Partition':
self.cov_bw = self.__BW_Partition(x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
x=x,
y=yy)
elif bw_select == 'LeaveOneOut':
self.cov_bw = self.__CV_Leave_One_Curve(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
x=x,
y=yy)
self.cov_dia_fun = lpr.Lpr(x=np.vstack(x),
y=np.hstack(yy),
x0=x0,
h=self.cov_diag_bw,
binning=binning,
bin_weight=bin_weight,
ker_fun=ker_fun,
dtype=dtype) - self.mean_fun**2
interval = np.array([(self.__grid_shape / 4).astype('int'),
(3 * self.__grid_shape / 4).astype('int')])
restruct_cov_fun = np.matmul(
np.matmul(self.eig_fun.T, np.diag(self.eig_val)), self.eig_fun)
sigma2_t = (self.cov_dia_fun - np.diag(restruct_cov_fun)).reshape(
self.__grid_shape)
for i in range(self.__d):
left, right = interval.take(i, 1)
sigma2_t = sigma2_t.take(np.arange(left, right), i)
self.sigma2 = (sigma2_t).mean()
self.sigma2 = 0 if self.sigma2 < 0 else self.sigma2
def __Fit_Cov(self,
x,
y,
x0,
candidate_h,
binning,
bin_weight,
ker_fun,
bw_select,
dtype,
bin_data=None):
cov_x0 = x0.reshape(
-1, self.__d)[np.mgrid[0:self.__grid_shape.prod(),
0:self.__grid_shape.prod()].T].reshape(
np.append(self.__grid_shape.repeat(2),
-1))
if binning == True:
if bw_select == 'Partition':
rand_index = np.random.permutation(self.__num_fun)
train_bin_data, test_bin_data = np.split(
bin_data.take(rand_index, 0), [self.__n_train])
train_cov_bin_data = self.__Get_Row_Cov(
[x[i] for i in rand_index[:self.__n_train]],
[y[i] for i in rand_index[:self.__n_train]], cov_x0,
binning, bin_weight, train_bin_data)
test_cov_bin_data = self.__Get_Row_Cov(
[x[i] for i in rand_index[self.__n_train:]],
[y[i] for i in rand_index[self.__n_train:]], cov_x0,
binning, bin_weight, test_bin_data)
self.cov_bw = self.__BW_Partition(
x0=cov_x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
train_bin_data=train_cov_bin_data,
test_bin_data=test_cov_bin_data)
elif bw_select == 'LeaveOneOut':
if self.__num_fun > 100:
test_index = np.random.random_integers(
0, self.__num_fun - 1, 100)
else:
test_index = range(self.__num_fun)
test_cov_bin_data = np.zeros((len(test_index), 2) +
cov_x0.shape[:-1])
for i in range(len(test_index)):
testi = test_index[i]
test_cov_bin_data[i] = self.__Get_Row_Cov(
[x[testi]], [y[testi]], cov_x0, binning, bin_weight,
bin_data.take(testi,
0).reshape((1, ) + bin_data.shape[1:]))
cov_bin_data = self.__Get_Row_Cov(x, y, cov_x0, binning,
bin_weight, bin_data)
self.cov_bw = self.__CV_Leave_One_Curve(
x0=cov_x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
bin_data=cov_bin_data,
test_bin_data=test_cov_bin_data)
fit_yy = lpr.Lpr_For_Bin(
bin_data=self.__Get_Row_Cov(x, y, cov_x0, binning, bin_weight,
bin_data),
bin_width=np.tile(self.__bin_width, 2),
h=self.cov_bw,
ker_fun=ker_fun,
dtype=dtype).reshape(np.repeat(np.prod(self.__grid_shape), 2))
else:
xx, yy, cov_x0 = self.__Get_Row_Cov(x, y, x0, binning, bin_weight)
if bw_select == 'Partition':
self.cov_bw = self.__BW_Partition(x0=cov_x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
bin_weight=bin_weight,
binning=binning,
dtype=dtype,
x=xx,
y=yy)
elif bw_select == 'LeaveOneOut':
self.cov_bw = self.__CV_Leave_One_Curve(
x0=cov_x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
bin_weight=bin_weight,
dtype=dtype,
x=xx,
y=yy)
fit_yy = lpr.Lpr(x=np.vstack(xx),
y=np.hstack(yy),
x0=cov_x0,
h=self.cov_bw,
binning=binning,
bin_weight=bin_weight,
ker_fun=ker_fun,
dtype=dtype).reshape(
np.repeat(np.prod(self.__grid_shape), 2))
fit_yy = (fit_yy.T + fit_yy) / 2
self.cov_fun = fit_yy - np.outer(self.mean_fun, self.mean_fun)
def __Fit_Mean(self,
x,
y,
x0,
candidate_h,
binning,
bin_weight,
ker_fun,
bw_select,
dtype,
bin_data=None):
if binning == True:
if bw_select == 'Partition':
rand_index = np.random.permutation(self.__num_fun)
train_bin_data, test_bin_data = np.split(
bin_data.take(rand_index, 0), [self.__n_train])
self.mean_bw = self.__BW_Partition(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
train_bin_data=train_bin_data.sum(0),
test_bin_data=test_bin_data.sum(0))
elif bw_select == 'LeaveOneOut':
if self.__num_fun > 100:
test_index = np.random.random_integers(
0, self.__num_fun - 1, 100)
else:
test_index = range(self.__num_fun)
test_bin_data = bin_data.take(test_index, 0)
self.mean_bw = self.__CV_Leave_One_Curve(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
bin_data=bin_data.sum(0),
test_bin_data=test_bin_data)
self.mean_fun = lpr.Lpr_For_Bin(bin_data=bin_data.sum(0),
bin_width=self.__bin_width,
h=self.mean_bw,
ker_fun=ker_fun,
dtype=dtype)
else:
if bw_select == 'Partition':
self.mean_bw = self.__BW_Partition(x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
x=x,
y=y)
elif bw_select == 'LeaveOneOut':
self.mean_bw = self.__CV_Leave_One_Curve(
x0=x0,
candidate_h=candidate_h,
ker_fun=ker_fun,
binning=binning,
dtype=dtype,
x=x,
y=y)
self.mean_fun = lpr.Lpr(np.vstack(x), np.hstack(y), x0,
self.mean_bw, binning, bin_weight, ker_fun,
dtype)