def ablate_Ktensor(tt_factors, fac_num_to_remove):
"""Create full matrix from an ablated (one factor removed) KTensor from tensortool."""
# turn factors into tuple, then remove factor from each mode's matrix
factors = tuple(tt_factors)
factors = tuple([np.delete(f, fac_num_to_remove, axis=1) for f in factors])
# create a KTensor from tensortools to speed up some math
kt = KTensor(factors)
# create full tensor
return kt.full()
def full_factor(tt_factors, fac_num_to_keep):
"""Create full matrix removing a single tensor component from your data."""
# turn factors into tuple, then select a single factor from each mode's matrix
factors = tuple(tt_factors)
factors = tuple([f[:, fac_num_to_keep][:, None] for f in factors])
# create a KTensor from tensortools to speed up some math
kt = KTensor(factors)
full_factor = kt.full()
# return a full tensor component
return full_factor
def model_forecast(
X,
exog_input,
model,
fit_dict={
'method': '{}-Divergence'.format(u'\u03B2'),
'tol': 1e-5,
'min_iter': 1,
'max_iter': 500,
'verbose': True
}):
"""
Use a trained NN-LDS model to forecast future states and observations.
Parameters
----------
X : np.ndarray, tensor_like with shape: [I_1, I_2, ..., I_N]
Tensor containing dimensionality of the system output.
Each Tensor fiber, I, is considered a mode of the system.
Example modes are channels, time, trials, spectral frequency, etc.
model : FitModel object
Model that was created using the init_model function. The `model`
must explicitly contain an LDS component.
exog_input: np.ndarray, shape: [t, p]
If LDS_dict is used, then exog_input specifies the
p-dimensional input signal, or control input, over time t.
Must match the length of the observed axis.
forecast_steps: int
Number of samples ahead to forecast using each time sample in X
as a starting-point.
fit_dict: dict, specifying fitting options.
tol: float, Stopping tolerance for reconstruction error.
max_iter: int, Max number of iterations to perform before exiting.
min_iter: int, Min number of iterations to perform before exiting.
verbose : bool, Display progress.
Returns
-------
Xp : list[np.ndarray], listtensor_like with shape: [I_1, I_2, ..., I_N]
Skeletal Tensor containing dimensionality of the system output.
Each Tensor fiber, I, is considered a mode of the system.
Example modes are channels, time, trials, spectral frequency, etc.
"""
# Check model
if 'NTF' not in model.model_param:
raise Exception('Model does not have a observation component.')
if 'LDS' not in model.model_param:
raise Exception('Model does not have a dynamical system component.')
# Check input matrix
optim_utils._check_cpd_inputs(X, model.model_param['rank'])
forecast_steps = (exog_input.shape[0] -
X.shape[model.model_param['LDS']['axis']])
if forecast_steps < 0:
raise Exception('Length of exogeneous input must be geq than ' +
'length of data tensor in order to filter/forecast.')
if exog_input.shape[1] != model.model_param['LDS']['AB'].B.shape[-1]:
raise Exception('Shape of input signal does not match shape of ' +
'control-input matrix.')
# Update model fit parameters
model.set_fit_param(**fit_dict)
# Reset the status of the model
model.reset_status()
# Set pointers to commonly used objects
mp = model.model_param
dAB = mp['LDS']['AB']
ax_t = mp['LDS']['axis']
Xn = unfold(X, ax_t)
# Initialize temporal state coefficients
assert model.model_param['NTF']['init'] in ['rand', 'randn']
if model.model_param['NTF']['init'] == 'randn':
H = np.random.randn(X.shape[ax_t], model.model_param['rank'])
else:
H = np.random.rand(X.shape[ax_t], model.model_param['rank'])
# Create a new model tensor with the temporal state mode replaced
W = KTensor([mp['NTF']['W'][j] if j != ax_t else H for j in range(X.ndim)])
mp['NTF']['W'] = W
# Use observation model to estimate the current temporal state mode
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Iterate algorithm until convergence or maxiter is reached
# i) compute the N gram matrices and multiply
# ii) Compute Khatri-Rao product
# iii) Update component U_1, U_2, ... U_N
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
if forecast_steps > 0:
Ufilter = exog_input[:-forecast_steps]
while model.still_optimizing:
# Select all components, but U_n
# i) Compute Khatri-Rao product
kr = khatri_rao([W[j] for j in range(X.ndim) if j != ax_t])
# ii) Compute unfolded prediction of X
p = W[ax_t].dot(kr.T)
# iii) Compute gradient for the observation model
neg, pos = calc_div_grad(Xn, p, kr, mp['NTF']['beta'])
# iv) Compute gradient for the dynamical model
mp['LDS']['AB'].as_ord_1()
WL = mp['LDS']['AB'].conv_state_to_lagged(W[ax_t].T)
UL = mp['LDS']['AB'].conv_exog_to_lagged(Ufilter.T)
lag_diff = mp['LDS']['AB'].lag_state - mp['LDS']['AB'].lag_exog
if lag_diff > 0:
UL = UL[:, int(np.abs(lag_diff)):]
elif lag_diff < 0:
WL = WL[:, int(np.abs(lag_diff)):]
neg1, pos1 = calc_time_grad(mp['LDS']['AB'].A, WL, mp['LDS']['AB'].B,
UL, mp['LDS']['beta'])
neg1 = mp['LDS']['AB'].conv_state_to_unlagged(neg1)
pos1 = mp['LDS']['AB'].conv_state_to_unlagged(pos1)
neg += neg1.T
pos += pos1.T
mp['LDS']['AB'].as_ord_p()
# vi) Update the observational component weights
W[ax_t] *= (neg / pos)**mm_gamma_func(mp['NTF']['beta'])
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Update the optimization model, checks for convergence.
# ~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
# Compute objective function
# Cost of the observation model
cost_obs = calc_cost(X, W.full(), mp['NTF']['beta'])
# Update the model
model.update(cost_obs)
# end optimization loop.
# Current temporal state mode is inferred, coefficients have been updated
model.finalize()
# Use LDS and current temporal state mode to forecast future state mode
dAB.as_ord_p()
Wn = list(W[ax_t])
Un = list(exog_input)
for p in range(forecast_steps):
W_ix = range(len(Wn) - 1, len(Wn) - 1 - dAB.lag_state, -1)
U_ix = range(len(Wn) - 1, len(Wn) - 1 - dAB.lag_exog, -1)
AX = np.array([
dAB.A[ii, :, :].dot(Wn[ij].reshape(-1, 1))
for ii, ij in enumerate(W_ix)
])[:, :, 0].sum(axis=0)
BU = np.array([
dAB.B[ii, :, :].dot(Un[ij].reshape(-1, 1))
for ii, ij in enumerate(U_ix)
])[:, :, 0].sum(axis=0)
Wn.append(AX + BU)
Wn = np.array(Wn)
Wn = Wn[-forecast_steps:, :]
# Re-mix forecasted state mode coefs through NTF
XP = KTensor([W[j] if j != ax_t else Wn for j in range(X.ndim)])
return XP