def get_issm_coeff(
self,
seasonal_indicators: Tensor # (batch_size, time_length)
) -> Tuple[Tensor, Tensor, Tensor]:
F = getF(seasonal_indicators)
emission_coeff_ls, transition_coeff_ls, innovation_coeff_ls = zip(
self.nonseasonal_issm.get_issm_coeff(seasonal_indicators),
*[
issm.get_issm_coeff(
seasonal_indicators.slice_axis(axis=-1,
begin=ix,
end=ix + 1))
for ix, issm in enumerate(self.seasonal_issms)
],
)
# stack emission and innovation coefficients
emission_coeff = F.concat(*emission_coeff_ls, dim=-1)
innovation_coeff = F.concat(*innovation_coeff_ls, dim=-1)
# transition coefficient is block diagonal!
transition_coeff = _make_block_diagonal(transition_coeff_ls)
return emission_coeff, transition_coeff, innovation_coeff
def lowrank_log_likelihood(
rank: int, mu: Tensor, D: Tensor, W: Tensor, x: Tensor
) -> Tensor:
F = getF(mu)
dim = F.ones_like(mu).sum(axis=-1).max()
dim_factor = dim * math.log(2 * math.pi)
batch_capacitance_tril = capacitance_tril(F=F, rank=rank, W=W, D=D)
log_det_factor = log_det(
F=F, batch_D=D, batch_capacitance_tril=batch_capacitance_tril
)
mahalanobis_factor = mahalanobis_distance(
F=F, W=W, D=D, capacitance_tril=batch_capacitance_tril, x=x - mu
)
ll: Tensor = -0.5 * (
F.broadcast_add(dim_factor, log_det_factor) + mahalanobis_factor
)
return ll
def __init__(
self, mu: Tensor, L: Tensor, F=None, float_type: DType = np.float32
) -> None:
self.mu = mu
self.F = F if F else getF(mu)
self.L = L
self.float_type = float_type
def s(mu: Tensor, D: Tensor, W: Tensor) -> Tensor:
F = getF(mu)
samples_D = F.sample_normal(
mu=F.zeros_like(mu), sigma=F.ones_like(mu), dtype=dtype
)
cov_D = D.sqrt() * samples_D
# dummy only use to get the shape (..., rank, 1)
dummy_tensor = F.linalg_gemm2(
W, mu.expand_dims(axis=-1), transpose_a=True
).squeeze(axis=-1)
samples_W = F.sample_normal(
mu=F.zeros_like(dummy_tensor),
sigma=F.ones_like(dummy_tensor),
dtype=dtype,
)
cov_W = F.linalg_gemm2(W, samples_W.expand_dims(axis=-1)).squeeze(
axis=-1
)
samples = mu + cov_D + cov_W
return samples
def __init__(self,
alpha: Tensor,
F=None,
float_type: DType = np.float32) -> None:
self.alpha = alpha
self.F = F if F else getF(alpha)
self.float_type = float_type
def __init__(self, dim: int, rank: int, mu: Tensor, D: Tensor,
W: Tensor) -> None:
self.dim = dim
self.rank = rank
self.mu = mu
self.D = D
self.W = W
self.F = getF(mu)
self.Cov = None
def s(alpha: Tensor) -> Tensor:
F = getF(alpha)
samples_gamma = F.sample_gamma(alpha=alpha,
beta=F.ones_like(alpha),
dtype=dtype)
sum_gamma = F.sum(samples_gamma, axis=-1, keepdims=True)
samples_s = F.broadcast_div(samples_gamma, sum_gamma)
return samples_s
def s(alpha: Tensor) -> Tensor:
F = getF(alpha)
samples_gamma = F.sample_gamma(alpha=alpha,
beta=F.ones_like(alpha),
dtype=dtype)
sum_gamma = F.sum(samples_gamma, axis=-1, keepdims=True)
samples_s = F.broadcast_div(samples_gamma, sum_gamma)
cat_samples = F.sample_multinomial(samples_s, shape=n_trials)
return F.sum(F.one_hot(cat_samples, dim), axis=-2)
def __init__(
self, gamma: Tensor, slopes: Tensor, knot_spacings: Tensor, F=None
) -> None:
self.F = F if F else getF(gamma)
self.gamma = gamma
# Since most of the calculations are easily expressed in the original parameters, we transform the
# learned parameters back
self.b, self.knot_positions = PiecewiseLinear._to_orig_params(
self.F, slopes, knot_spacings
)
def crps(self, y: Tensor) -> Tensor:
# TODO: use event_shape
F = getF(y)
x = y
scale = 1.0
for t in self.transforms[::-1]:
assert isinstance(
t, AffineTransformation), "Not an AffineTransformation"
x = t.f_inv(x)
scale *= t.scale
p = self.base_distribution.crps(x)
return F.broadcast_mul(p, scale)
def __init__(
self,
dim: int,
n_trials: int,
alpha: Tensor,
F=None,
float_type: DType = np.float32,
) -> None:
self.dim = dim
self.n_trials = n_trials
self.alpha = alpha
self.F = F if F else getF(alpha)
self.float_type = float_type
def distribution(
self,
feat_static_cat: Tensor,
feat_static_real: Tensor,
past_time_feat: Tensor,
past_target: Tensor,
past_observed_values: Tensor,
future_time_feat: Tensor,
future_target: Tensor,
future_observed_values: Tensor,
) -> Distribution:
"""
Returns the distribution predicted by the model on the range of
past_target and future_target.
The distribution is obtained by unrolling the network with the true
target, this is also the distribution that is being minimized during
training. This can be used in anomaly detection, see for instance
examples/anomaly_detection.py.
Input arguments are the same as for the hybrid_forward method.
Returns
-------
Distribution
a distribution object whose mean has shape:
(batch_size, context_length + prediction_length).
"""
# unroll the decoder in "training mode"
# i.e. by providing future data as well
F = getF(feat_static_cat)
rnn_outputs, _, scale, _ = self.unroll_encoder(
F=F,
feat_static_cat=feat_static_cat,
feat_static_real=feat_static_real,
past_time_feat=past_time_feat,
past_target=past_target,
past_observed_values=past_observed_values,
future_time_feat=future_time_feat,
future_target=future_target,
)
distr_args_m = self.proj_distr_args_m(rnn_outputs)
distr_args_q = self.proj_distr_args_q(rnn_outputs)
return (
self.distr_output_m.distribution(distr_args_m, scale=scale),
self.distr_output_q.distribution(distr_args_q, scale=scale),
)
def distribution(
self,
feat_static_cat: Tensor,
past_time_feat: Tensor,
past_target: Tensor,
past_observed_values: Tensor,
future_time_feat: Tensor,
future_target: Tensor,
future_observed_values: Tensor,
) -> Distribution:
"""
Returns the distribution predicted by the model on the range of past_target and future_target.
The distribution is obtained by unrolling the network with the true target, this is also the distribution
that is being minimized during training.
This can be used in anomaly detection, see for instance examples/anomaly_detection.py.
Parameters
----------
feat_static_cat
past_time_feat
past_target
past_observed_values
future_time_feat
future_target
future_observed_values
Returns
-------
sample_paths : Distribution
a distribution object whose mean has shape: (batch_size, context_length + prediction_length).
"""
# unroll the decoder in "training mode", i.e. by providing future data as well
F = getF(feat_static_cat)
rnn_outputs, _, scale, _ = self.unroll_encoder(
F=F,
feat_static_cat=feat_static_cat,
past_time_feat=past_time_feat,
past_target=past_target,
past_observed_values=past_observed_values,
future_time_feat=future_time_feat,
future_target=future_target,
)
distr_args = self.proj_distr_args(rnn_outputs)
return self.distr_output.distribution(distr_args, scale=scale)
def __init__(
self,
emission_coeff: Tensor,
transition_coeff: Tensor,
innovation_coeff: Tensor,
noise_std: Tensor,
residuals: Tensor,
prior_mean: Tensor,
prior_cov: Tensor,
latent_dim: int,
output_dim: int,
seq_length: int,
F=None,
) -> None:
self.latent_dim = latent_dim
self.output_dim = output_dim
self.seq_length = seq_length
# Split coefficients along time axis for easy access
# emission_coef[t]: (batch_size, obs_dim, latent_dim)
self.emission_coeff = emission_coeff.split(
axis=1, num_outputs=self.seq_length, squeeze_axis=True
)
# innovation_coef[t]: (batch_size, latent_dim)
self.innovation_coeff = innovation_coeff.split(
axis=1, num_outputs=self.seq_length, squeeze_axis=False
)
# transition_coeff: (batch_size, latent_dim, latent_dim)
self.transition_coeff = transition_coeff.split(
axis=1, num_outputs=self.seq_length, squeeze_axis=True
)
# noise_std[t]: (batch_size, obs_dim)
self.noise_std = noise_std.split(
axis=1, num_outputs=self.seq_length, squeeze_axis=True
)
# residuals[t]: (batch_size, obs_dim)
self.residuals = residuals.split(
axis=1, num_outputs=self.seq_length, squeeze_axis=True
)
self.prior_mean = prior_mean
self.prior_cov = prior_cov
self.F = F if F else getF(noise_std)
def _make_block_diagonal(blocks: List[Tensor]) -> Tensor:
assert (len(blocks) >
0), "You need at least one tensor to make a block-diagonal tensor"
if len(blocks) == 1:
return blocks[0]
F = getF(blocks[0])
# transition coefficient is block diagonal!
block_diagonal = _make_2_block_diagonal(F, blocks[0], blocks[1])
for i in range(2, len(blocks)):
block_diagonal = _make_2_block_diagonal(F=F,
left=block_diagonal,
right=blocks[i])
return block_diagonal
def crps(self, y: Tensor) -> Tensor:
# TODO: use event_shape
F = getF(y)
for t in self.transforms[::-1]:
assert isinstance(
t, AffineTransformation), "Not an AffineTransformation"
assert (t.scale is not None
and t.loc is None), "Not a scaling transformation"
scale = t.scale
x = t.f_inv(y)
# (..., 1)
p = self.base_distribution.crps(x)
return F.broadcast_mul(p, scale)
def emission_coeff(
self,
seasonal_indicators: Tensor # (batch_size, time_length)
) -> Tensor:
F = getF(seasonal_indicators)
_emission_coeff = F.ones(shape=(1, 1, 1, self.latent_dim()))
# get the right shape: (batch_size, seq_length, obs_dim, latent_dim)
zeros = _broadcast_param(
F.zeros_like(
seasonal_indicators.slice_axis(axis=-1, begin=0,
end=1).squeeze(axis=-1)),
axes=[2, 3],
sizes=[1, self.latent_dim()],
)
return _emission_coeff.broadcast_like(zeros)
def __init__(self,
amplitude: Tensor,
length_scale: Tensor,
F=None) -> None:
"""
Parameters
----------
amplitude : Tensor
RBF kernel amplitude hyper-parameter of shape (batch_size, 1, 1).
length_scale : Tensor
RBF kernel length scale hyper-parameter of of shape (batch_size, 1, 1).
F : ModuleType
A module that can either refer to the Symbol API or the NDArray
API in MXNet.
"""
self.F = F if F else getF(amplitude)
self.amplitude = amplitude
self.length_scale = length_scale
def transition_coeff(
self,
seasonal_indicators: Tensor # (batch_size, time_length)
) -> Tensor:
F = getF(seasonal_indicators)
_transition_coeff = (F.eye(
self.latent_dim()).expand_dims(axis=0).expand_dims(axis=0))
# get the right shape: (batch_size, seq_length, latent_dim, latent_dim)
zeros = _broadcast_param(
F.zeros_like(
seasonal_indicators.slice_axis(axis=-1, begin=0,
end=1).squeeze(axis=-1)),
axes=[2, 3],
sizes=[self.latent_dim(), self.latent_dim()],
)
return _transition_coeff.broadcast_like(zeros)
def distr(
self,
rnn_outputs: Tensor,
time_features: Tensor,
scale: Tensor,
lags_scaled: Tensor,
target_dimension_indicator: Tensor,
seq_len: int,
):
"""
Returns the distribution of GPVAR with respect to the RNN outputs.
Parameters
----------
rnn_outputs
Outputs of the unrolled RNN (batch_size, seq_len, num_cells)
time_features
Dynamic time features (batch_size, seq_len, num_features)
scale
Mean scale for each time series (batch_size, 1, target_dim)
lags_scaled
Scaled lags used for RNN input
(batch_size, seq_len, target_dim, num_lags)
target_dimension_indicator
Indices of the target dimension (batch_size, target_dim)
seq_len
Length of the sequences
Returns
-------
distr
Distribution instance
distr_args
Distribution arguments
"""
F = getF(rnn_outputs)
# (batch_size, target_dim, embed_dim)
index_embeddings = self.embed(target_dimension_indicator)
# broadcast to (batch_size, seq_len, target_dim, embed_dim)
repeated_index_embeddings = index_embeddings.expand_dims(
axis=1
).repeat(axis=1, repeats=seq_len)
# broadcast to (batch_size, seq_len, target_dim, num_features)
time_features = time_features.expand_dims(axis=2).repeat(
axis=2, repeats=self.target_dim_sample
)
# (batch_size, seq_len, target_dim, embed_dim + num_cells + num_inputs)
distr_input = F.concat(
rnn_outputs, repeated_index_embeddings, time_features, dim=-1
)
# TODO 1 pass inputs in proj args
distr_args = self.proj_dist_args(distr_input)
# compute likelihood of target given the predicted parameters
distr = self.distr_output.distribution(
distr_args, scale=scale, dim=self.target_dim_sample
)
return distr, distr_args
def __init__(self, mu: Tensor, L: Tensor, F=None) -> None:
self.mu = mu
self.F = F if F else getF(mu)
self.L = L
def innovation_coeff(self, seasonal_indicators: Tensor) -> Tensor:
F = getF(seasonal_indicators)
# seasonal_indicators = F.modulo(seasonal_indicators - 1, self.latent_dim)
return F.one_hot(seasonal_indicators,
depth=self.latent_dim()).squeeze(axis=2)
def emission_coeff(self, seasonal_indicators: Tensor) -> Tensor:
F = getF(seasonal_indicators)
return F.one_hot(seasonal_indicators, depth=self.latent_dim())
def __init__(
self,
sigma: Tensor,
kernel: Kernel,
prediction_length: Optional[int] = None,
context_length: Optional[int] = None,
num_samples: Optional[int] = None,
ctx: mx.Context = mx.Context("cpu"),
float_type: DType = np.float64,
jitter_method: str = "iter",
max_iter_jitter: int = 10,
neg_tol: float = -1e-8,
diag_weight: float = 1e-6,
increase_jitter: int = 10,
sample_noise: bool = True,
F=None,
) -> None:
r"""
Parameters
----------
sigma
Noise parameter of shape (batch_size, num_data_points, 1),
where num_data_points is the number of rows in the Cholesky matrix.
kernel
Kernel object.
prediction_length
Prediction length.
context_length
Training length.
num_samples
The number of samples to be drawn.
ctx
Determines whether to compute on the cpu or gpu.
float_type
Determines whether to use single or double precision.
jitter_method
Iteratively jitter method or use eigenvalue decomposition depending on problem size.
max_iter_jitter
Maximum number of iterations for jitter to iteratively make the matrix positive definite.
neg_tol
Parameter in the jitter methods to eliminate eliminate matrices with diagonal elements smaller than this
when checking if a matrix is positive definite.
diag_weight
Multiple of mean of diagonal entries to initialize the jitter.
increase_jitter
Each iteration multiply by jitter by this amount
sample_noise
Boolean to determine whether to add :math:`\sigma^2I` to the predictive covariance matrix.
F
A module that can either refer to the Symbol API or the NDArray
API in MXNet.
"""
assert (prediction_length is None or prediction_length > 0
), "The value of `prediction_length` should be > 0"
assert (context_length is None or context_length > 0
), "The value of `context_length` should be > 0"
assert (num_samples is None
or num_samples > 0), "The value of `num_samples` should be > 0"
self.sigma = sigma
self.kernel = kernel
self.prediction_length = prediction_length
self.context_length = (context_length if context_length is not None
else prediction_length)
self.num_samples = num_samples
self.F = F if F else getF(sigma)
self.ctx = ctx
self.float_type = float_type
self.jitter_method = jitter_method
self.max_iter_jitter = max_iter_jitter
self.neg_tol = neg_tol
self.diag_weight = diag_weight
self.increase_jitter = increase_jitter
self.sample_noise = sample_noise