def _get_mu(self, ranks, x, y):
"""Initializes latent inputs expectations mu.
Either loads pretrained values of tt-cores of mu, or initializes it
according to optimal formulas from the given data.
Args:
ranks: tt-ranks of mu
x: features of a batch of objects
y: targets of a batch of objects
"""
# TODO: test if this is needed.
w = self.inputs.interpolate_on_batch(self.cov.project(x))
Sigma = ops.tt_tt_matmul(self.sigma_l, ops.transpose(self.sigma_l))
temp = ops.tt_tt_matmul(w, y)
anc = ops.tt_tt_matmul(Sigma, temp)
res = TensorTrain([core[0, :, :, :, :] for core in anc.tt_cores],
tt_ranks=[1]*(anc.ndims()+1))
res = res
for i in range(1, anc.get_shape()[0]):
elem = TensorTrain([core[i, :, :, :, :] for core in anc.tt_cores],
tt_ranks=[1]*(anc.ndims()+1))
res = ops.add(res, elem)
mu_ranks = [1] + [ranks] * (res.ndims() - 1) + [1]
return t3f.get_variable('tt_mu', initializer=TensorTrain(res.tt_cores,
res.get_raw_shape(), mu_ranks))
def _unary_complexity_penalty(self):
"""Computes the complexity penalty for unary potentials.
This function computes KL-divergence between prior and variational
distribution over the values of GPs at inducing inputs.
Returns:
A scalar `tf.Tensor` containing the complexity penalty for GPs
determining unary potentials.
"""
# TODO: test this
mus = self.mus
sigma_ls = _kron_tril(self.sigma_ls)
sigmas = ops.tt_tt_matmul(sigma_ls, ops.transpose(sigma_ls))
sigmas_logdet = _kron_logdet(sigma_ls)
K_mms = self._K_mms()
K_mms_inv = kron.inv(K_mms)
K_mms_logdet = kron.slog_determinant(K_mms)[1]
penalty = 0
penalty += -K_mms_logdet
penalty += sigmas_logdet
penalty += -ops.tt_tt_flat_inner(sigmas, K_mms_inv)
penalty += -ops.tt_tt_flat_inner(mus, ops.tt_tt_matmul(K_mms_inv, mus))
return tf.reduce_sum(penalty) / 2
def _get_mus(self, mu_ranks):
"""Initialize expectations of var distribution over unary potentials.
Args:
mu_ranks: TT-ranks of mus.
"""
# TODO: is this a good initialization?
x_init = tf.random_normal([mu_ranks, self.d], dtype=tf.float64)
y_init = tf.random_normal([mu_ranks], dtype=tf.float64)
w = self.inputs.interpolate_on_batch(x_init)
y_init_cores = [tf.reshape(y_init, (-1, 1, 1, 1, 1))]
for core_idx in range(1, w.ndims()):
y_init_cores += [tf.ones((mu_ranks, 1, 1, 1, 1), dtype=tf.float64)]
y_init = t3f.TensorTrainBatch(y_init_cores)
Sigma = ops.tt_tt_matmul(self.sigma_ls[0],
ops.transpose(self.sigma_ls[0]))
res_batch = t3f.tt_tt_matmul(Sigma, t3f.tt_tt_matmul(w, y_init))
res = res_batch[0]
for i in range(1, mu_ranks):
res = res + res_batch[i]
mu_ranks = [1] + [mu_ranks] * (res.ndims() - 1) + [1]
mu_cores = []
for core in res.tt_cores:
mu_cores.append(
tf.tile(core[None, ...], [self.n_labels, 1, 1, 1, 1]))
return t3f.get_variable('tt_mus',
initializer=TensorTrainBatch(
mu_cores, res.get_raw_shape(), mu_ranks))
def _get_mus(self, ranks, x_init, y_init):
w = self.inputs.interpolate_on_batch(self.cov.project(x_init))
Sigma = ops.tt_tt_matmul(self.sigma_ls[0], ops.transpose(self.sigma_ls[0]))
temp = ops.tt_tt_matmul(w, y_init)
anc = ops.tt_tt_matmul(Sigma, temp)
res = TensorTrain([core[0, :, :, :, :] for core in anc.tt_cores],
tt_ranks=[1]*(anc.ndims()+1))
res = res
for i in range(1, anc.get_shape()[0]):
elem = TensorTrain([core[i, :, :, :, :] for core in anc.tt_cores],
tt_ranks=[1]*(anc.ndims()+1))
res = ops.add(res, elem)
mu_ranks = [1] + [ranks] * (res.ndims() - 1) + [1]
mu_cores = []
for core in res.tt_cores:
mu_cores.append(tf.tile(core[None, ...], [self.n_class, 1, 1, 1, 1]))
return t3f.get_variable('tt_mus',
initializer=TensorTrainBatch(mu_cores, res.get_raw_shape(), mu_ranks))
def complexity_penalty(self):
"""Returns the complexity penalty term for ELBO.
"""
mus = self.mus
sigma_ls = _kron_tril(self.sigma_ls)
sigmas = ops.tt_tt_matmul(sigma_ls, ops.transpose(sigma_ls))
sigmas_logdet = _kron_logdet(sigma_ls)
K_mms = self._K_mms()
K_mms_inv = kron.inv(K_mms)
K_mms_logdet = kron.slog_determinant(K_mms)[1]
penalty = 0
penalty += - K_mms_logdet
penalty += sigmas_logdet
penalty += - ops.tt_tt_flat_inner(sigmas, K_mms_inv)
penalty += - ops.tt_tt_flat_inner(mus,
ops.tt_tt_matmul(K_mms_inv, mus))
return penalty / 2
def complexity_penalty(self):
"""Returns the complexity penalty term for ELBO of different GP models.
"""
mu = self.mu
sigma_l = _kron_tril(self.sigma_l)
sigma = ops.tt_tt_matmul(sigma_l, ops.transpose(sigma_l))
sigma_logdet = _kron_logdet(sigma_l)
K_mm = self.K_mm()
K_mm_inv = kron.inv(K_mm)
K_mm_logdet = kron.slog_determinant(K_mm)[1]
elbo = 0
elbo += - K_mm_logdet
elbo += sigma_logdet
elbo += - ops.tt_tt_flat_inner(sigma, K_mm_inv)
elbo += - ops.tt_tt_flat_inner(mu,
ops.tt_tt_matmul(K_mm_inv, mu))
return elbo / 2
def predict_process_value(self, x, with_variance=False):
"""Predicts the value of the process at point x.
Args:
x: data features
with_variance: if True, returns process variance at x
"""
mu = self.mu
w = self.inputs.interpolate_on_batch(self.cov.project(x))
mean = ops.tt_tt_flat_inner(w, mu)
if not with_variance:
return mean
K_mm = self.K_mm()
variance = self.cov.cov_0()
sigma_l_w = ops.tt_tt_matmul(ops.transpose(self.sigma_l), w)
variance += ops.tt_tt_flat_inner(sigma_l_w, sigma_l_w)
variance -= ops.tt_tt_flat_inner(w, ops.tt_tt_matmul(K_mm, w))
return mean, variance
def _latent_vars_distribution(self, x, seq_lens):
"""Computes the parameters of the variational distribution over potentials.
Args:
x: `tf.Tensor` of shape `batch_size` x `max_seq_len` x d;
sequences of features for the current batch.
seq_lens: `tf.Tensor` of shape `bach_size`; lenghts of input sequences.
Returns:
A tuple containing 4 `tf.Tensors`.
`m_un`: a `tf.Tensor` of shape `n_labels` x `batch_size` x `max_seq_len`;
the expectations of the unary potentials.
`S_un`: a `tf.Tensor` of shape
`n_labels` x `batch_size` x `max_seq_len` x `max_seq_len`; the
covariance matrix of unary potentials.
`m_bin`: a `tf.Tensor` of shape `max_seq_len`^2; the expectations
of binary potentials.
`S_bin`: a `tf.Tensor` of shape `max_seq_len`^2 x `max_seq_len`^2; the
covariance matrix of binary potentials.
"""
batch_size, max_len, d = x.get_shape().as_list()
n_labels = self.n_labels
sequence_mask = tf.sequence_mask(seq_lens, maxlen=max_len)
indices = tf.cast(tf.where(sequence_mask), tf.int32)
x_flat = tf.gather_nd(x, indices)
print('_latent_vars_distribution/x_flat', x_flat.get_shape(), '=',
'sum_len', 'x', d)
w = self.inputs.interpolate_on_batch(self.cov.project(x_flat))
m_un_flat = batch_ops.pairwise_flat_inner(w, self.mus)
print('_latent_vars_distribution/m_un_flat', m_un_flat.get_shape(),
'=', 'sum_len', 'x', self.n_labels)
shape = tf.concat([[batch_size], [max_len], [n_labels]], axis=0)
m_un = tf.scatter_nd(indices, m_un_flat, shape)
m_un = tf.transpose(m_un, [2, 0, 1])
sigmas = ops.tt_tt_matmul(self.sigma_ls, t3f.transpose(self.sigma_ls))
K_mms = self._K_mms()
K_nn = self._K_nns(x)
S_un = K_nn
S_un += _kron_sequence_pairwise_quadratic_form(sigmas, w, seq_lens,
max_len)
S_un -= _kron_sequence_pairwise_quadratic_form(K_mms, w, seq_lens,
max_len)
S_un = self._remove_extra_elems(seq_lens, S_un)
m_bin = tf.identity(self.bin_mu)
S_bin = tf.matmul(self.bin_sigma_l, tf.transpose(self.bin_sigma_l))
return m_un, S_un, m_bin, S_bin
def _predict_process_values(self, x, with_variance=False, test=False):
w = self.inputs.interpolate_on_batch(self.cov.project(x, test=test))
mean = batch_ops.pairwise_flat_inner(w, self.mus)
if not with_variance:
return mean
K_mms = self._K_mms()
sigma_ls = _kron_tril(self.sigma_ls)
variances = []
sigmas = ops.tt_tt_matmul(sigma_ls, ops.transpose(sigma_ls))
variances = pairwise_quadratic_form(sigmas, w, w)
variances -= pairwise_quadratic_form(K_mms, w, w)
variances += self.cov.cov_0()[None, :]
return mean, variances
def elbo(self, w, y):
'''Evidence lower bound.
Args:
w: interpolation vector for the current batch.
y: target values for the current batch.
'''
l = tf.cast(tf.shape(y)[0], tf.float64) # batch size
N = tf.cast(self.N, dtype=tf.float64)
y = tf.reshape(y, [-1])
mu = self.gp.mu
sigma_l = _kron_tril(self.gp.sigma_l)
sigma = ops.tt_tt_matmul(sigma_l, ops.transpose(sigma_l))
sigma_n = self.gp.cov.noise_variance()
K_mm = self.gp.K_mm()
tilde_K_ii = l * self.gp.cov.cov_0()
tilde_K_ii -= tf.reduce_sum(ops.tt_tt_flat_inner(w,
ops.tt_tt_matmul(K_mm, w)))
elbo = 0
elbo -= tf.reduce_sum(tf.square(y - ops.tt_tt_flat_inner(w, mu)))
elbo -= tilde_K_ii
# TODO: wtf?
# elbo -= ops.tt_tt_flat_inner(w, ops.tt_tt_matmul(sigma, w))
elbo -= tf.reduce_sum(ops.tt_tt_flat_inner(w, ops.tt_tt_matmul(sigma, w)))
elbo /= 2 * sigma_n**2 * l
elbo += self.gp.complexity_penalty() / N
# TODO: wtf?
# elbo -= tf.log(tf.abs(sigma_n))
return -elbo[0]