def argmax_crf1d(cost, xs):
"""Computes a state that maximizes a joint probability of the given CRF.
Args:
cost (Variable): A :math:`K \\times K` matrix which holds transition
cost between two labels, where :math:`K` is the number of labels.
xs (list of Variable): Input vector for each label.
``len(xs)`` denotes the length of the sequence,
and each :class:`~chainer.Variable` holds a :math:`B \\times K`
matrix, where :math:`B` is mini-batch size, :math:`K` is the number
of labels.
Note that :math:`B`\\ s in all the variables are not necessary
the same, i.e., it accepts the input sequences with different
lengths.
Returns:
tuple: A tuple of :class:`~chainer.Variable` object ``s`` and a
:class:`list` ``ps``.
The shape of ``s`` is ``(B,)``, where ``B`` is the mini-batch size.
i-th element of ``s``, ``s[i]``, represents log-likelihood of i-th
data.
``ps`` is a list of :class:`numpy.ndarray` or
:class:`cupy.ndarray`, and denotes the state that maximizes the
point probability.
``len(ps)`` is equal to ``len(xs)``, and shape of each ``ps[i]`` is
the mini-batch size of the corresponding ``xs[i]``. That means,
``ps[i].shape == xs[i].shape[0:1]``.
"""
alpha = xs[0]
alphas = []
max_inds = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
else:
alphas.append(None)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
scores = b_alpha + b_cost
max_ind = minmax.argmax(scores, axis=1)
max_inds.append(max_ind)
alpha = minmax.max(scores, axis=1) + x
inds = minmax.argmax(alpha, axis=1)
path = [inds.data]
for m, a in zip(max_inds[::-1], alphas[::-1]):
inds = select_item.select_item(m, inds)
if a is not None:
inds = concat.concat([inds, minmax.argmax(a, axis=1)], axis=0)
path.append(inds.data)
path.reverse()
score = minmax.max(alpha, axis=1)
for a in alphas[::-1]:
if a is None:
continue
score = concat.concat([score, minmax.max(a, axis=1)], axis=0)
return score, path
def argmax_crf1d(cost, xs):
"""Computes a state that maximizes a joint probability of the given CRF.
Args:
cost (Variable): A :math:`K \\times K` matrix which holds transition
cost between two labels, where :math:`K` is the number of labels.
xs (list of Variable): Input vector for each label.
``len(xs)`` denotes the length of the sequence,
and each :class:`~chainer.Variable` holds a :math:`B \\times K`
matrix, where :math:`B` is mini-batch size, :math:`K` is the number
of labels.
Note that :math:`B` s in all the variables are not necessary
the same, i.e., it accepts the input sequences with different
lengths.
Returns:
tuple: A tuple of :class:`~chainer.Variable` object ``s`` and a
:class:`list` ``ps``.
The shape of ``s`` is ``(B,)``, where ``B`` is the mini-batch size.
i-th element of ``s``, ``s[i]``, represents log-likelihood of i-th
data.
``ps`` is a list of :class:`numpy.ndarray` or
:class:`cupy.ndarray`, and denotes the state that maximizes the
point probability.
``len(ps)`` is equal to ``len(xs)``, and shape of each ``ps[i]`` is
the mini-batch size of the corresponding ``xs[i]``. That means,
``ps[i].shape == xs[i].shape[0:1]``.
"""
alpha = xs[0]
alphas = []
max_inds = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
else:
alphas.append(None)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
scores = b_alpha + b_cost
max_ind = minmax.argmax(scores, axis=1)
max_inds.append(max_ind)
alpha = minmax.max(scores, axis=1) + x
inds = minmax.argmax(alpha, axis=1)
path = [inds.data]
for m, a in zip(max_inds[::-1], alphas[::-1]):
inds = select_item.select_item(m, inds)
if a is not None:
inds = concat.concat([inds, minmax.argmax(a, axis=1)], axis=0)
path.append(inds.data)
path.reverse()
score = minmax.max(alpha, axis=1)
for a in alphas[::-1]:
if a is None:
continue
score = concat.concat([score, minmax.max(a, axis=1)], axis=0)
return score, path
def argmax_crf1d(cost, xs):
alpha = xs[0]
alphas = []
max_inds = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
else:
alphas.append(None)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
scores = b_alpha + b_cost
max_ind = minmax.argmax(scores, axis=1)
max_inds.append(max_ind)
alpha = minmax.max(scores, axis=1) + x
inds = minmax.argmax(alpha, axis=1)
path = [inds.data]
for m, a in zip(max_inds[::-1], alphas[::-1]):
inds = select_item.select_item(m, inds)
if a is not None:
inds = concat.concat([inds, minmax.argmax(a, axis=1)], axis=0)
path.append(inds.data)
path.reverse()
score = minmax.max(alpha, axis=1)
for a in alphas[::-1]:
if a is None:
continue
score = concat.concat([score, minmax.max(a, axis=1)], axis=0)
return score, path
def argmax_crf1d(cost, xs):
alpha = xs[0]
alphas = []
max_inds = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
else:
alphas.append(None)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
scores = b_alpha + b_cost
max_ind = minmax.argmax(scores, axis=1)
max_inds.append(max_ind)
alpha = minmax.max(scores, axis=1) + x
inds = minmax.argmax(alpha, axis=1)
path = [inds.data]
for m, a in zip(max_inds[::-1], alphas[::-1]):
inds = select_item.select_item(m, inds)
if a is not None:
inds = concat.concat([inds, minmax.argmax(a, axis=1)], axis=0)
path.append(inds.data)
path.reverse()
score = minmax.max(alpha, axis=1)
for a in alphas[::-1]:
if a is None:
continue
score = concat.concat([score, minmax.max(a, axis=1)], axis=0)
return score, path
def crf1d(cost, xs, ys):
"""Calculates negative log-likelihood of linear-chain CRF.
It takes a transition cost matrix, a sequence of costs, and a sequence of
labels. Let :math:`c_{st}` be a transition cost from a label :math:`s` to
a label :math:`t`, :math:`x_{it}` be a cost of a label :math:`t` at
position :math:`i`, and :math:`y_i` be an expected label at position
:math:`i`. The negative log-likelihood of linear-chain CRF is defined as
.. math::
L = -\\left( \\sum_{i=1}^l x_{iy_i} + \\
\\sum_{i=1}^{l-1} c_{y_i y_{i+1}} - {\\log(Z)} \\right) ,
where :math:`l` is the length of the input sequence and :math:`Z` is the
normalizing constant called partition function.
Args:
cost (Variable): A :math:`K \\times K` matrix which holds transition
cost between two labels, where :math:`K` is the number of labels.
xs (list of Variable): Input feature vector for each label. Each
:class:`~chainer.Variable` holds a :math:`B \\times K`
matrix, where :math:`B` is mini-batch size, :math:`K` is the number
of labels.
ys (list of Variable): Expected output labels. Each
:class:`~chainer.Variable` holds a :math:`B` integer vector.
Returns:
~chainer.Variable: A variable holding the average negative
log-likelihood of the input sequences.
.. note::
See detail in the original paper: `Conditional Random Fields:
Probabilistic Models for Segmenting and Labeling Sequence Data
<http://repository.upenn.edu/cis_papers/159/>`_.
"""
assert xs[0].data.shape[1] == cost.data.shape[0]
n_label = cost.data.shape[0]
n_batch = xs[0].data.shape[0]
alpha = xs[0]
for x in xs[1:]:
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
alpha = logsumexp.logsumexp(b_alpha + b_cost, axis=1) + x
logz = logsumexp.logsumexp(alpha, axis=1)
score = 0
cost = reshape.reshape(cost, (cost.data.size, 1))
for y1, y2 in zip(ys[:-1], ys[1:]):
score += reshape.reshape(
embed_id.embed_id(y1 * n_label + y2, cost), (n_batch,))
for x, y in zip(xs, ys):
score += select_item.select_item(x, y)
return _sum.sum(logz - score) / n_batch
def argmax_crf1d(cost, xs):
alpha = xs[0]
max_inds = []
for x in xs[1:]:
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
scores = b_alpha + b_cost
max_ind = minmax.argmax(scores, axis=1)
max_inds.append(max_ind)
alpha = minmax.max(scores, axis=1) + x
inds = minmax.argmax(alpha, axis=1)
path = [inds.data]
for m in reversed(max_inds):
inds = select_item.select_item(m, inds)
path.append(inds.data)
path.reverse()
return minmax.max(alpha, axis=1), path
def crf1d(cost, xs, ys, reduce='mean'):
"""Calculates negative log-likelihood of linear-chain CRF.
It takes a transition cost matrix, a sequence of costs, and a sequence of
labels. Let :math:`c_{st}` be a transition cost from a label :math:`s` to
a label :math:`t`, :math:`x_{it}` be a cost of a label :math:`t` at
position :math:`i`, and :math:`y_i` be an expected label at position
:math:`i`. The negative log-likelihood of linear-chain CRF is defined as
.. math::
L = -\\left( \\sum_{i=1}^l x_{iy_i} + \\
\\sum_{i=1}^{l-1} c_{y_i y_{i+1}} - {\\log(Z)} \\right) ,
where :math:`l` is the length of the input sequence and :math:`Z` is the
normalizing constant called partition function.
.. note::
When you want to calculate the negative log-likelihood of sequences
which have different lengths, sort the sequences in descending order of
lengths and transpose the sequences.
For example, you have three input sequences:
>>> a1 = a2 = a3 = a4 = np.random.uniform(-1, 1, 3).astype(np.float32)
>>> b1 = b2 = b3 = np.random.uniform(-1, 1, 3).astype(np.float32)
>>> c1 = c2 = np.random.uniform(-1, 1, 3).astype(np.float32)
>>> a = [a1, a2, a3, a4]
>>> b = [b1, b2, b3]
>>> c = [c1, c2]
where ``a1`` and all other variables are arrays with ``(K,)`` shape.
Make a transpose of the sequences:
>>> x1 = np.stack([a1, b1, c1])
>>> x2 = np.stack([a2, b2, c2])
>>> x3 = np.stack([a3, b3])
>>> x4 = np.stack([a4])
and make a list of the arrays:
>>> xs = [x1, x2, x3, x4]
You need to make label sequences in the same fashion.
And then, call the function:
>>> cost = chainer.Variable(
... np.random.uniform(-1, 1, (3, 3)).astype(np.float32))
>>> ys = [np.zeros(x.shape[0:1], dtype=np.int32) for x in xs]
>>> loss = F.crf1d(cost, xs, ys)
It calculates mean of the negative log-likelihood of the three
sequences.
The output is a variable whose value depends on the value of
the option ``reduce``. If it is ``'no'``, it holds the elementwise
loss values. If it is ``'mean'``, it holds mean of the loss values.
Args:
cost (Variable): A :math:`K \\times K` matrix which holds transition
cost between two labels, where :math:`K` is the number of labels.
xs (list of Variable): Input vector for each label.
``len(xs)`` denotes the length of the sequence,
and each :class:`~chainer.Variable` holds a :math:`B \\times K`
matrix, where :math:`B` is mini-batch size, :math:`K` is the number
of labels.
Note that :math:`B`\\ s in all the variables are not necessary
the same, i.e., it accepts the input sequences with different
lengths.
ys (list of Variable): Expected output labels. It needs to have the
same length as ``xs``. Each :class:`~chainer.Variable` holds a
:math:`B` integer vector.
When ``x`` in ``xs`` has the different :math:`B`, correspoding
``y`` has the same :math:`B`. In other words, ``ys`` must satisfy
``ys[i].shape == xs[i].shape[0:1]`` for all ``i``.
reduce (str): Reduction option. Its value must be either
``'mean'`` or ``'no'``. Otherwise, :class:`ValueError` is raised.
Returns:
~chainer.Variable: A variable holding the average negative
log-likelihood of the input sequences.
.. note::
See detail in the original paper: `Conditional Random Fields:
Probabilistic Models for Segmenting and Labeling Sequence Data
<https://repository.upenn.edu/cis_papers/159/>`_.
"""
if reduce not in ('mean', 'no'):
raise ValueError(
"only 'mean' and 'no' are valid for 'reduce', but '%s' is "
'given' % reduce)
assert xs[0].shape[1] == cost.shape[0]
n_label = cost.shape[0]
n_batch = xs[0].shape[0]
alpha = xs[0]
alphas = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
alpha = logsumexp.logsumexp(b_alpha + b_cost, axis=1) + x
if len(alphas) > 0:
alphas.append(alpha)
alpha = concat.concat(alphas[::-1], axis=0)
logz = logsumexp.logsumexp(alpha, axis=1)
cost = reshape.reshape(cost, (cost.size, 1))
score = select_item.select_item(xs[0], ys[0])
scores = []
for x, y, y_prev in zip(xs[1:], ys[1:], ys[:-1]):
batch = x.shape[0]
if score.shape[0] > batch:
y_prev, _ = split_axis.split_axis(y_prev, [batch], axis=0)
score, score_rest = split_axis.split_axis(score, [batch], axis=0)
scores.append(score_rest)
score += (select_item.select_item(x, y) + reshape.reshape(
embed_id.embed_id(y_prev * n_label + y, cost), (batch,)))
if len(scores) > 0:
scores.append(score)
score = concat.concat(scores[::-1], axis=0)
loss = logz - score
if reduce == 'mean':
return _sum.sum(loss) / n_batch
else:
return loss
def crf1d(cost, xs, ys, reduce='mean'):
"""Calculates negative log-likelihood of linear-chain CRF.
It takes a transition cost matrix, a sequence of costs, and a sequence of
labels. Let :math:`c_{st}` be a transition cost from a label :math:`s` to
a label :math:`t`, :math:`x_{it}` be a cost of a label :math:`t` at
position :math:`i`, and :math:`y_i` be an expected label at position
:math:`i`. The negative log-likelihood of linear-chain CRF is defined as
.. math::
L = -\\left( \\sum_{i=1}^l x_{iy_i} + \\
\\sum_{i=1}^{l-1} c_{y_i y_{i+1}} - {\\log(Z)} \\right) ,
where :math:`l` is the length of the input sequence and :math:`Z` is the
normalizing constant called partition function.
.. note::
When you want to calculate the negative log-likelihood of sequences
which have different lengths, sort the sequences in descending order of
lengths and transpose the sequences.
For example, you have three input sequences:
>>> a1 = a2 = a3 = a4 = np.random.uniform(-1, 1, 3).astype('f')
>>> b1 = b2 = b3 = np.random.uniform(-1, 1, 3).astype('f')
>>> c1 = c2 = np.random.uniform(-1, 1, 3).astype('f')
>>> a = [a1, a2, a3, a4]
>>> b = [b1, b2, b3]
>>> c = [c1, c2]
where ``a1`` and all other variables are arrays with ``(K,)`` shape.
Make a transpose of the sequences:
>>> x1 = np.stack([a1, b1, c1])
>>> x2 = np.stack([a2, b2, c2])
>>> x3 = np.stack([a3, b3])
>>> x4 = np.stack([a4])
and make a list of the arrays:
>>> xs = [x1, x2, x3, x4]
You need to make label sequences in the same fashion.
And then, call the function:
>>> cost = chainer.Variable(
... np.random.uniform(-1, 1, (3, 3)).astype('f'))
>>> ys = [np.zeros(x.shape[0:1], dtype='i') for x in xs]
>>> loss = F.crf1d(cost, xs, ys)
It calculates mean of the negative log-likelihood of the three
sequences.
The output is a variable whose value depends on the value of
the option ``reduce``. If it is ``'no'``, it holds the elementwise
loss values. If it is ``'mean'``, it holds mean of the loss values.
Args:
cost (Variable): A :math:`K \\times K` matrix which holds transition
cost between two labels, where :math:`K` is the number of labels.
xs (list of Variable): Input vector for each label.
``len(xs)`` denotes the length of the sequence,
and each :class:`~chainer.Variable` holds a :math:`B \\times K`
matrix, where :math:`B` is mini-batch size, :math:`K` is the number
of labels.
Note that :math:`B` s in all the variables are not necessary
the same, i.e., it accepts the input sequences with different
lengths.
ys (list of Variable): Expected output labels. It needs to have the
same length as ``xs``. Each :class:`~chainer.Variable` holds a
:math:`B` integer vector.
When ``x`` in ``xs`` has the different :math:`B`, correspoding
``y`` has the same :math:`B`. In other words, ``ys`` must satisfy
``ys[i].shape == xs[i].shape[0:1]`` for all ``i``.
reduce (str): Reduction option. Its value must be either
``'mean'`` or ``'no'``. Otherwise, :class:`ValueError` is raised.
Returns:
~chainer.Variable: A variable holding the average negative
log-likelihood of the input sequences.
.. note::
See detail in the original paper: `Conditional Random Fields:
Probabilistic Models for Segmenting and Labeling Sequence Data
<http://repository.upenn.edu/cis_papers/159/>`_.
"""
if reduce not in ('mean', 'no'):
raise ValueError(
"only 'mean' and 'no' are valid for 'reduce', but '%s' is "
'given' % reduce)
assert xs[0].shape[1] == cost.shape[0]
n_label = cost.shape[0]
n_batch = xs[0].shape[0]
alpha = xs[0]
alphas = []
for x in xs[1:]:
batch = x.shape[0]
if alpha.shape[0] > batch:
alpha, alpha_rest = split_axis.split_axis(alpha, [batch], axis=0)
alphas.append(alpha_rest)
b_alpha, b_cost = broadcast.broadcast(alpha[..., None], cost)
alpha = logsumexp.logsumexp(b_alpha + b_cost, axis=1) + x
if len(alphas) > 0:
alphas.append(alpha)
alpha = concat.concat(alphas[::-1], axis=0)
logz = logsumexp.logsumexp(alpha, axis=1)
cost = reshape.reshape(cost, (cost.size, 1))
score = select_item.select_item(xs[0], ys[0])
scores = []
for x, y, y_prev in zip(xs[1:], ys[1:], ys[:-1]):
batch = x.shape[0]
if score.shape[0] > batch:
y_prev, _ = split_axis.split_axis(y_prev, [batch], axis=0)
score, score_rest = split_axis.split_axis(score, [batch], axis=0)
scores.append(score_rest)
score += (
select_item.select_item(x, y) +
reshape.reshape(embed_id.embed_id(y_prev * n_label + y, cost),
(batch, )))
if len(scores) > 0:
scores.append(score)
score = concat.concat(scores[::-1], axis=0)
loss = logz - score
if reduce == 'mean':
return _sum.sum(loss) / n_batch
else:
return loss