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# Copyright 2016 The TensorFlow Authors. All Rights Reserved.
#
# Licensed under the Apache License, Version 2.0 (the "License");
# you may not use this file except in compliance with the License.
# You may obtain a copy of the License at
#
# http://www.apache.org/licenses/LICENSE-2.0
#
# Unless required by applicable law or agreed to in writing, software
# distributed under the License is distributed on an "AS IS" BASIS,
# WITHOUT WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
# See the License for the specific language governing permissions and
# limitations under the License.
# ==============================================================================
"""Ops for matrix factorization."""
from __future__ import absolute_import
from __future__ import division
from __future__ import print_function
import collections
import numbers
from six.moves import xrange # pylint: disable=redefined-builtin
from tensorflow.contrib.factorization.python.ops import gen_factorization_ops
from tensorflow.contrib.util import loader
from tensorflow.python.framework import constant_op
from tensorflow.python.framework import dtypes
from tensorflow.python.framework import ops
from tensorflow.python.framework import sparse_tensor
from tensorflow.python.ops import array_ops
from tensorflow.python.ops import check_ops
from tensorflow.python.ops import control_flow_ops
from tensorflow.python.ops import data_flow_ops
from tensorflow.python.ops import embedding_ops
from tensorflow.python.ops import linalg_ops
from tensorflow.python.ops import math_ops
from tensorflow.python.ops import random_ops
from tensorflow.python.ops import sparse_ops
from tensorflow.python.ops import state_ops
from tensorflow.python.ops import variable_scope
from tensorflow.python.ops import variables
from tensorflow.python.platform import resource_loader
_factorization_ops = loader.load_op_library(
resource_loader.get_path_to_datafile("_factorization_ops.so"))
class WALSModel(object):
r"""A model for Weighted Alternating Least Squares matrix factorization.
It minimizes the following loss function over U, V:
$$
\|\sqrt W \odot (A - U V^T)\|_F^2 + \lambda (\|U\|_F^2 + \|V\|_F^2)
$$
where,
A: input matrix,
W: weight matrix. Note that the (element-wise) square root of the weights
is used in the objective function.
U, V: row_factors and column_factors matrices,
\\(\lambda)\\: regularization.
Also we assume that W is of the following special form:
\\( W_{ij} = W_0 + R_i * C_j \\) if \\(A_{ij} \ne 0\\),
\\(W_{ij} = W_0\\) otherwise.
where,
\\(W_0\\): unobserved_weight,
\\(R_i\\): row_weights,
\\(C_j\\): col_weights.
Note that the current implementation supports two operation modes: The default
mode is for the condition where row_factors and col_factors can individually
fit into the memory of each worker and these will be cached. When this
condition can't be met, setting use_factors_weights_cache to False allows the
larger problem sizes with slight performance penalty as this will avoid
creating the worker caches and instead the relevant weight and factor values
are looked up from parameter servers at each step.
Loss computation: The loss can be computed efficiently by decomposing it into
a sparse term and a Gramian term, see wals.md.
The loss is returned by the update_{col, row}_factors(sp_input), and is
normalized as follows:
_, _, unregularized_loss, regularization, sum_weights =
update_row_factors(sp_input)
if sp_input contains the rows \\({A_i, i \in I}\\), and the input matrix A
has n total rows, then the minibatch loss = unregularized_loss +
regularization is
$$
(\|\sqrt W_I \odot (A_I - U_I V^T)\|_F^2 + \lambda \|U_I\|_F^2) * n / |I| +
\lambda \|V\|_F^2
$$
The sum_weights tensor contains the normalized sum of weights
\\(sum(W_I) * n / |I|\\).
A typical usage example (pseudocode):
with tf.Graph().as_default():
# Set up the model object.
model = tf.contrib.factorization.WALSModel(....)
# To be run only once as part of session initialization. In distributed
# training setting, this should only be run by the chief trainer and all
# other trainers should block until this is done.
model_init_op = model.initialize_op
# To be run once per worker after session is available, prior to
# the prep_gramian_op for row(column) can be run.
worker_init_op = model.worker_init
# To be run once per iteration sweep before the row(column) update
# initialize ops can be run. Note that in the distributed training
# situations, this should only be run by the chief trainer. All other
# trainers need to block until this is done.
row_update_prep_gramian_op = model.row_update_prep_gramian_op
col_update_prep_gramian_op = model.col_update_prep_gramian_op
# To be run once per worker per iteration sweep. Must be run before
# any actual update ops can be run.
init_row_update_op = model.initialize_row_update_op
init_col_update_op = model.initialize_col_update_op
# Ops to update row(column). This can either take the entire sparse
# tensor or slices of sparse tensor. For distributed trainer, each
# trainer handles just part of the matrix.
_, row_update_op, unreg_row_loss, row_reg, _ = model.update_row_factors(
sp_input=matrix_slices_from_queue_for_worker_shard)
row_loss = unreg_row_loss + row_reg
_, col_update_op, unreg_col_loss, col_reg, _ = model.update_col_factors(
sp_input=transposed_matrix_slices_from_queue_for_worker_shard,
transpose_input=True)
col_loss = unreg_col_loss + col_reg
...
# model_init_op is passed to Supervisor. Chief trainer runs it. Other
# trainers wait.
sv = tf.compat.v1.train.Supervisor(is_chief=is_chief,
...,
init_op=tf.group(..., model_init_op, ...), ...)
...
with sv.managed_session(...) as sess:
# All workers/trainers run it after session becomes available.
worker_init_op.run(session=sess)
...
while i in iterations:
# All trainers need to sync up here.
while not_all_ready:
wait
# Row update sweep.
if is_chief:
row_update_prep_gramian_op.run(session=sess)
else:
wait_for_chief
# All workers run upate initialization.
init_row_update_op.run(session=sess)
# Go through the matrix.
reset_matrix_slices_queue_for_worker_shard
while_matrix_slices:
row_update_op.run(session=sess)
# All trainers need to sync up here.
while not_all_ready:
wait
# Column update sweep.
if is_chief:
col_update_prep_gramian_op.run(session=sess)
else:
wait_for_chief
# All workers run upate initialization.
init_col_update_op.run(session=sess)
# Go through the matrix.
reset_transposed_matrix_slices_queue_for_worker_shard
while_transposed_matrix_slices:
col_update_op.run(session=sess)
"""
def __init__(self,
input_rows,
input_cols,
n_components,
unobserved_weight=0.1,
regularization=None,
row_init="random",
col_init="random",
num_row_shards=1,
num_col_shards=1,
row_weights=1,
col_weights=1,
use_factors_weights_cache=True,
use_gramian_cache=True,
use_scoped_vars=False):
"""Creates model for WALS matrix factorization.
Args:
input_rows: total number of rows for input matrix.
input_cols: total number of cols for input matrix.
n_components: number of dimensions to use for the factors.
unobserved_weight: weight given to unobserved entries of matrix.
regularization: weight of L2 regularization term. If None, no
regularization is done.
row_init: initializer for row factor. Can be a tensor or numpy constant.
If set to "random", the value is initialized randomly.
col_init: initializer for column factor. See row_init for details.
num_row_shards: number of shards to use for row factors.
num_col_shards: number of shards to use for column factors.
row_weights: Must be in one of the following three formats: None, a list
of lists of non-negative real numbers (or equivalent iterables) or a
single non-negative real number.
- When set to None, w_ij = unobserved_weight, which simplifies to ALS.
Note that col_weights must also be set to "None" in this case.
- If it is a list of lists of non-negative real numbers, it needs to be
in the form of [[w_0, w_1, ...], [w_k, ... ], [...]], with the number of
inner lists matching the number of row factor shards and the elements in
each inner list are the weights for the rows of the corresponding row
factor shard. In this case, w_ij = unobserved_weight +
row_weights[i] * col_weights[j].
- If this is a single non-negative real number, this value is used for
all row weights and \\(w_ij\\) = unobserved_weight + row_weights *
col_weights[j].
Note that it is allowed to have row_weights as a list while col_weights
a single number or vice versa.
col_weights: See row_weights.
use_factors_weights_cache: When True, the factors and weights will be
cached on the workers before the updates start. Defaults to True. Note
that the weights cache is initialized through `worker_init`, and the
row/col factors cache is initialized through
`initialize_{col/row}_update_op`. In the case where the weights are
computed outside and set before the training iterations start, it is
important to ensure the `worker_init` op is run afterwards for the
weights cache to take effect.
use_gramian_cache: When True, the Gramians will be cached on the workers
before the updates start. Defaults to True.
use_scoped_vars: When True, the factor and weight vars will also be nested
in a tf.name_scope.
"""
self._input_rows = input_rows
self._input_cols = input_cols
self._num_row_shards = num_row_shards
self._num_col_shards = num_col_shards
self._n_components = n_components
self._unobserved_weight = unobserved_weight
self._regularization = regularization
self._regularization_matrix = (
regularization * linalg_ops.eye(self._n_components)
if regularization is not None else None)
assert (row_weights is None) == (col_weights is None)
self._use_factors_weights_cache = use_factors_weights_cache
self._use_gramian_cache = use_gramian_cache
if use_scoped_vars:
with ops.name_scope("row_weights"):
self._row_weights = WALSModel._create_weights(
row_weights, self._input_rows, self._num_row_shards, "row_weights")
with ops.name_scope("col_weights"):
self._col_weights = WALSModel._create_weights(
col_weights, self._input_cols, self._num_col_shards, "col_weights")
with ops.name_scope("row_factors"):
self._row_factors = self._create_factors(
self._input_rows, self._n_components, self._num_row_shards,
row_init, "row_factors")
with ops.name_scope("col_factors"):
self._col_factors = self._create_factors(
self._input_cols, self._n_components, self._num_col_shards,
col_init, "col_factors")
else:
self._row_weights = WALSModel._create_weights(
row_weights, self._input_rows, self._num_row_shards, "row_weights")
self._col_weights = WALSModel._create_weights(
col_weights, self._input_cols, self._num_col_shards, "col_weights")
self._row_factors = self._create_factors(
self._input_rows, self._n_components, self._num_row_shards, row_init,
"row_factors")
self._col_factors = self._create_factors(
self._input_cols, self._n_components, self._num_col_shards, col_init,
"col_factors")
self._row_gramian = self._create_gramian(self._n_components, "row_gramian")
self._col_gramian = self._create_gramian(self._n_components, "col_gramian")
with ops.name_scope("row_prepare_gramian"):
self._row_update_prep_gramian = self._prepare_gramian(
self._col_factors, self._col_gramian)
with ops.name_scope("col_prepare_gramian"):
self._col_update_prep_gramian = self._prepare_gramian(
self._row_factors, self._row_gramian)
with ops.name_scope("transient_vars"):
self._create_transient_vars()
@property
def row_factors(self):
"""Returns a list of tensors corresponding to row factor shards."""
return self._row_factors
@property
def col_factors(self):
"""Returns a list of tensors corresponding to column factor shards."""
return self._col_factors
@property
def row_weights(self):
"""Returns a list of tensors corresponding to row weight shards."""
return self._row_weights
@property
def col_weights(self):
"""Returns a list of tensors corresponding to col weight shards."""
return self._col_weights
@property
def initialize_op(self):
"""Returns an op for initializing tensorflow variables."""
all_vars = self._row_factors + self._col_factors
all_vars.extend([self._row_gramian, self._col_gramian])
if self._row_weights is not None:
assert self._col_weights is not None
all_vars.extend(self._row_weights + self._col_weights)
return variables.variables_initializer(all_vars)
@classmethod
def _shard_sizes(cls, dims, num_shards):
"""Helper function to split dims values into num_shards."""
shard_size, residual = divmod(dims, num_shards)
return [shard_size + 1] * residual + [shard_size] * (num_shards - residual)
@classmethod
def _create_factors(cls, rows, cols, num_shards, init, name):
"""Helper function to create row and column factors."""
if callable(init):
init = init()
if isinstance(init, list):
assert len(init) == num_shards
elif isinstance(init, str) and init == "random":
pass
elif num_shards == 1:
init = [init]
sharded_matrix = []
sizes = cls._shard_sizes(rows, num_shards)
assert len(sizes) == num_shards
def make_initializer(i, size):
def initializer():
if init == "random":
return random_ops.random_normal([size, cols])
else:
return init[i]
return initializer
for i, size in enumerate(sizes):
var_name = "%s_shard_%d" % (name, i)
var_init = make_initializer(i, size)
sharded_matrix.append(
variable_scope.variable(
var_init, dtype=dtypes.float32, name=var_name))
return sharded_matrix
@classmethod
def _create_weights(cls, wt_init, num_wts, num_shards, name):
"""Helper function to create sharded weight vector.
Args:
wt_init: init value for the weight. If None, weights are not created. This
can be one of the None, a list of non-negative real numbers or a single
non-negative real number (or equivalent iterables).
num_wts: total size of all the weight shards
num_shards: number of shards for the weights
name: name for the new Variables.
Returns:
A list of weight shard Tensors.
Raises:
ValueError: If wt_init is not the right format.
"""
if wt_init is None:
return None
init_mode = "list"
if isinstance(wt_init, collections.Iterable):
if num_shards == 1 and len(wt_init) == num_wts:
wt_init = [wt_init]
assert len(wt_init) == num_shards
elif isinstance(wt_init, numbers.Real) and wt_init >= 0:
init_mode = "scalar"
else:
raise ValueError(
"Invalid weight initialization argument. Must be one of these: "
"None, a real non-negative real number, or a list of lists of "
"non-negative real numbers (or equivalent iterables) corresponding "
"to sharded factors.")
sizes = cls._shard_sizes(num_wts, num_shards)
assert len(sizes) == num_shards
def make_wt_initializer(i, size):
def initializer():
if init_mode == "scalar":
return wt_init * array_ops.ones([size])
else:
return wt_init[i]
return initializer
sharded_weight = []
for i, size in enumerate(sizes):
var_name = "%s_shard_%d" % (name, i)
var_init = make_wt_initializer(i, size)
sharded_weight.append(
variable_scope.variable(
var_init, dtype=dtypes.float32, name=var_name))
return sharded_weight
@staticmethod
def _create_gramian(n_components, name):
"""Helper function to create the gramian variable.
Args:
n_components: number of dimensions of the factors from which the gramian
will be calculated.
name: name for the new Variables.
Returns:
A gramian Tensor with shape of [n_components, n_components].
"""
return variable_scope.variable(
array_ops.zeros([n_components, n_components]),
dtype=dtypes.float32,
name=name)
@staticmethod
def _transient_var(name):
"""Helper function to create a Variable."""
return variable_scope.variable(
1.0,
trainable=False,
collections=[ops.GraphKeys.LOCAL_VARIABLES],
validate_shape=False,
name=name)
def _prepare_gramian(self, factors, gramian):
"""Helper function to create ops to prepare/calculate gramian.
Args:
factors: Variable or list of Variable representing (sharded) factors.
Used to compute the updated corresponding gramian value.
gramian: Variable storing the gramian calculated from the factors.
Returns:
An op that updates the gramian with the calculated value from the factors.
"""
partial_gramians = []
for f in factors:
with ops.colocate_with(f):
partial_gramians.append(math_ops.matmul(f, f, transpose_a=True))
with ops.colocate_with(gramian):
prep_gramian = state_ops.assign(gramian,
math_ops.add_n(partial_gramians)).op
return prep_gramian
def _cached_copy(self, var, name, pass_through=False):
"""Helper function to create a worker cached copy of a Variable.
This assigns the var (either a single Variable or a list of Variables) to
local transient cache Variable(s). Note that if var is a list of Variables,
the assignment is done sequentially to minimize the memory overheads.
Also note that if pass_through is set to True, this does not create new
Variables but simply return the input back.
Args:
var: A Variable or a list of Variables to cache.
name: name of cached Variable.
pass_through: when set to True, this simply pass through the var back
through identity operator and does not actually creates a cache.
Returns:
Tuple consisting of following three entries:
cache: the new transient Variable or list of transient Variables
corresponding one-to-one with var.
cache_init: op to initialize the Variable or the list of Variables.
cache_reset: op to reset the Variable or the list of Variables to some
default value.
"""
if var is None:
return None, None, None
elif pass_through:
cache = var
cache_init = control_flow_ops.no_op()
cache_reset = control_flow_ops.no_op()
elif isinstance(var, variables.Variable):
cache = WALSModel._transient_var(name=name)
with ops.colocate_with(cache):
cache_init = state_ops.assign(cache, var, validate_shape=False)
cache_reset = state_ops.assign(cache, 1.0, validate_shape=False)
else:
assert isinstance(var, list)
assert var
cache = [
WALSModel._transient_var(name="%s_shard_%d" % (name, i))
for i in xrange(len(var))
]
reset_ops = []
for i, c in enumerate(cache):
with ops.colocate_with(c):
if i == 0:
cache_init = state_ops.assign(c, var[i], validate_shape=False)
else:
with ops.control_dependencies([cache_init]):
cache_init = state_ops.assign(c, var[i], validate_shape=False)
reset_ops.append(state_ops.assign(c, 1.0, validate_shape=False))
cache_reset = control_flow_ops.group(*reset_ops)
return cache, cache_init, cache_reset
def _create_transient_vars(self):
"""Creates local cache of factors, weights and gramian for rows and columns.
Note that currently the caching strategy is as follows:
When initiating a row (resp. column) update:
- The column (resp. row) gramian is computed.
- Optionally, if use_gramian_cache is True, the column (resp. row) Gramian
is cached, while the row (resp. column) gramian is reset.
- Optionally, if use_factors_weights_cache is True, the column (resp. row)
factors and weights are cached, while the row (resp. column) factors and
weights are reset.
"""
(self._row_factors_cache, row_factors_cache_init,
row_factors_cache_reset) = self._cached_copy(
self._row_factors,
"row_factors_cache",
pass_through=not self._use_factors_weights_cache)
(self._col_factors_cache, col_factors_cache_init,
col_factors_cache_reset) = self._cached_copy(
self._col_factors,
"col_factors_cache",
pass_through=not self._use_factors_weights_cache)
(self._row_wt_cache, row_wt_cache_init, _) = self._cached_copy(
self._row_weights,
"row_wt_cache",
pass_through=not self._use_factors_weights_cache)
(self._col_wt_cache, col_wt_cache_init, _) = self._cached_copy(
self._col_weights,
"col_wt_cache",
pass_through=not self._use_factors_weights_cache)
(self._row_gramian_cache, row_gramian_cache_init,
row_gramian_cache_reset) = self._cached_copy(
self._row_gramian,
"row_gramian_cache",
pass_through=not self._use_gramian_cache)
(self._col_gramian_cache, col_gramian_cache_init,
col_gramian_cache_reset) = self._cached_copy(
self._col_gramian,
"col_gramian_cache",
pass_through=not self._use_gramian_cache)
self._row_updates_init = control_flow_ops.group(
col_factors_cache_init, row_factors_cache_reset, col_gramian_cache_init,
row_gramian_cache_reset)
self._col_updates_init = control_flow_ops.group(
row_factors_cache_init, col_factors_cache_reset, row_gramian_cache_init,
col_gramian_cache_reset)
if self._row_wt_cache is not None:
assert self._col_wt_cache is not None
self._worker_init = control_flow_ops.group(
row_wt_cache_init, col_wt_cache_init, name="worker_init")
else:
self._worker_init = control_flow_ops.no_op(name="worker_init")
@property
def worker_init(self):
"""Op to initialize worker state once before starting any updates.
Note that specifically this initializes the cache of the row and column
weights on workers when `use_factors_weights_cache` is True. In this case,
if these weights are being calculated and reset after the object is created,
it is important to ensure this ops is run afterwards so the cache reflects
the correct values.
"""
return self._worker_init
@property
def row_update_prep_gramian_op(self):
"""Op to form the gramian before starting row updates.
Must be run before initialize_row_update_op and should only be run by one
trainer (usually the chief) when doing distributed training.
Returns:
Op to form the gramian.
"""
return self._row_update_prep_gramian
@property
def col_update_prep_gramian_op(self):
"""Op to form the gramian before starting col updates.
Must be run before initialize_col_update_op and should only be run by one
trainer (usually the chief) when doing distributed training.
Returns:
Op to form the gramian.
"""
return self._col_update_prep_gramian
@property
def initialize_row_update_op(self):
"""Op to initialize worker state before starting row updates."""
return self._row_updates_init
@property
def initialize_col_update_op(self):
"""Op to initialize worker state before starting column updates."""
return self._col_updates_init
@staticmethod
def _get_sharding_func(size, num_shards):
"""Create sharding function for scatter update."""
def func(ids):
if num_shards == 1:
return None, ids
else:
ids_per_shard = size // num_shards
extras = size % num_shards
assignments = math_ops.maximum(ids // (ids_per_shard + 1),
(ids - extras) // ids_per_shard)
new_ids = array_ops.where(assignments < extras,
ids % (ids_per_shard + 1),
(ids - extras) % ids_per_shard)
return assignments, new_ids
return func
@classmethod
def scatter_update(cls, factor, indices, values, sharding_func, name=None):
"""Helper function for doing sharded scatter update."""
assert isinstance(factor, list)
if len(factor) == 1:
with ops.colocate_with(factor[0]):
# TODO(agarwal): assign instead of scatter update for full batch update.
return state_ops.scatter_update(
factor[0], indices, values, name=name).op
else:
num_shards = len(factor)
assignments, new_ids = sharding_func(indices)
assert assignments is not None
assignments = math_ops.cast(assignments, dtypes.int32)
sharded_ids = data_flow_ops.dynamic_partition(new_ids, assignments,
num_shards)
sharded_values = data_flow_ops.dynamic_partition(values, assignments,
num_shards)
updates = []
for i in xrange(num_shards):
updates.append(
state_ops.scatter_update(factor[i], sharded_ids[i], sharded_values[
i]))
return control_flow_ops.group(*updates, name=name)
def update_row_factors(self, sp_input=None, transpose_input=False):
r"""Updates the row factors.
Args:
sp_input: A SparseTensor representing a subset of rows of the full input
in any order. Please note that this SparseTensor must retain the
indexing as the original input.
transpose_input: If true, the input will be logically transposed and the
rows corresponding to the transposed input are updated.
Returns:
A tuple consisting of the following elements:
new_values: New values for the row factors.
update_op: An op that assigns the newly computed values to the row
factors.
unregularized_loss: A tensor (scalar) that contains the normalized
minibatch loss corresponding to sp_input, without the regularization
term. If sp_input contains the rows \\({A_{i, :}, i \in I}\\), and the
input matrix A has n total rows, then the unregularized loss is:
\\(\|\sqrt W_I \odot (A_I - U_I V^T)\|_F^2 * n / |I|\\)
The total loss is unregularized_loss + regularization.
regularization: A tensor (scalar) that contains the normalized
regularization term for the minibatch loss corresponding to sp_input.
If sp_input contains the rows \\({A_{i, :}, i \in I}\\), and the input
matrix A has n total rows, then the regularization term is:
\\(\lambda \|U_I\|_F^2) * n / |I| + \lambda \|V\|_F^2\\).
sum_weights: The sum of the weights W_I corresponding to sp_input,
normalized by a factor of \\(n / |I|\\). The root weighted squared
error is: \sqrt(unregularized_loss / sum_weights).
"""
return self._process_input_helper(
True, sp_input=sp_input, transpose_input=transpose_input)
def update_col_factors(self, sp_input=None, transpose_input=False):
r"""Updates the column factors.
Args:
sp_input: A SparseTensor representing a subset of columns of the full
input. Please refer to comments for update_row_factors for
restrictions.
transpose_input: If true, the input will be logically transposed and the
columns corresponding to the transposed input are updated.
Returns:
A tuple consisting of the following elements:
new_values: New values for the column factors.
update_op: An op that assigns the newly computed values to the column
factors.
unregularized_loss: A tensor (scalar) that contains the normalized
minibatch loss corresponding to sp_input, without the regularization
term. If sp_input contains the columns \\({A_{:, j}, j \in J}\\), and
the input matrix A has m total columns, then the unregularized loss is:
\\(\|\sqrt W_J \odot (A_J - U V_J^T)\|_F^2 * m / |I|\\)
The total loss is unregularized_loss + regularization.
regularization: A tensor (scalar) that contains the normalized
regularization term for the minibatch loss corresponding to sp_input.
If sp_input contains the columns \\({A_{:, j}, j \in J}\\), and the
input matrix A has m total columns, then the regularization term is:
\\(\lambda \|V_J\|_F^2) * m / |J| + \lambda \|U\|_F^2\\).
sum_weights: The sum of the weights W_J corresponding to sp_input,
normalized by a factor of \\(m / |J|\\). The root weighted squared
error is: \sqrt(unregularized_loss / sum_weights).
"""
return self._process_input_helper(
False, sp_input=sp_input, transpose_input=transpose_input)
def project_row_factors(self,
sp_input=None,
transpose_input=False,
projection_weights=None):
"""Projects the row factors.
This computes the row embedding \\(u_i\\) for an observed row \\(a_i\\) by
solving one iteration of the update equations.
Args:
sp_input: A SparseTensor representing a set of rows. Please note that the
column indices of this SparseTensor must match the model column feature
indexing while the row indices are ignored. The returned results will be
in the same ordering as the input rows.
transpose_input: If true, the input will be logically transposed and the
rows corresponding to the transposed input are projected.
projection_weights: The row weights to be used for the projection. If None
then 1.0 is used. This can be either a scaler or a rank-1 tensor with
the number of elements matching the number of rows to be projected.
Note that the column weights will be determined by the underlying WALS
model.
Returns:
Projected row factors.
"""
if projection_weights is None:
projection_weights = 1
return self._process_input_helper(
True,
sp_input=sp_input,
transpose_input=transpose_input,
row_weights=projection_weights)[0]
def project_col_factors(self,
sp_input=None,
transpose_input=False,
projection_weights=None):
"""Projects the column factors.
This computes the column embedding \\(v_j\\) for an observed column
\\(a_j\\) by solving one iteration of the update equations.
Args:
sp_input: A SparseTensor representing a set of columns. Please note that
the row indices of this SparseTensor must match the model row feature
indexing while the column indices are ignored. The returned results will
be in the same ordering as the input columns.
transpose_input: If true, the input will be logically transposed and the
columns corresponding to the transposed input are projected.
projection_weights: The column weights to be used for the projection. If
None then 1.0 is used. This can be either a scaler or a rank-1 tensor
with the number of elements matching the number of columns to be
projected. Note that the row weights will be determined by the
underlying WALS model.
Returns:
Projected column factors.
"""
if projection_weights is None:
projection_weights = 1
return self._process_input_helper(
False,
sp_input=sp_input,
transpose_input=transpose_input,
row_weights=projection_weights)[0]
def _process_input_helper(self,
update_row_factors,
sp_input=None,
transpose_input=False,
row_weights=None):
"""Creates the graph for processing a sparse slice of input.
Args:
update_row_factors: if True, update or project the row_factors, else
update or project the column factors.
sp_input: Please refer to comments for update_row_factors,
update_col_factors, project_row_factors, and project_col_factors for
restrictions.
transpose_input: If True, the input is logically transposed and then the
corresponding rows/columns of the transposed input are updated.
row_weights: If not None, this is the row/column weights to be used for
the update or projection. If None, use the corresponding weights from
the model. Note that the feature (column/row) weights will be
determined by the model. When not None, it can either be a scalar or
a rank-1 tensor with the same number of elements as the number of rows
of columns to be updated/projected.
Returns:
A tuple consisting of the following elements:
new_values: New values for the row/column factors.
update_op: An op that assigns the newly computed values to the row/column
factors.
unregularized_loss: A tensor (scalar) that contains the normalized
minibatch loss corresponding to sp_input, without the regularization
term. Add the regularization term below to yield the loss.
regularization: A tensor (scalar) that contains the normalized
regularization term for the minibatch loss corresponding to sp_input.
sum_weights: The sum of the weights corresponding to sp_input. This
can be used with unregularized loss to calculate the root weighted
squared error.
"""
assert isinstance(sp_input, sparse_tensor.SparseTensor)
if update_row_factors:
left = self._row_factors
right_factors = self._col_factors_cache
row_wt = self._row_wt_cache
col_wt = self._col_wt_cache
total_rows = self._input_rows
total_cols = self._input_cols
sharding_func = WALSModel._get_sharding_func(self._input_rows,
self._num_row_shards)
gramian = self._col_gramian_cache
else:
left = self._col_factors
right_factors = self._row_factors_cache
row_wt = self._col_wt_cache
col_wt = self._row_wt_cache
total_rows = self._input_cols
total_cols = self._input_rows
sharding_func = WALSModel._get_sharding_func(self._input_cols,
self._num_col_shards)
gramian = self._row_gramian_cache
transpose_input = not transpose_input
# Note that the row indices of sp_input are based on the original full input
# Here we reindex the rows and give them contiguous ids starting at 0.
# We use tf.unique to achieve this reindexing. Note that this is done so
# that the downstream kernel can assume that the input is "dense" along the
# row dimension.
row_ids, col_ids = array_ops.split(
value=sp_input.indices, num_or_size_splits=2, axis=1)
update_row_indices, all_row_ids = array_ops.unique(row_ids[:, 0])
update_col_indices, all_col_ids = array_ops.unique(col_ids[:, 0])
col_ids = array_ops.expand_dims(math_ops.cast(all_col_ids, dtypes.int64), 1)
row_ids = array_ops.expand_dims(math_ops.cast(all_row_ids, dtypes.int64), 1)
if transpose_input:
update_indices = update_col_indices
row_shape = [
math_ops.cast(array_ops.shape(update_row_indices)[0], dtypes.int64)
]
gather_indices = update_row_indices
else:
update_indices = update_row_indices
row_shape = [
math_ops.cast(array_ops.shape(update_col_indices)[0], dtypes.int64)
]
gather_indices = update_col_indices
num_rows = math_ops.cast(array_ops.shape(update_indices)[0], dtypes.int64)
col_shape = [num_rows]
right = embedding_ops.embedding_lookup(
right_factors, gather_indices, partition_strategy="div")
new_sp_indices = array_ops.concat([row_ids, col_ids], 1)
new_sp_shape = (array_ops.concat([row_shape, col_shape], 0)
if transpose_input else
array_ops.concat([col_shape, row_shape], 0))
new_sp_input = sparse_tensor.SparseTensor(
indices=new_sp_indices,
values=sp_input.values,
dense_shape=new_sp_shape)
# Compute lhs and rhs of the normal equations
total_lhs = (self._unobserved_weight * gramian)
if self._regularization_matrix is not None:
total_lhs += self._regularization_matrix
if self._row_weights is None:
# Special case of ALS. Use a much simpler update rule.
total_rhs = (
self._unobserved_weight * sparse_ops.sparse_tensor_dense_matmul(
new_sp_input, right, adjoint_a=transpose_input))
# TODO(rmlarsen): handle transposing in tf.linalg.solve instead of
# transposing explicitly.
# TODO(rmlarsen): multi-thread tf.matrix_solve.
new_left_values = array_ops.transpose(
linalg_ops.matrix_solve(total_lhs, array_ops.transpose(total_rhs)))
else:
if row_weights is None:
# TODO(yifanchen): Add special handling for single shard without using
# embedding_lookup and perform benchmarks for those cases. Same for
# col_weights lookup below.
row_weights_slice = embedding_ops.embedding_lookup(
row_wt, update_indices, partition_strategy="div")
else:
num_indices = array_ops.shape(update_indices)[0]
with ops.control_dependencies(
[check_ops.assert_less_equal(array_ops.rank(row_weights), 1)]):
row_weights_slice = control_flow_ops.cond(
math_ops.equal(array_ops.rank(row_weights), 0),
lambda: (array_ops.ones([num_indices]) * row_weights),
lambda: math_ops.cast(row_weights, dtypes.float32))
col_weights = embedding_ops.embedding_lookup(
col_wt, gather_indices, partition_strategy="div")
partial_lhs, total_rhs = (
gen_factorization_ops.wals_compute_partial_lhs_and_rhs(
right,
col_weights,
self._unobserved_weight,
row_weights_slice,
new_sp_input.indices,
new_sp_input.values,
[],
num_rows,
transpose_input,
name="wals_compute_partial_lhs_rhs"))
total_lhs = array_ops.expand_dims(total_lhs, 0) + partial_lhs
total_rhs = array_ops.expand_dims(total_rhs, -1)
new_left_values = array_ops.squeeze(
linalg_ops.matrix_solve(total_lhs, total_rhs), [2])
update_op_name = "row_update" if update_row_factors else "col_update"
update_op = self.scatter_update(
left,
update_indices,
new_left_values,
sharding_func,
name=update_op_name)
# Create the loss subgraph
loss_sp_input = (sparse_ops.sparse_transpose(new_sp_input)
if transpose_input else new_sp_input)
# sp_approx is the low rank estimate of the input matrix, formed by
# computing the product <\\(u_i, v_j\\)> for (i, j) in loss_sp_input.indices.
sp_approx_vals = gen_factorization_ops.masked_matmul(
new_left_values,
right,
loss_sp_input.indices,
transpose_a=False,
transpose_b=True)
sp_approx = sparse_tensor.SparseTensor(
loss_sp_input.indices, sp_approx_vals, loss_sp_input.dense_shape)
sp_approx_sq = math_ops.square(sp_approx)
sp_residual = sparse_ops.sparse_add(loss_sp_input, sp_approx * (-1))
sp_residual_sq = math_ops.square(sp_residual)
row_wt_mat = (constant_op.constant(0.)
if self._row_weights is None else array_ops.expand_dims(
row_weights_slice, 1))
col_wt_mat = (constant_op.constant(0.)
if self._col_weights is None else array_ops.expand_dims(
col_weights, 0))
# We return the normalized loss
partial_row_gramian = math_ops.matmul(
new_left_values, new_left_values, transpose_a=True)
normalization_factor = total_rows / math_ops.cast(num_rows, dtypes.float32)
unregularized_loss = (
self._unobserved_weight * ( # pyformat line break
sparse_ops.sparse_reduce_sum(sp_residual_sq) - # pyformat break
sparse_ops.sparse_reduce_sum(sp_approx_sq) + # pyformat break
math_ops.trace(math_ops.matmul(partial_row_gramian, gramian))) +
sparse_ops.sparse_reduce_sum(row_wt_mat * (sp_residual_sq * col_wt_mat))
) * normalization_factor
if self._regularization is not None:
regularization = self._regularization * (
math_ops.trace(partial_row_gramian) * normalization_factor +
math_ops.trace(gramian))
else:
regularization = constant_op.constant(0.)
sum_weights = self._unobserved_weight * math_ops.cast(
total_rows * total_cols, dtypes.float32)
if self._row_weights is not None and self._col_weights is not None:
ones = sparse_tensor.SparseTensor(
indices=loss_sp_input.indices,
values=array_ops.ones(array_ops.shape(loss_sp_input.values)),
dense_shape=loss_sp_input.dense_shape)
sum_weights += sparse_ops.sparse_reduce_sum(row_wt_mat * (
ones * col_wt_mat)) * normalization_factor
return (new_left_values, update_op, unregularized_loss, regularization,
sum_weights)