def __init__(self, latent_vars=None, data=None):
"""Initialization.
Parameters
----------
latent_vars : dict, optional
Collection of latent variables (of type ``RandomVariable`` or
``tf.Tensor``) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data : dict, optional
Data dictionary which binds observed variables (of type
``RandomVariable`` or ``tf.Tensor``) to their realizations (of
type ``tf.Tensor``). It can also bind placeholders (of type
``tf.Tensor``) used in the model to their realizations; and
prior latent variables (of type ``RandomVariable``) to posterior
latent variables (of type ``RandomVariable``).
Examples
--------
>>> mu = Normal(loc=tf.constant(0.0), scale=tf.constant(1.0))
>>> x = Normal(loc=tf.ones(50) * mu, scale=tf.constant(1.0))
>>>
>>> qmu_loc = tf.Variable(tf.random_normal([]))
>>> qmu_scale = tf.nn.softplus(tf.Variable(tf.random_normal([])))
>>> qmu = Normal(loc=qmu_loc, scale=qmu_scale)
>>>
>>> inference = ed.Inference({mu: qmu}, data={x: tf.zeros(50)})
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(
value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope("data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def __init__(self, latent_vars=None, data=None):
"""Create an inference algorithm.
Args:
latent_vars: dict, optional.
Collection of latent variables (of type `RandomVariable` or
`tf.Tensor`) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data: dict, optional.
Data dictionary which binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations; and
prior latent variables (of type `RandomVariable`) to posterior
latent variables (of type `RandomVariable`).
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(
value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope(None, default_name="data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def __init__(self, latent_vars=None, data=None):
"""Create an inference algorithm.
Args:
latent_vars: dict, optional.
Collection of latent variables (of type `RandomVariable` or
`tf.Tensor`) to perform inference on. Each random variable is
binded to another random variable; the latter will infer the
former conditional on data.
data: dict, optional.
Data dictionary which binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations; and
prior latent variables (of type `RandomVariable`) to posterior
latent variables (of type `RandomVariable`).
"""
sess = get_session()
if latent_vars is None:
latent_vars = {}
if data is None:
data = {}
check_latent_vars(latent_vars)
self.latent_vars = latent_vars
check_data(data)
self.data = {}
for key, value in six.iteritems(data):
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type:
self.data[key] = value
elif isinstance(key, (RandomVariable, tf.Tensor)):
if isinstance(value, (RandomVariable, tf.Tensor)):
self.data[key] = value
elif isinstance(value, (float, list, int, np.ndarray, np.number, str)):
# If value is a Python type, store it in the graph.
# Assign its placeholder with the key's data type.
with tf.variable_scope("data"):
ph = tf.placeholder(key.dtype, np.shape(value))
var = tf.Variable(ph, trainable=False, collections=[])
sess.run(var.initializer, {ph: value})
self.data[key] = var
def ppc(T, data, latent_vars=None, n_samples=100):
"""Posterior predictive check
(Rubin, 1984; Meng, 1994; Gelman, Meng, and Stern, 1996).
PPC's form an empirical distribution for the predictive discrepancy,
$p(T\mid x) = \int p(T(x^{\\text{rep}})\mid z) p(z\mid x) dz$
by drawing replicated data sets $x^{\\text{rep}}$ and
calculating $T(x^{\\text{rep}})$ for each data set. Then it
compares it to $T(x)$.
If `data` is inputted with the prior predictive distribution, then
it is a prior predictive check (Box, 1980).
Args:
T: function.
Discrepancy function, which takes a dictionary of data and
dictionary of latent variables as input and outputs a `tf.Tensor`.
data: dict.
Data to compare to. It binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
latent_vars: dict, optional.
Collection of random variables (of type `RandomVariable` or
`tf.Tensor`) binded to their inferred posterior. This argument
is used when the discrepancy is a function of latent variables.
n_samples: int, optional.
Number of replicated data sets.
Returns:
list of np.ndarray.
List containing the reference distribution, which is a NumPy array
with `n_samples` elements,
$(T(x^{{\\text{rep}},1}, z^{1}), ...,
T(x^{\\text{rep,nsamples}}, z^{\\text{nsamples}}))$
and the realized discrepancy, which is a NumPy array with
`n_samples` elements,
$(T(x, z^{1}), ..., T(x, z^{\\text{nsamples}})).$
#### Examples
```python
# build posterior predictive after inference:
# it is parameterized by a posterior sample
x_post = ed.copy(x, {z: qz, beta: qbeta})
# posterior predictive check
# T is a user-defined function of data, T(data)
T = lambda xs, zs: tf.reduce_mean(xs[x_post])
ed.ppc(T, data={x_post: x_train})
# in general T is a discrepancy function of the data (both response and
# covariates) and latent variables, T(data, latent_vars)
T = lambda xs, zs: tf.reduce_mean(zs[z])
ed.ppc(T, data={y_post: y_train, x_ph: x_train},
latent_vars={z: qz, beta: qbeta})
# prior predictive check
# run ppc on original x
ed.ppc(T, data={x: x_train})
```
"""
sess = get_session()
if not callable(T):
raise TypeError("T must be a callable function.")
check_data(data)
if latent_vars is None:
latent_vars = {}
check_latent_vars(latent_vars)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
# Build replicated latent variables.
zrep = {key: tf.convert_to_tensor(value)
for key, value in six.iteritems(latent_vars)}
# Build replicated data.
xrep = {x: (x.value() if isinstance(x, RandomVariable) else obs)
for x, obs in six.iteritems(data)}
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {key: value for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type}
# Calculate discrepancy over many replicated data sets and latent
# variables.
Trep = T(xrep, zrep)
Tobs = T(data, zrep)
Treps = []
Ts = []
for _ in range(n_samples):
# Take a forward pass (session run) to get new samples for
# each calculation of the discrepancy.
# Alternatively, we could unroll the graph by registering this
# operation `n_samples` times, each for different parent nodes
# representing `xrep` and `zrep`. But it's expensive.
Treps += [sess.run(Trep, feed_dict)]
Ts += [sess.run(Tobs, feed_dict)]
return [np.stack(Treps), np.stack(Ts)]
def evaluate(metrics, data, n_samples=500, output_key=None):
"""Evaluate fitted model using a set of metrics.
A metric, or scoring rule (Winkler, 1994), is a function of observed
data under the posterior predictive distribution. For example in
supervised metrics such as classification accuracy, the observed
data (true output) is compared to the posterior predictive's mean
(predicted output). In unsupervised metrics such as log-likelihood,
the probability of observing the data is calculated under the
posterior predictive's log-density.
Parameters
----------
metrics : list of str or str
List of metrics or a single metric:
``'binary_accuracy'``,
``'categorical_accuracy'``,
``'sparse_categorical_accuracy'``,
``'log_loss'`` or ``'binary_crossentropy'``,
``'categorical_crossentropy'``,
``'sparse_categorical_crossentropy'``,
``'hinge'``,
``'squared_hinge'``,
``'mse'`` or ``'MSE'`` or ``'mean_squared_error'``,
``'mae'`` or ``'MAE'`` or ``'mean_absolute_error'``,
``'mape'`` or ``'MAPE'`` or ``'mean_absolute_percentage_error'``,
``'msle'`` or ``'MSLE'`` or ``'mean_squared_logarithmic_error'``,
``'poisson'``,
``'cosine'`` or ``'cosine_proximity'``,
``'log_lik'`` or ``'log_likelihood'``.
data : dict
Data to evaluate model with. It binds observed variables (of type
``RandomVariable`` or ``tf.Tensor``) to their realizations (of
type ``tf.Tensor``). It can also bind placeholders (of type
``tf.Tensor``) used in the model to their realizations.
n_samples : int, optional
Number of posterior samples for making predictions, using the
posterior predictive distribution.
output_key : RandomVariable or tf.Tensor, optional
It is the key in ``data`` which corresponds to the model's output.
Returns
-------
list of float or float
A list of evaluations or a single evaluation.
Raises
------
NotImplementedError
If an input metric does not match an implemented metric in Edward.
Examples
--------
>>> # build posterior predictive after inference: it is
>>> # parameterized by a posterior sample
>>> x_post = ed.copy(x, {z: qz, beta: qbeta})
>>>
>>> # log-likelihood performance
>>> ed.evaluate('log_likelihood', data={x_post: x_train})
>>>
>>> # classification accuracy
>>> # here, ``x_ph`` is any features the model is defined with respect to,
>>> # and ``y_post`` is the posterior predictive distribution
>>> ed.evaluate('binary_accuracy', data={y_post: y_train, x_ph: x_train})
>>>
>>> # mean squared error
>>> ed.evaluate('mean_squared_error', data={y: y_data, x: x_data})
"""
sess = get_session()
if isinstance(metrics, str):
metrics = [metrics]
elif not isinstance(metrics, list):
raise TypeError("metrics must have type str or list.")
check_data(data)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
if output_key is None:
# Default output_key to the only data key that isn't a placeholder.
keys = [
key for key in six.iterkeys(data) if
not isinstance(key, tf.Tensor) or "Placeholder" not in key.op.type
]
if len(keys) == 1:
output_key = keys[0]
else:
raise KeyError("User must specify output_key.")
elif not isinstance(output_key, RandomVariable):
raise TypeError("output_key must have type RandomVariable.")
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {
key: value
for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type
}
# Form true data.
y_true = data[output_key]
# Make predictions (if there are any supervised metrics).
if metrics != ['log_lik'] and metrics != ['log_likelihood']:
binary_discrete = (Bernoulli, Binomial)
categorical_discrete = (Categorical, Multinomial, OneHotCategorical)
if isinstance(output_key, binary_discrete + categorical_discrete):
# Average over realizations of their probabilities, then predict
# via argmax over probabilities.
probs = [
sess.run(output_key.probs, feed_dict) for _ in range(n_samples)
]
probs = tf.add_n(probs) / tf.cast(n_samples, tf.float32)
if isinstance(output_key, binary_discrete):
# make random prediction whenever probs is exactly 0.5
random = tf.random_uniform(shape=tf.shape(probs))
y_pred = tf.round(tf.where(tf.equal(0.5, probs), random,
probs))
else:
y_pred = tf.argmax(probs, len(probs.shape) - 1)
else:
# Monte Carlo estimate the mean of the posterior predictive.
y_pred = [
sess.run(output_key, feed_dict) for _ in range(n_samples)
]
y_pred = tf.cast(tf.add_n(y_pred), tf.float32) / \
tf.cast(n_samples, tf.float32)
# Evaluate y_true (according to y_pred if supervised) for all metrics.
evaluations = []
for metric in metrics:
if metric == 'accuracy' or metric == 'crossentropy':
# automate binary or sparse cat depending on its support
support = sess.run(tf.reduce_max(y_true), feed_dict)
if support <= 1:
metric = 'binary_' + metric
else:
metric = 'sparse_categorical_' + metric
if metric == 'binary_accuracy':
evaluations += [binary_accuracy(y_true, y_pred)]
elif metric == 'categorical_accuracy':
evaluations += [categorical_accuracy(y_true, y_pred)]
elif metric == 'sparse_categorical_accuracy':
evaluations += [sparse_categorical_accuracy(y_true, y_pred)]
elif metric == 'log_loss' or metric == 'binary_crossentropy':
evaluations += [binary_crossentropy(y_true, y_pred)]
elif metric == 'categorical_crossentropy':
evaluations += [categorical_crossentropy(y_true, y_pred)]
elif metric == 'sparse_categorical_crossentropy':
evaluations += [sparse_categorical_crossentropy(y_true, y_pred)]
elif metric == 'hinge':
evaluations += [hinge(y_true, y_pred)]
elif metric == 'squared_hinge':
evaluations += [squared_hinge(y_true, y_pred)]
elif (metric == 'mse' or metric == 'MSE'
or metric == 'mean_squared_error'):
evaluations += [mean_squared_error(y_true, y_pred)]
elif (metric == 'mae' or metric == 'MAE'
or metric == 'mean_absolute_error'):
evaluations += [mean_absolute_error(y_true, y_pred)]
elif (metric == 'mape' or metric == 'MAPE'
or metric == 'mean_absolute_percentage_error'):
evaluations += [mean_absolute_percentage_error(y_true, y_pred)]
elif (metric == 'msle' or metric == 'MSLE'
or metric == 'mean_squared_logarithmic_error'):
evaluations += [mean_squared_logarithmic_error(y_true, y_pred)]
elif metric == 'poisson':
evaluations += [poisson(y_true, y_pred)]
elif metric == 'cosine' or metric == 'cosine_proximity':
evaluations += [cosine_proximity(y_true, y_pred)]
elif metric == 'log_lik' or metric == 'log_likelihood':
# Monte Carlo estimate the log-density of the posterior predictive.
tensor = tf.reduce_mean(output_key.log_prob(y_true))
log_pred = [sess.run(tensor, feed_dict) for _ in range(n_samples)]
log_pred = tf.add_n(log_pred) / tf.cast(n_samples, tf.float32)
evaluations += [log_pred]
else:
raise NotImplementedError(
"Metric is not implemented: {}".format(metric))
if len(evaluations) == 1:
return sess.run(evaluations[0], feed_dict)
else:
return sess.run(evaluations, feed_dict)
def ppc(T, data, latent_vars=None, n_samples=100):
"""Posterior predictive check
[@rubin1984bayesianly; @meng1994posterior; @gelman1996posterior].
PPC's form an empirical distribution for the predictive discrepancy,
$p(T\mid x) = \int p(T(x^{\\text{rep}})\mid z) p(z\mid x) dz$
by drawing replicated data sets $x^{\\text{rep}}$ and
calculating $T(x^{\\text{rep}})$ for each data set. Then it
compares it to $T(x)$.
If `data` is inputted with the prior predictive distribution, then
it is a prior predictive check [@box1980sampling].
Args:
T: function.
Discrepancy function, which takes a dictionary of data and
dictionary of latent variables as input and outputs a `tf.Tensor`.
data: dict.
Data to compare to. It binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
latent_vars: dict, optional.
Collection of random variables (of type `RandomVariable` or
`tf.Tensor`) binded to their inferred posterior. This argument
is used when the discrepancy is a function of latent variables.
n_samples: int, optional.
Number of replicated data sets.
Returns:
list of np.ndarray.
List containing the reference distribution, which is a NumPy array
with `n_samples` elements,
$(T(x^{{\\text{rep}},1}, z^{1}), ...,
T(x^{\\text{rep,nsamples}}, z^{\\text{nsamples}}))$
and the realized discrepancy, which is a NumPy array with
`n_samples` elements,
$(T(x, z^{1}), ..., T(x, z^{\\text{nsamples}})).$
#### Examples
```python
# build posterior predictive after inference:
# it is parameterized by a posterior sample
x_post = ed.copy(x, {z: qz, beta: qbeta})
# posterior predictive check
# T is a user-defined function of data, T(data)
T = lambda xs, zs: tf.reduce_mean(xs[x_post])
ed.ppc(T, data={x_post: x_train})
# in general T is a discrepancy function of the data (both response and
# covariates) and latent variables, T(data, latent_vars)
T = lambda xs, zs: tf.reduce_mean(zs[z])
ed.ppc(T, data={y_post: y_train, x_ph: x_train},
latent_vars={z: qz, beta: qbeta})
# prior predictive check
# run ppc on original x
ed.ppc(T, data={x: x_train})
```
"""
sess = get_session()
if not callable(T):
raise TypeError("T must be a callable function.")
check_data(data)
if latent_vars is None:
latent_vars = {}
check_latent_vars(latent_vars)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
# Build replicated latent variables.
zrep = {
key: tf.convert_to_tensor(value)
for key, value in six.iteritems(latent_vars)
}
# Build replicated data.
xrep = {
x: (x.value() if isinstance(x, RandomVariable) else obs)
for x, obs in six.iteritems(data)
}
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {
key: value
for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type
}
# Calculate discrepancy over many replicated data sets and latent
# variables.
Trep = T(xrep, zrep)
Tobs = T(data, zrep)
Treps = []
Ts = []
for _ in range(n_samples):
# Take a forward pass (session run) to get new samples for
# each calculation of the discrepancy.
# Alternatively, we could unroll the graph by registering this
# operation `n_samples` times, each for different parent nodes
# representing `xrep` and `zrep`. But it's expensive.
Treps += [sess.run(Trep, feed_dict)]
Ts += [sess.run(Tobs, feed_dict)]
return [np.stack(Treps), np.stack(Ts)]
def evaluate(metrics, data, n_samples=500, output_key=None, seed=None):
"""Evaluate fitted model using a set of metrics.
A metric, or scoring rule [@winkler1994evaluating], is a function of
observed data under the posterior predictive distribution. For
example in supervised metrics such as classification accuracy, the
observed data (true output) is compared to the posterior
predictive's mean (predicted output). In unsupervised metrics such
as log-likelihood, the probability of observing the data is
calculated under the posterior predictive's log-density.
Args:
metrics: list of str and/or (str, params: dict) tuples, str,
or (str, params: dict) tuple.
List of metrics or a single metric:
`'binary_accuracy'`,
`'categorical_accuracy'`,
`'sparse_categorical_accuracy'`,
`'log_loss'` or `'binary_crossentropy'`,
`'categorical_crossentropy'`,
`'sparse_categorical_crossentropy'`,
`'hinge'`,
`'squared_hinge'`,
`'mse'` or `'MSE'` or `'mean_squared_error'`,
`'mae'` or `'MAE'` or `'mean_absolute_error'`,
`'mape'` or `'MAPE'` or `'mean_absolute_percentage_error'`,
`'msle'` or `'MSLE'` or `'mean_squared_logarithmic_error'`,
`'poisson'`,
`'cosine'` or `'cosine_proximity'`,
`'crps'` or `'continuous_ranked_probability_score'`,
`'log_lik'` or `'log_likelihood'`.
In lieu of a metric string, this method also accepts (str, params: dict)
tuples; the first element of this tuple is the metric string, and
the second is a dict of associated params. At present, this dict only
expects one key, `'average'`, which stipulates the type of averaging to
perform on those metrics that permit binary averaging. Permissible
options include: `None`, `'macro'` and `'micro'`.
data: dict.
Data to evaluate model with. It binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
n_samples: int.
Number of posterior samples for making predictions, using the
posterior predictive distribution.
output_key: RandomVariable or tf.Tensor.
It is the key in `data` which corresponds to the model's output.
seed: a Python integer. Used to create a random seed for the
distribution
Returns:
list of float or float.
A list of evaluations or a single evaluation.
Raises:
NotImplementedError.
If an input metric does not match an implemented metric in Edward.
#### Examples
```python
# build posterior predictive after inference: it is
# parameterized by a posterior sample
x_post = ed.copy(x, {z: qz, beta: qbeta})
# log-likelihood performance
ed.evaluate('log_likelihood', data={x_post: x_train})
# classification accuracy
# here, `x_ph` is any features the model is defined with respect to,
# and `y_post` is the posterior predictive distribution
ed.evaluate('binary_accuracy', data={y_post: y_train, x_ph: x_train})
# mean squared error
ed.evaluate('mean_squared_error', data={y: y_data, x: x_data})
```
# mean squared logarithmic error with `'micro'` averaging
ed.evaluate(('mean_squared_logarithmic_error', {'average': 'micro'}),
data={y: y_data, x: x_data})
"""
sess = get_session()
if isinstance(metrics, str):
metrics = [metrics]
elif callable(metrics):
metrics = [metrics]
elif not isinstance(metrics, list):
raise TypeError("metrics must have type str or list, or be callable.")
check_data(data)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
if output_key is None:
# Default output_key to the only data key that isn't a placeholder.
keys = [
key for key in six.iterkeys(data) if
not isinstance(key, tf.Tensor) or "Placeholder" not in key.op.type
]
if len(keys) == 1:
output_key = keys[0]
else:
raise KeyError("User must specify output_key.")
elif not isinstance(output_key, RandomVariable):
raise TypeError("output_key must have type RandomVariable.")
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {
key: value
for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type
}
# Form true data.
y_true = data[output_key]
# Make predictions (if there are any supervised metrics).
if metrics != ['log_lik'] and metrics != ['log_likelihood']:
binary_discrete = (Bernoulli, Binomial)
categorical_discrete = (Categorical, Multinomial, OneHotCategorical)
total_count = sess.run(
getattr(output_key, 'total_count', tf.constant(1.)))
if isinstance(output_key, binary_discrete + categorical_discrete):
# Average over realizations of their probabilities, then predict
# via argmax over probabilities.
probs = [
sess.run(output_key.probs, feed_dict) for _ in range(n_samples)
]
probs = np.sum(probs, axis=0) / n_samples
if isinstance(output_key, binary_discrete):
# make random prediction whenever probs is exactly 0.5
random = tf.random_uniform(shape=tf.shape(probs))
y_pred = tf.round(tf.where(tf.equal(0.5, probs), random,
probs))
else:
if total_count > 1:
mode = compute_multinomial_mode(probs, total_count, seed)
if len(output_key.sample_shape):
y_pred = tf.reshape(
tf.tile(mode, output_key.sample_shape),
[-1, len(probs)])
else:
y_pred = mode
else:
y_pred = tf.argmax(probs, len(probs.shape) - 1)
probs = tf.constant(probs)
else:
# Monte Carlo estimate the mean of the posterior predictive.
y_pred = [
sess.run(output_key, feed_dict) for _ in range(n_samples)
]
y_pred = tf.cast(tf.add_n(y_pred), y_pred[0].dtype) / \
tf.cast(n_samples, y_pred[0].dtype)
if len(y_true.shape) == 0:
y_true = tf.expand_dims(y_true, 0)
y_pred = tf.expand_dims(y_pred, 0)
# Evaluate y_true (according to y_pred if supervised) for all metrics.
evaluations = []
for metric in metrics:
if isinstance(metric, tuple):
metric, params = metric
else:
params = {}
if metric == 'accuracy' or metric == 'crossentropy':
# automate binary or sparse cat depending on its support
support = sess.run(tf.reduce_max(y_true), feed_dict)
if support <= 1:
metric = 'binary_' + metric
else:
metric = 'sparse_categorical_' + metric
if metric == 'binary_accuracy':
evaluations += [binary_accuracy(y_true, y_pred, **params)]
elif metric == 'categorical_accuracy':
evaluations += [categorical_accuracy(y_true, y_pred, **params)]
elif metric == 'sparse_categorical_accuracy':
evaluations += [
sparse_categorical_accuracy(y_true, y_pred, **params)
]
elif metric == 'log_loss' or metric == 'binary_crossentropy':
evaluations += [binary_crossentropy(y_true, y_pred, **params)]
elif metric == 'categorical_crossentropy':
evaluations += [categorical_crossentropy(y_true, y_pred, **params)]
elif metric == 'sparse_categorical_crossentropy':
evaluations += [
sparse_categorical_crossentropy(y_true, y_pred, **params)
]
elif metric == 'multinomial_accuracy':
evaluations += [multinomial_accuracy(y_true, y_pred, **params)]
elif metric == 'kl_divergence':
y_true_ = y_true / total_count
y_pred_ = probs
evaluations += [kl_divergence(y_true_, y_pred_, **params)]
elif metric == 'hinge':
evaluations += [hinge(y_true, y_pred, **params)]
elif metric == 'squared_hinge':
evaluations += [squared_hinge(y_true, y_pred, **params)]
elif (metric == 'mse' or metric == 'MSE'
or metric == 'mean_squared_error'):
evaluations += [mean_squared_error(y_true, y_pred, **params)]
elif (metric == 'mae' or metric == 'MAE'
or metric == 'mean_absolute_error'):
evaluations += [mean_absolute_error(y_true, y_pred, **params)]
elif (metric == 'mape' or metric == 'MAPE'
or metric == 'mean_absolute_percentage_error'):
evaluations += [
mean_absolute_percentage_error(y_true, y_pred, **params)
]
elif (metric == 'msle' or metric == 'MSLE'
or metric == 'mean_squared_logarithmic_error'):
evaluations += [
mean_squared_logarithmic_error(y_true, y_pred, **params)
]
elif metric == 'poisson':
evaluations += [poisson(y_true, y_pred, **params)]
elif metric == 'cosine' or metric == 'cosine_proximity':
evaluations += [cosine_proximity(y_true, y_pred, **params)]
elif metric == 'crps' or metric == 'continuous_ranked_probability_score':
evaluations += [
continuous_ranked_probability_score(y_true, y_pred, **params)
]
elif metric == 'log_lik' or metric == 'log_likelihood':
# Monte Carlo estimate the log-density of the posterior predictive.
tensor = tf.reduce_mean(output_key.log_prob(y_true))
log_pred = [sess.run(tensor, feed_dict) for _ in range(n_samples)]
log_pred = tf.add_n(log_pred) / tf.cast(n_samples, tensor.dtype)
evaluations += [log_pred]
elif callable(metric):
evaluations += [metric(y_true, y_pred, **params)]
else:
raise NotImplementedError(
"Metric is not implemented: {}".format(metric))
if len(evaluations) == 1:
return sess.run(evaluations[0], feed_dict)
else:
return sess.run(evaluations, feed_dict)
def get_model_probs(data, metrics='probs', n_samples=500):
output_key = None
# seed = None
sess = get_session()
if isinstance(metrics, str):
metrics = [metrics]
elif not isinstance(metrics, list):
raise TypeError("metrics must have type str or list.")
check_data(data)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
if output_key is None:
# Default output_key to the only data key that isn't a placeholder.
keys = [key for key in six.iterkeys(data) if not
isinstance(key, tf.Tensor) or "Placeholder" not in key.op.type]
if len(keys) == 1:
output_key = keys[0]
else:
raise KeyError("User must specify output_key.")
elif not isinstance(output_key, RandomVariable):
raise TypeError("output_key must have type RandomVariable.")
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {key: value for key, value in six.iteritems(data)
if
isinstance(key, tf.Tensor) and "Placeholder" in key.op.type}
# Form true data.
y_true = data[output_key]
# Make predictions (if there are any supervised metrics).
if metrics != ['log_lik'] and metrics != ['log_likelihood']:
binary_discrete = (Bernoulli, Binomial)
categorical_discrete = (Categorical, Multinomial, OneHotCategorical)
total_count = sess.run(
getattr(output_key, 'total_count', tf.constant(1.)))
if isinstance(output_key, binary_discrete + categorical_discrete):
# Average over realizations of their probabilities, then predict
# via argmax over probabilities.
probs = [sess.run(output_key.probs, feed_dict) for _ in
range(n_samples)]
probs = np.sum(probs, axis=0) / n_samples
if isinstance(output_key, binary_discrete):
# make random prediction whenever probs is exactly 0.5
random = tf.random_uniform(shape=tf.shape(probs))
y_pred = tf.round(
tf.where(tf.equal(0.5, probs), random, probs))
else:
if total_count > 1:
raise Exception('todo multinomial')
# if len(output_key.sample_shape):
# y_pred = tf.reshape(
# tf.tile(mode, output_key.sample_shape),
# [-1, len(probs)])
# else:
# y_pred = mode
else:
y_pred = tf.argmax(probs, len(probs.shape) - 1)
probs = tf.constant(probs)
else:
# Monte Carlo estimate the mean of the posterior predictive.
y_pred = [sess.run(output_key, feed_dict) for _ in
range(n_samples)]
y_pred = tf.cast(tf.add_n(y_pred), y_pred[0].dtype) / \
tf.cast(n_samples, y_pred[0].dtype)
if len(y_true.shape) == 0:
y_true = tf.expand_dims(y_true, 0)
y_pred = tf.expand_dims(y_pred, 0)
return probs
def test(self):
with self.test_session():
x = Normal(0.0, 1.0)
qx = Normal(0.0, 1.0)
x_ph = tf.placeholder(tf.float32, [])
check_data({x: tf.constant(0.0)})
check_data({x: np.float64(0.0)})
check_data({x: np.int64(0)})
check_data({x: 0.0})
check_data({x: 0})
check_data({x: False})
check_data({x: '0'})
check_data({x: x_ph})
check_data({x: qx})
check_data({2.0 * x: tf.constant(0.0)})
self.assertRaises(TypeError, check_data, {0.0: x})
self.assertRaises(TypeError, check_data, {x: tf.zeros(5)})
self.assertRaises(TypeError, check_data, {x_ph: x})
self.assertRaises(TypeError, check_data, {x_ph: x})
self.assertRaises(TypeError, check_data,
{x: tf.constant(0, tf.float64)})
self.assertRaises(TypeError, check_data, {x_ph: tf.constant(0.0)})
x_vec = Normal(tf.constant([0.0]), tf.constant([1.0]))
qx_vec = Normal(tf.constant([0.0]), tf.constant([1.0]))
check_data({x_vec: qx_vec})
check_data({x_vec: [0.0]})
check_data({x_vec: [0]})
check_data({x_vec: ['0']})
self.assertRaises(TypeError, check_data, {x: qx_vec})
def evaluate(metrics, data, n_samples=500, output_key=None):
"""Evaluate fitted model using a set of metrics.
A metric, or scoring rule (Winkler, 1994), is a function of observed
data under the posterior predictive distribution. For example in
supervised metrics such as classification accuracy, the observed
data (true output) is compared to the posterior predictive's mean
(predicted output). In unsupervised metrics such as log-likelihood,
the probability of observing the data is calculated under the
posterior predictive's log-density.
Args:
metrics: list of str or str.
List of metrics or a single metric:
`'binary_accuracy'`,
`'categorical_accuracy'`,
`'sparse_categorical_accuracy'`,
`'log_loss'` or `'binary_crossentropy'`,
`'categorical_crossentropy'`,
`'sparse_categorical_crossentropy'`,
`'hinge'`,
`'squared_hinge'`,
`'mse'` or `'MSE'` or `'mean_squared_error'`,
`'mae'` or `'MAE'` or `'mean_absolute_error'`,
`'mape'` or `'MAPE'` or `'mean_absolute_percentage_error'`,
`'msle'` or `'MSLE'` or `'mean_squared_logarithmic_error'`,
`'poisson'`,
`'cosine'` or `'cosine_proximity'`,
`'log_lik'` or `'log_likelihood'`.
data: dict.
Data to evaluate model with. It binds observed variables (of type
`RandomVariable` or `tf.Tensor`) to their realizations (of
type `tf.Tensor`). It can also bind placeholders (of type
`tf.Tensor`) used in the model to their realizations.
n_samples: int, optional.
Number of posterior samples for making predictions, using the
posterior predictive distribution.
output_key: RandomVariable or tf.Tensor, optional.
It is the key in `data` which corresponds to the model's output.
Returns:
list of float or float.
A list of evaluations or a single evaluation.
Raises:
NotImplementedError.
If an input metric does not match an implemented metric in Edward.
#### Examples
```python
# build posterior predictive after inference: it is
# parameterized by a posterior sample
x_post = ed.copy(x, {z: qz, beta: qbeta})
# log-likelihood performance
ed.evaluate('log_likelihood', data={x_post: x_train})
# classification accuracy
# here, `x_ph` is any features the model is defined with respect to,
# and `y_post` is the posterior predictive distribution
ed.evaluate('binary_accuracy', data={y_post: y_train, x_ph: x_train})
# mean squared error
ed.evaluate('mean_squared_error', data={y: y_data, x: x_data})
```
"""
sess = get_session()
if isinstance(metrics, str):
metrics = [metrics]
elif not isinstance(metrics, list):
raise TypeError("metrics must have type str or list.")
check_data(data)
if not isinstance(n_samples, int):
raise TypeError("n_samples must have type int.")
if output_key is None:
# Default output_key to the only data key that isn't a placeholder.
keys = [key for key in six.iterkeys(data) if not
isinstance(key, tf.Tensor) or "Placeholder" not in key.op.type]
if len(keys) == 1:
output_key = keys[0]
else:
raise KeyError("User must specify output_key.")
elif not isinstance(output_key, RandomVariable):
raise TypeError("output_key must have type RandomVariable.")
# Create feed_dict for data placeholders that the model conditions
# on; it is necessary for all session runs.
feed_dict = {key: value for key, value in six.iteritems(data)
if isinstance(key, tf.Tensor) and "Placeholder" in key.op.type}
# Form true data.
y_true = data[output_key]
# Make predictions (if there are any supervised metrics).
if metrics != ['log_lik'] and metrics != ['log_likelihood']:
binary_discrete = (Bernoulli, Binomial)
categorical_discrete = (Categorical, Multinomial, OneHotCategorical)
if isinstance(output_key, binary_discrete + categorical_discrete):
# Average over realizations of their probabilities, then predict
# via argmax over probabilities.
probs = [sess.run(output_key.probs, feed_dict) for _ in range(n_samples)]
probs = tf.add_n(probs) / tf.cast(n_samples, tf.float32)
if isinstance(output_key, binary_discrete):
# make random prediction whenever probs is exactly 0.5
random = tf.random_uniform(shape=tf.shape(probs))
y_pred = tf.round(tf.where(tf.equal(0.5, probs), random, probs))
else:
y_pred = tf.argmax(probs, len(probs.shape) - 1)
else:
# Monte Carlo estimate the mean of the posterior predictive.
y_pred = [sess.run(output_key, feed_dict) for _ in range(n_samples)]
y_pred = tf.cast(tf.add_n(y_pred), tf.float32) / \
tf.cast(n_samples, tf.float32)
# Evaluate y_true (according to y_pred if supervised) for all metrics.
evaluations = []
for metric in metrics:
if metric == 'accuracy' or metric == 'crossentropy':
# automate binary or sparse cat depending on its support
support = sess.run(tf.reduce_max(y_true), feed_dict)
if support <= 1:
metric = 'binary_' + metric
else:
metric = 'sparse_categorical_' + metric
if metric == 'binary_accuracy':
evaluations += [binary_accuracy(y_true, y_pred)]
elif metric == 'categorical_accuracy':
evaluations += [categorical_accuracy(y_true, y_pred)]
elif metric == 'sparse_categorical_accuracy':
evaluations += [sparse_categorical_accuracy(y_true, y_pred)]
elif metric == 'log_loss' or metric == 'binary_crossentropy':
evaluations += [binary_crossentropy(y_true, y_pred)]
elif metric == 'categorical_crossentropy':
evaluations += [categorical_crossentropy(y_true, y_pred)]
elif metric == 'sparse_categorical_crossentropy':
evaluations += [sparse_categorical_crossentropy(y_true, y_pred)]
elif metric == 'hinge':
evaluations += [hinge(y_true, y_pred)]
elif metric == 'squared_hinge':
evaluations += [squared_hinge(y_true, y_pred)]
elif (metric == 'mse' or metric == 'MSE' or
metric == 'mean_squared_error'):
evaluations += [mean_squared_error(y_true, y_pred)]
elif (metric == 'mae' or metric == 'MAE' or
metric == 'mean_absolute_error'):
evaluations += [mean_absolute_error(y_true, y_pred)]
elif (metric == 'mape' or metric == 'MAPE' or
metric == 'mean_absolute_percentage_error'):
evaluations += [mean_absolute_percentage_error(y_true, y_pred)]
elif (metric == 'msle' or metric == 'MSLE' or
metric == 'mean_squared_logarithmic_error'):
evaluations += [mean_squared_logarithmic_error(y_true, y_pred)]
elif metric == 'poisson':
evaluations += [poisson(y_true, y_pred)]
elif metric == 'cosine' or metric == 'cosine_proximity':
evaluations += [cosine_proximity(y_true, y_pred)]
elif metric == 'log_lik' or metric == 'log_likelihood':
# Monte Carlo estimate the log-density of the posterior predictive.
tensor = tf.reduce_mean(output_key.log_prob(y_true))
log_pred = [sess.run(tensor, feed_dict) for _ in range(n_samples)]
log_pred = tf.add_n(log_pred) / tf.cast(n_samples, tf.float32)
evaluations += [log_pred]
else:
raise NotImplementedError("Metric is not implemented: {}".format(metric))
if len(evaluations) == 1:
return sess.run(evaluations[0], feed_dict)
else:
return sess.run(evaluations, feed_dict)
def test(self):
with self.test_session():
x = Normal(0.0, 1.0)
qx = Normal(0.0, 1.0)
x_ph = tf.placeholder(tf.float32, [])
check_data({x: tf.constant(0.0)})
check_data({x: np.float64(0.0)})
check_data({x: np.int64(0)})
check_data({x: 0.0})
check_data({x: 0})
check_data({x: False})
check_data({x: '0'})
check_data({x: x_ph})
check_data({x: qx})
check_data({2.0 * x: tf.constant(0.0)})
self.assertRaises(TypeError, check_data, {0.0: x})
self.assertRaises(TypeError, check_data, {x: tf.zeros(5)})
self.assertRaises(TypeError, check_data, {x_ph: x})
self.assertRaises(TypeError, check_data, {x_ph: x})
self.assertRaises(TypeError, check_data,
{x: tf.constant(0, tf.float64)})
self.assertRaises(TypeError, check_data,
{x_ph: tf.constant(0.0)})
x_vec = Normal(tf.constant([0.0]), tf.constant([1.0]))
qx_vec = Normal(tf.constant([0.0]), tf.constant([1.0]))
check_data({x_vec: qx_vec})
check_data({x_vec: [0.0]})
check_data({x_vec: [0]})
check_data({x_vec: ['0']})
self.assertRaises(TypeError, check_data, {x: qx_vec})
