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The Laplace distribution with location loc and scale parameters.
Inherits From: Distribution
tf.compat.v1.distributions.Laplace(
loc,
scale,
validate_args=False,
allow_nan_stats=True,
name='Laplace'
)
The probability density function (pdf) of this distribution is,
pdf(x; mu, sigma) = exp(-|x - mu| / sigma) / Z
Z = 2 sigma
where loc = mu, scale = sigma, and Z is the normalization constant.
Note that the Laplace distribution can be thought of two exponential distributions spliced together "back-to-back."
The Lpalce distribution is a member of the location-scale family, i.e., it can be constructed as,
X ~ Laplace(loc=0, scale=1)
Y = loc + scale * X
loc
scale
validate_args
bool, default False. When True distribution
parameters are checked for validity despite possibly degrading runtime
performance. When False invalid inputs may silently render incorrect
outputs.
allow_nan_stats
bool, default True. When True,
statistics (e.g., mean, mode, variance) use the value "NaN" to
indicate the result is undefined. When False, an exception is raised
if one or more of the statistic's batch members are undefined.
name
str name prefixed to Ops created by this class.
TypeError
loc and scale are of different dtype.
allow_nan_stats
bool describing behavior when a stat is undefined.
Stats return +/- infinity when it makes sense. E.g., the variance of a
Cauchy distribution is infinity. However, sometimes the statistic is
undefined, e.g., if a distribution's pdf does not achieve a maximum within
the support of the distribution, the mode is undefined. If the mean is
undefined, then by definition the variance is undefined. E.g. the mean for
Student's T for df = 1 is undefined (no clear way to say it is either + or -
infinity), so the variance = E[(X - mean)**2] is also undefined.
batch_shape
TensorShape.
May be partially defined or unknown.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.dtype
DType of Tensors handled by this Distribution.
event_shape
TensorShape.
May be partially defined or unknown.
loc
name
Distribution.
parameters
Distribution.
reparameterization_type
Currently this is one of the static instances
distributions.FULLY_REPARAMETERIZED
or distributions.NOT_REPARAMETERIZED.
scale
validate_args
bool indicating possibly expensive checks are enabled.
batch_shape_tensorbatch_shape_tensor(
name='batch_shape_tensor'
)
Shape of a single sample from a single event index as a 1-D Tensor.
The batch dimensions are indexes into independent, non-identical parameterizations of this distribution.
name
batch_shape
Tensor.
cdfcdf(
value, name='cdf'
)
Cumulative distribution function.
Given random variable X, the cumulative distribution function cdf is:
cdf(x) := P[X <= x]
value
float or double Tensor.
name
str prepended to names of ops created by this function.
cdf
Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
copycopy(
**override_parameters_kwargs
)
Creates a deep copy of the distribution.
**override_parameters_kwargs
distribution
type(self) initialized from the union
of self.parameters and override_parameters_kwargs, i.e.,
dict(self.parameters, **override_parameters_kwargs).
covariancecovariance(
name='covariance'
)
Covariance.
Covariance is (possibly) defined only for non-scalar-event distributions.
For example, for a length-k, vector-valued distribution, it is calculated
as,
Cov[i, j] = Covariance(X_i, X_j) = E[(X_i - E[X_i]) (X_j - E[X_j])]
where Cov is a (batch of) k x k matrix, 0 <= (i, j) < k, and E
denotes expectation.
Alternatively, for non-vector, multivariate distributions (e.g.,
matrix-valued, Wishart), Covariance shall return a (batch of) matrices
under some vectorization of the events, i.e.,
Cov[i, j] = Covariance(Vec(X)_i, Vec(X)_j) = [as above]
where Cov is a (batch of) k' x k' matrices,
0 <= (i, j) < k' = reduce_prod(event_shape), and Vec is some function
mapping indices of this distribution's event dimensions to indices of a
length-k' vector.
name
str prepended to names of ops created by this function.
covariance
Tensor with shape [B1, ..., Bn, k', k']
where the first n dimensions are batch coordinates and
k' = reduce_prod(self.event_shape).
cross_entropycross_entropy(
other, name='cross_entropy'
)
Computes the (Shannon) cross entropy.
Denote this distribution (self) by P and the other distribution by
Q. Assuming P, Q are absolutely continuous with respect to
one another and permit densities p(x) dr(x) and q(x) dr(x), (Shanon)
cross entropy is defined as:
H[P, Q] = E_p[-log q(X)] = -int_F p(x) log q(x) dr(x)
where F denotes the support of the random variable X ~ P.
other
tfp.distributions.Distribution instance.
name
str prepended to names of ops created by this function.
cross_entropy
self.dtype Tensor with shape [B1, ..., Bn]
representing n different calculations of (Shanon) cross entropy.
entropyentropy(
name='entropy'
)
Shannon entropy in nats.
event_shape_tensorevent_shape_tensor(
name='event_shape_tensor'
)
Shape of a single sample from a single batch as a 1-D int32 Tensor.
name
event_shape
Tensor.
is_scalar_batchis_scalar_batch(
name='is_scalar_batch'
)
Indicates that batch_shape == [].
name
str prepended to names of ops created by this function.
is_scalar_batch
bool scalar Tensor.
is_scalar_eventis_scalar_event(
name='is_scalar_event'
)
Indicates that event_shape == [].
name
str prepended to names of ops created by this function.
is_scalar_event
bool scalar Tensor.
kl_divergencekl_divergence(
other, name='kl_divergence'
)
Computes the Kullback--Leibler divergence.
Denote this distribution (self) by p and the other distribution by
q. Assuming p, q are absolutely continuous with respect to reference
measure r, the KL divergence is defined as:
KL[p, q] = E_p[log(p(X)/q(X))]
= -int_F p(x) log q(x) dr(x) + int_F p(x) log p(x) dr(x)
= H[p, q] - H[p]
where F denotes the support of the random variable X ~ p, H[., .]
denotes (Shanon) cross entropy, and H[.] denotes (Shanon) entropy.
other
tfp.distributions.Distribution instance.
name
str prepended to names of ops created by this function.
kl_divergence
self.dtype Tensor with shape [B1, ..., Bn]
representing n different calculations of the Kullback-Leibler
divergence.
log_cdflog_cdf(
value, name='log_cdf'
)
Log cumulative distribution function.
Given random variable X, the cumulative distribution function cdf is:
log_cdf(x) := Log[ P[X <= x] ]
Often, a numerical approximation can be used for log_cdf(x) that yields
a more accurate answer than simply taking the logarithm of the cdf when
x << -1.
value
float or double Tensor.
name
str prepended to names of ops created by this function.
logcdf
Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
log_problog_prob(
value, name='log_prob'
)
Log probability density/mass function.
value
float or double Tensor.
name
str prepended to names of ops created by this function.
log_prob
Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
log_survival_functionlog_survival_function(
value, name='log_survival_function'
)
Log survival function.
Given random variable X, the survival function is defined:
log_survival_function(x) = Log[ P[X > x] ]
= Log[ 1 - P[X <= x] ]
= Log[ 1 - cdf(x) ]
Typically, different numerical approximations can be used for the log
survival function, which are more accurate than 1 - cdf(x) when x >> 1.
value
float or double Tensor.
name
str prepended to names of ops created by this function.
Tensor of shape sample_shape(x) + self.batch_shape with values of type
self.dtype.
meanmean(
name='mean'
)
Mean.
modemode(
name='mode'
)
Mode.
param_shapes@classmethodparam_shapes( sample_shape, name='DistributionParamShapes' )
Shapes of parameters given the desired shape of a call to sample().
This is a class method that describes what key/value arguments are required
to instantiate the given Distribution so that a particular shape is
returned for that instance's call to sample().
Subclasses should override class method _param_shapes.
sample_shape
Tensor or python list/tuple. Desired shape of a call to
sample().
name
dict of parameter name to Tensor shapes.
param_static_shapes@classmethodparam_static_shapes( sample_shape )
param_shapes with static (i.e. TensorShape) shapes.
This is a class method that describes what key/value arguments are required
to instantiate the given Distribution so that a particular shape is
returned for that instance's call to sample(). Assumes that the sample's
shape is known statically.
Subclasses should override class method _param_shapes to return
constant-valued tensors when constant values are fed.
sample_shape
TensorShape or python list/tuple. Desired shape of a call
to sample().
dict of parameter name to TensorShape.
ValueError
sample_shape is a TensorShape and is not fully defined.
probprob(
value, name='prob'
)
Probability density/mass function.
value
float or double Tensor.
name
str prepended to names of ops created by this function.
prob
Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
quantilequantile(
value, name='quantile'
)
Quantile function. Aka "inverse cdf" or "percent point function".
Given random variable X and p in [0, 1], the quantile is:
quantile(p) := x such that P[X <= x] == p
value
float or double Tensor.
name
str prepended to names of ops created by this function.
quantile
Tensor of shape sample_shape(x) + self.batch_shape with
values of type self.dtype.
samplesample(
sample_shape=(), seed=None, name='sample'
)
Generate samples of the specified shape.
Note that a call to sample() without arguments will generate a single
sample.
sample_shape
int32 Tensor. Shape of the generated samples.
seed
name
samples
Tensor with prepended dimensions sample_shape.
stddevstddev(
name='stddev'
)
Standard deviation.
Standard deviation is defined as,
stddev = E[(X - E[X])**2]**0.5
where X is the random variable associated with this distribution, E
denotes expectation, and stddev.shape = batch_shape + event_shape.
name
str prepended to names of ops created by this function.
stddev
Tensor with shape identical to
batch_shape + event_shape, i.e., the same shape as self.mean().
survival_functionsurvival_function(
value, name='survival_function'
)
Survival function.
Given random variable X, the survival function is defined:
survival_function(x) = P[X > x]
= 1 - P[X <= x]
= 1 - cdf(x).
value
float or double Tensor.
name
str prepended to names of ops created by this function.
Tensor of shape sample_shape(x) + self.batch_shape with values of type
self.dtype.
variancevariance(
name='variance'
)
Variance.
Variance is defined as,
Var = E[(X - E[X])**2]
where X is the random variable associated with this distribution, E
denotes expectation, and Var.shape = batch_shape + event_shape.
name
str prepended to names of ops created by this function.
variance
Tensor with shape identical to
batch_shape + event_shape, i.e., the same shape as self.mean().
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Last updated 2024-04-26 UTC.