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Computes diagonal of the Jacobian matrix of
tfp.experimental.substrates.numpy.math.diag_jacobian( xs, ys=None, sample_shape=None, fn=None, parallel_iterations=10, name=None )
ys is a tensor or a list of tensors of the form
(ys_1, .., ys_n) and
xs is of the form
(xs_1, .., xs_n), the function
computes the diagonal of the Jacobian matrix, i.e., the partial derivatives
(dys_1/dxs_1,.., dys_n/dxs_n). For definition details, see
Diagonal Hessian of the log-density of a 3D Gaussian distribution
In this example we sample from a standard univariate normal
distribution using MALA with
step_size equal to 0.75.
from tensorflow_probability.python.internal.backend import numpy as tf import tensorflow_probability as tfp; tfp = tfp.experimental.substrates.numpy import numpy as np tfd = tfp.distributions dtype = np.float32 with tf.Session(graph=tf.Graph()) as sess: true_mean = dtype([0, 0, 0]) true_cov = dtype([[1, 0.25, 0.25], [0.25, 2, 0.25], [0.25, 0.25, 3]]) chol = tf.linalg.cholesky(true_cov) target = tfd.MultivariateNormalTriL(loc=true_mean, scale_tril=chol) # Assume that the state is passed as a list of tensors `x` and `y`. # Then the target function is defined as follows: def target_fn(x, y): # Stack the input tensors together z = tf.concat([x, y], axis=-1) - true_mean return target.log_prob(z) sample_shape = [3, 5] state = [tf.ones(sample_shape + , dtype=dtype), tf.ones(sample_shape + , dtype=dtype)] fn_val, grads = tfp.math.value_and_gradient(target_fn, state) # We can either pass the `sample_shape` of the `state` or not, which impacts # computational speed of `diag_jacobian` _, diag_jacobian_shape_passed = diag_jacobian( xs=state, ys=grads, sample_shape=tf.shape(fn_val)) _, diag_jacobian_shape_none = diag_jacobian( xs=state, ys=grads) diag_jacobian_shape_passed_ = sess.run(diag_jacobian_shape_passed) diag_jacobian_shape_none_ = sess.run(diag_jacobian_shape_none) print('hessian computed through `diag_jacobian`, sample_shape passed: ', np.concatenate(diag_jacobian_shape_passed_, -1)) print('hessian computed through `diag_jacobian`, sample_shape skipped', np.concatenate(diag_jacobian_shape_none_, -1))
Tensoror a python
Tensorsof real-like dtypes and shapes
event_shape_ican be different for different tensors.
Tensoror a python
Tensorsof the same dtype as
xs. Must broadcast with the shape of
xs. Can be omitted if
sample_shape: A common
sample_shapeof the input tensors of
xs. If not, provided, assumed to be
, which may result in a slow performance of
fn: Python callable that takes
xsas an argument (or
*xs, if it is a list) and returns
ys. Might be skipped if
ysis provided and
intthat specifies the allowed number of coordinates of the input tensor
xs, for which the partial derivatives
dys_i/dxs_ican be computed in parallel.
strname prefixed to
Opscreated by this function. Default value:
ys: a list, which coincides with the input
ys, when provided. If the input
fn(*xs)gets computed and returned as a list.
Tensoror a Python list of
Tensors of the same dtypes and shapes as the input
xs. This is the diagonal of the Jacobian of ys wrt xs.
ValueError: if lists
yshave different length or both
fnis None in the eager execution mode.