Improve backprop performance through experimental kalman filter, by c…

…hanging out MVN log_prob calculation.

PiperOrigin-RevId: 579184615

tensorflow_probability/python/experimental/parallel_filter/parallel_kalman_filter_lib.py

@@ -21,6 +21,7 @@
 import tensorflow.compat.v2 as tf
 
 from tensorflow_probability.python.distributions import mvn_tril
+from tensorflow_probability.python.internal import dtype_util
 from tensorflow_probability.python.internal import prefer_static as ps
 from tensorflow_probability.python.internal import samplers
 from tensorflow_probability.python.math import linalg
@@ -625,11 +626,8 @@ def kalman_filter(transition_matrix,
                                                       axis=0),
                                         added_cov=time_dep.observation_cov)
 
-      # TODO(srvasude): The JVP for this can be implemented more efficiently.
-      log_likelihoods = mvn_tril.MultivariateNormalTriL(
-          loc=observation_means,
-          scale_tril=tf.linalg.cholesky(observation_covs)).log_prob(
-              observation.y)
+      log_likelihoods = _mvn_log_prob(
+          observation_means, observation_covs, observation.y)
       if observation.mask is not None:
         log_likelihoods = tf.where(observation.mask,
                                    tf.zeros([], dtype=log_likelihoods.dtype),
@@ -644,6 +642,17 @@ def kalman_filter(transition_matrix,
                          observation_covs)
 
 
+def _mvn_log_prob(mean, covariance, y):
+  cholesky_matrix = tf.linalg.cholesky(covariance)
+  log_prob = -0.5 * linalg.hpsd_quadratic_form_solvevec(
+      covariance, y - mean, cholesky_matrix=cholesky_matrix)
+  log_prob = log_prob - 0.5 * linalg.hpsd_logdet(
+      covariance, cholesky_matrix=cholesky_matrix)
+  event_dims = ps.shape(mean)[-1]
+  return log_prob - 0.5 * event_dims * dtype_util.as_numpy_dtype(
+      mean.dtype)(np.log(2 * np.pi))
+
+
 def _extract_batch_shape(x, sample_ndims, event_ndims):
   """Slice out the batch component of `x`'s shape."""
   if x is None: