Adds the VonMisesFisher distribution over points on the unit hypersphere.

The sampling algorithm is due to Wood'94.
The pdf currently uses a recurrence for bessel_iN which isn't great for large N (WIP on better bessel_ive).

Tests are based on importance sampling the surface area of a [hyper]spherical cap.

Fixes tensorflow/tensorflow#6141

PiperOrigin-RevId: 205891121

Author: brianwa84

tensorflow_probability/python/distributions/BUILD

@@ -75,6 +75,7 @@ py_library(
         ":vector_laplace_linear_operator",
         ":vector_sinh_arcsinh_diag",
         ":vector_student_t",
+        ":von_mises_fisher",
         ":wishart",
         # numpy dep,
         # tensorflow dep,
@@ -497,6 +498,15 @@ py_library(
     ],
 )
 
+py_library(
+    name = "von_mises_fisher",
+    srcs = ["von_mises_fisher.py"],
+    deps = [
+        # numpy dep,
+        # tensorflow dep,
+    ],
+)
+
 py_library(
     name = "wishart",
     srcs = ["wishart.py"],
@@ -1026,6 +1036,19 @@ py_test(
     ],
 )
 
+py_test(
+    name = "von_mises_fisher_test",
+    size = "medium",
+    srcs = ["von_mises_fisher_test.py"],
+    deps = [
+        ":distributions",
+        # numpy dep,
+        # tensorflow dep,
+        "//tensorflow_probability",
+        "//tensorflow_probability/python/internal:test_util",
+    ],
+)
+
 py_test(
     name = "vector_student_t_test",
     size = "medium",

tensorflow_probability/python/distributions/__init__.py

@@ -74,6 +74,7 @@
 from tensorflow_probability.python.distributions.vector_exponential_diag import VectorExponentialDiag
 from tensorflow_probability.python.distributions.vector_laplace_diag import VectorLaplaceDiag
 from tensorflow_probability.python.distributions.vector_sinh_arcsinh_diag import VectorSinhArcsinhDiag
+from tensorflow_probability.python.distributions.von_mises_fisher import VonMisesFisher
 from tensorflow_probability.python.distributions.wishart import Wishart
 
 from tensorflow_probability.python.internal.distribution_util import fill_triangular
@@ -174,6 +175,7 @@
     'VectorDiffeomixture',
     'VectorLaplaceDiag',
     'VectorSinhArcsinhDiag',
+    'VonMisesFisher',
     'Wishart',
     'TransformedDistribution',
     'QuantizedDistribution',