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Buku catatan Catatan Rilis TFP (0.13.0)

Maksud dari notebook ini adalah untuk membantu TFP 0.13.0 "menjadi hidup" melalui beberapa cuplikan kecil - demo kecil dari hal-hal yang dapat Anda capai dengan TFP.

Lihat di TensorFlow.org

Jalankan di Google Colab

Lihat sumber di GitHub

Unduh buku catatan

Pemasangan & impor

!pip3 install -qU tensorflow==2.5.0 tensorflow_probability==0.13.0 tensorflow-datasets inference_gym

import tensorflow as tf
import tensorflow_probability as tfp
assert '0.13' in tfp.__version__, tfp.__version__
assert '2.5' in tf.__version__, tf.__version__

physical_devices = tf.config.list_physical_devices('CPU')
tf.config.set_logical_device_configuration(
    physical_devices[0],
    [tf.config.LogicalDeviceConfiguration(),
     tf.config.LogicalDeviceConfiguration()])

tfd = tfp.distributions
tfb = tfp.bijectors
tfpk = tfp.math.psd_kernels

import matplotlib.pyplot as plt
import numpy as np
import scipy.interpolate
import IPython
import seaborn as sns
import logging

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[?25h

Distribusi [matematika inti]

`BetaQuotient`

Rasio dua variabel acak terdistribusi Beta independen

plt.hist(tfd.BetaQuotient(concentration1_numerator=5.,
                          concentration0_numerator=2.,
                          concentration1_denominator=3.,
                          concentration0_denominator=8.).sample(1_000, seed=(1, 23)),
         bins='auto');

png

`DeterminantalPointProcess`

Distribusi atas himpunan bagian (diwakili sebagai satu-panas) dari himpunan yang diberikan. Sampel mengikuti properti tolakan (probabilitas sebanding dengan volume yang direntang oleh vektor yang sesuai dengan subset titik yang dipilih), yang cenderung ke arah pengambilan sampel subset yang beragam. [Bandingkan dengan sampel Bernoulli iid.]

grid_size = 16
# Generate grid_size**2 pts on the unit square.
grid = np.arange(0, 1, 1./grid_size).astype(np.float32)
import itertools
points = np.array(list(itertools.product(grid, grid)))

# Create the kernel L that parameterizes the DPP.
kernel_amplitude = 2.
kernel_lengthscale = [.1, .15, .2, .25]  # Increasing length scale indicates more points are "nearby", tending toward smaller subsets.
kernel = tfpk.ExponentiatedQuadratic(kernel_amplitude, kernel_lengthscale)
kernel_matrix = kernel.matrix(points, points)

eigenvalues, eigenvectors = tf.linalg.eigh(kernel_matrix)
dpp = tfd.DeterminantalPointProcess(eigenvalues, eigenvectors)
print(dpp)

# The inner-most dimension of the result of `dpp.sample` is a multi-hot
# encoding of a subset of {1, ..., ground_set_size}.
# We will compare against a bernoulli distribution.
samps_dpp = dpp.sample(seed=(1, 2))  # 4 x grid_size**2
logits = tf.broadcast_to([[-1.], [-1.5], [-2], [-2.5]], [4, grid_size**2])
samps_bern = tfd.Bernoulli(logits=logits).sample(seed=(2, 3))

plt.figure(figsize=(12, 6))
for i, (samp, samp_bern) in enumerate(zip(samps_dpp, samps_bern)):
  plt.subplot(241 + i)
  plt.scatter(*points[np.where(samp)].T)
  plt.title(f'DPP, length scale={kernel_lengthscale[i]}')
  plt.xticks([])
  plt.yticks([])
  plt.gca().set_aspect(1.)
  plt.subplot(241 + i + 4)
  plt.scatter(*points[np.where(samp_bern)].T)
  plt.title(f'bernoulli, logit={logits[i,0]}')
  plt.xticks([])
  plt.yticks([])
  plt.gca().set_aspect(1.)

plt.tight_layout()
plt.show()

tfp.distributions.DeterminantalPointProcess("DeterminantalPointProcess", batch_shape=[4], event_shape=[256], dtype=int32)

png

`SigmoidBeta`

Log-peluang dari dua distribusi gamma. Lebih numerik ruang sampel stabil daripada Beta .

plt.hist(tfd.SigmoidBeta(concentration1=.01, concentration0=2.).sample(10_000, seed=(1, 23)),
         bins='auto', density=True);
plt.show()

print('Old way, fractions non-finite:')
print(np.sum(~tf.math.is_finite(
    tfb.Invert(tfb.Sigmoid())(tfd.Beta(concentration1=.01, concentration0=2.)).sample(10_000, seed=(1, 23)))) / 10_000)
print(np.sum(~tf.math.is_finite(
    tfb.Invert(tfb.Sigmoid())(tfd.Beta(concentration1=2., concentration0=.01)).sample(10_000, seed=(2, 34)))) / 10_000)

png

Old way, fractions non-finite:
0.4215
0.8624

Zipf

Menambahkan dukungan JAX.

plt.hist(tfd.Zipf(3.).sample(1_000, seed=(12, 34)).numpy(), bins='auto', density=True, log=True);

png

`NormalInverseGaussian`

Keluarga parametrik fleksibel yang mendukung ekor berat, miring, dan vanilla Normal.

`MatrixNormalLinearOperator`

Distribusi normal matriks.

# Initialize a single 2 x 3 Matrix Normal.
mu = [[1., 2, 3], [3., 4, 5]]
col_cov = [[ 0.36,  0.12,  0.06],
           [ 0.12,  0.29, -0.13],
           [ 0.06, -0.13,  0.26]]
scale_column = tf.linalg.LinearOperatorLowerTriangular(tf.linalg.cholesky(col_cov))
scale_row = tf.linalg.LinearOperatorDiag([0.9, 0.8])

mvn = tfd.MatrixNormalLinearOperator(loc=mu, scale_row=scale_row, scale_column=scale_column)
mvn.sample()

WARNING:tensorflow:From /usr/local/lib/python3.7/dist-packages/tensorflow/python/ops/linalg/linear_operator_kronecker.py:224: LinearOperator.graph_parents (from tensorflow.python.ops.linalg.linear_operator) is deprecated and will be removed in a future version.
Instructions for updating:
Do not call `graph_parents`.
<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[1.2495145, 1.549366 , 3.2748342],
       [3.7330258, 4.3413105, 4.83423  ]], dtype=float32)>

`MatrixStudentTLinearOperator`

Distribusi matriks T.

mu = [[1., 2, 3], [3., 4, 5]]
col_cov = [[ 0.36,  0.12,  0.06],
           [ 0.12,  0.29, -0.13],
           [ 0.06, -0.13,  0.26]]
scale_column = tf.linalg.LinearOperatorLowerTriangular(tf.linalg.cholesky(col_cov))
scale_row = tf.linalg.LinearOperatorDiag([0.9, 0.8])

mvn = tfd.MatrixTLinearOperator(
    df=2.,
    loc=mu,
    scale_row=scale_row,
    scale_column=scale_column)
mvn.sample()

<tf.Tensor: shape=(2, 3), dtype=float32, numpy=
array([[1.6549466, 2.6708362, 2.8629923],
       [2.1222284, 3.6904747, 5.08014  ]], dtype=float32)>

Distribusi [perangkat lunak / pembungkus]

`Sharded`

Pecahan bagian acara independen dari distribusi di beberapa prosesor. Agregat log_prob seluruh perangkat, menangani gradien dalam konser dengan tfp.experimental.distribute.JointDistribution* . Jauh lebih dalam Inference Distributed notebook.

strategy = tf.distribute.MirroredStrategy()

@tf.function
def sample_and_lp(seed):
  d = tfp.experimental.distribute.Sharded(tfd.Normal(0, 1))
  s = d.sample(seed=seed)
  return s, d.log_prob(s)

strategy.run(sample_and_lp, args=(tf.constant([12,34]),))

WARNING:tensorflow:There are non-GPU devices in `tf.distribute.Strategy`, not using nccl allreduce.
WARNING:tensorflow:Collective ops is not configured at program startup. Some performance features may not be enabled.
INFO:tensorflow:Using MirroredStrategy with devices ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1')
INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').
(PerReplica:{
   0: <tf.Tensor: shape=(), dtype=float32, numpy=0.0051413667>,
   1: <tf.Tensor: shape=(), dtype=float32, numpy=-0.3393052>
 }, PerReplica:{
   0: <tf.Tensor: shape=(), dtype=float32, numpy=-1.8954543>,
   1: <tf.Tensor: shape=(), dtype=float32, numpy=-1.8954543>
 })

`BatchBroadcast`

Secara implisit menyiarkan dimensi batch distribusi yang mendasari dengan atau bentuk batch yang diberikan.

underlying = tfd.MultivariateNormalDiag(tf.zeros([7, 1, 5]), tf.ones([5]))
print('underlying:', underlying)

d = tfd.BatchBroadcast(underlying, [8, 1, 6])
print('broadcast [7, 1] *with* [8, 1, 6]:', d)

try:
  tfd.BatchBroadcast(underlying, to_shape=[8, 1, 6])
except ValueError as e:
  print('broadcast [7, 1] *to* [8, 1, 6] is invalid:', e)

d = tfd.BatchBroadcast(underlying, to_shape=[8, 7, 6])
print('broadcast [7, 1] *to* [8, 7, 6]:', d)

underlying: tfp.distributions.MultivariateNormalDiag("MultivariateNormalDiag", batch_shape=[7, 1], event_shape=[5], dtype=float32)
broadcast [7, 1] *with* [8, 1, 6]: tfp.distributions.BatchBroadcast("BatchBroadcastMultivariateNormalDiag", batch_shape=[8, 7, 6], event_shape=[5], dtype=float32)
broadcast [7, 1] *to* [8, 1, 6] is invalid: Argument `to_shape` ([8 1 6]) is incompatible with underlying distribution batch shape ((7, 1)).
broadcast [7, 1] *to* [8, 7, 6]: tfp.distributions.BatchBroadcast("BatchBroadcastMultivariateNormalDiag", batch_shape=[8, 7, 6], event_shape=[5], dtype=float32)

`Masked`

Untuk single-Program / multiple-data atau penggunaan-kasus jarang-sebagai-bertopeng padat, distribusi yang masker keluar log_prob distribusi yang mendasari tidak valid.

d = tfd.Masked(tfd.Normal(tf.zeros([7]), 1), 
               validity_mask=tf.sequence_mask([3, 4], 7))
print(d.log_prob(d.sample(seed=(1, 1))))

d = tfd.Masked(tfd.Normal(0, 1), 
               validity_mask=[False, True, False],
               safe_sample_fn=tfd.Distribution.mode)
print(d.log_prob(d.sample(seed=(2, 2))))

tf.Tensor(
[[-2.3054113 -1.8524303 -1.2220721  0.         0.         0.

   0.       ]
 [-1.118623  -1.1370811 -1.1574132 -5.884986   0.         0.
   0.       ]], shape=(2, 7), dtype=float32)
tf.Tensor([ 0.         -0.93683904  0.        ], shape=(3,), dtype=float32)

Bijektor

Bijektor
- Menambahkan bijectors ke meniru tf.nest.flatten ( tfb.tree_flatten ) dan tf.nest.pack_sequence_as ( tfb.pack_sequence_as ).
- Menambahkan tfp.experimental.bijectors.Sharded
- Hapus usang tfb.ScaleTrilL . Gunakan tfb.FillScaleTriL gantinya.
- Menambahkan cls.parameter_properties() penjelasan untuk Bijectors.
- Memperluas jangkauan tfb.Power untuk semua real untuk kekuatan bilangan bulat ganjil.
- Menyimpulkan log-deg-jacobian bijector skalar menggunakan autodiff, jika tidak ditentukan lain.

Restrukturisasi bijector

ex = (tf.constant(1.), dict(b=tf.constant(2.), c=tf.constant(3.)))
b = tfb.tree_flatten(ex)
print(b.forward(ex))
print(b.inverse(list(tf.constant([1., 2, 3]))))

b = tfb.pack_sequence_as(ex)
print(b.forward(list(tf.constant([1., 2, 3]))))
print(b.inverse(ex))

[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>, <tf.Tensor: shape=(), dtype=float32, numpy=2.0>, <tf.Tensor: shape=(), dtype=float32, numpy=3.0>]
(<tf.Tensor: shape=(), dtype=float32, numpy=1.0>, {'b': <tf.Tensor: shape=(), dtype=float32, numpy=2.0>, 'c': <tf.Tensor: shape=(), dtype=float32, numpy=3.0>})
(<tf.Tensor: shape=(), dtype=float32, numpy=1.0>, {'b': <tf.Tensor: shape=(), dtype=float32, numpy=2.0>, 'c': <tf.Tensor: shape=(), dtype=float32, numpy=3.0>})
[<tf.Tensor: shape=(), dtype=float32, numpy=1.0>, <tf.Tensor: shape=(), dtype=float32, numpy=2.0>, <tf.Tensor: shape=(), dtype=float32, numpy=3.0>]

`Sharded`

Pengurangan SPMD di log-determinan. Lihat Sharded di Distribusi, di bawah ini.

strategy = tf.distribute.MirroredStrategy()

def sample_lp_logdet(seed):
  d = tfd.TransformedDistribution(tfp.experimental.distribute.Sharded(tfd.Normal(0, 1), shard_axis_name='i'),
                                  tfp.experimental.bijectors.Sharded(tfb.Sigmoid(), shard_axis_name='i'))
  s = d.sample(seed=seed)
  return s, d.log_prob(s), d.bijector.inverse_log_det_jacobian(s)
strategy.run(sample_lp_logdet, (tf.constant([1, 2]),))

WARNING:tensorflow:There are non-GPU devices in `tf.distribute.Strategy`, not using nccl allreduce.
WARNING:tensorflow:Collective ops is not configured at program startup. Some performance features may not be enabled.
INFO:tensorflow:Using MirroredStrategy with devices ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1')
WARNING:tensorflow:Using MirroredStrategy eagerly has significant overhead currently. We will be working on improving this in the future, but for now please wrap `call_for_each_replica` or `experimental_run` or `run` inside a tf.function to get the best performance.
INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').
INFO:tensorflow:Reduce to /job:localhost/replica:0/task:0/device:CPU:0 then broadcast to ('/job:localhost/replica:0/task:0/device:CPU:0', '/job:localhost/replica:0/task:0/device:CPU:1').
(PerReplica:{
   0: <tf.Tensor: shape=(), dtype=float32, numpy=0.87746525>,
   1: <tf.Tensor: shape=(), dtype=float32, numpy=0.24580425>
 }, PerReplica:{
   0: <tf.Tensor: shape=(), dtype=float32, numpy=-0.48870325>,
   1: <tf.Tensor: shape=(), dtype=float32, numpy=-0.48870325>
 }, PerReplica:{
   0: <tf.Tensor: shape=(), dtype=float32, numpy=3.9154015>,
   1: <tf.Tensor: shape=(), dtype=float32, numpy=3.9154015>
 })

VI

Menambahkan build_split_flow_surrogate_posterior untuk tfp.experimental.vi untuk build terstruktur VI posteriors pengganti dari normalisasi mengalir.
Menambahkan build_affine_surrogate_posterior untuk tfp.experimental.vi untuk pembangunan advi posteriors pengganti dari bentuk acara.
Menambahkan build_affine_surrogate_posterior_from_base_distribution untuk tfp.experimental.vi untuk memungkinkan pembangunan posteriors advi pengganti dengan struktur korelasi yang disebabkan oleh transformasi affine.

VI/MAP/MLE

Ditambahkan metode convenience tfp.experimental.util.make_trainable(cls) untuk membuat contoh dilatih distribusi dan bijectors.

d = tfp.experimental.util.make_trainable(tfd.Gamma)
print(d.trainable_variables)
print(d)

(<tf.Variable 'Gamma_trainable_variables/concentration:0' shape=() dtype=float32, numpy=1.0296053>, <tf.Variable 'Gamma_trainable_variables/log_rate:0' shape=() dtype=float32, numpy=-0.3465951>)
tfp.distributions.Gamma("Gamma", batch_shape=[], event_shape=[], dtype=float32)

MCMC

Diagnostik MCMC mendukung struktur status yang berubah-ubah, bukan hanya daftar.
remc_thermodynamic_integrals ditambahkan ke tfp.experimental.mcmc
Menambahkan tfp.experimental.mcmc.windowed_adaptive_hmc
Menambahkan API eksperimental untuk menginisialisasi rantai Markov dari distribusi seragam yang mendekati nol di ruang yang tidak dibatasi. tfp.experimental.mcmc.init_near_unconstrained_zero
Menambahkan utilitas eksperimental untuk mencoba ulang inisialisasi Rantai Markov hingga titik yang dapat diterima ditemukan. tfp.experimental.mcmc.retry_init
Mengacak-acak API MCMC streaming eksperimental ke slot ke tfp.mcmc dengan gangguan minimal.
Menambahkan ThinningKernel ke experimental.mcmc .
Menambahkan experimental.mcmc.run_kernel driver sebagai calon streaming yang berbasis pengganti untuk mcmc.sample_chain

`init_near_unconstrained_zero` , `retry_init`

@tfd.JointDistributionCoroutine
def model():
  Root = tfd.JointDistributionCoroutine.Root
  c0 = yield Root(tfd.Gamma(2, 2, name='c0'))
  c1 = yield Root(tfd.Gamma(2, 2, name='c1'))
  counts = yield tfd.Sample(tfd.BetaBinomial(23, c1, c0), 10, name='counts')
jd = model.experimental_pin(counts=model.sample(seed=[20, 30]).counts)

init_dist = tfp.experimental.mcmc.init_near_unconstrained_zero(jd)
print(init_dist)

tfp.experimental.mcmc.retry_init(init_dist.sample, jd.unnormalized_log_prob)

tfp.distributions.TransformedDistribution("default_joint_bijectorrestructureJointDistributionSequential", batch_shape=StructTuple(
  c0=[],
  c1=[]
), event_shape=StructTuple(
  c0=[],
  c1=[]
), dtype=StructTuple(
  c0=float32,
  c1=float32
))
StructTuple(
  c0=<tf.Tensor: shape=(), dtype=float32, numpy=1.7879653>,
  c1=<tf.Tensor: shape=(), dtype=float32, numpy=0.34548905>
)

Sampler HMC dan NUTS adaptif berjendela

fig, ax = plt.subplots(1, 2, figsize=(10, 4))
for i, n_evidence in enumerate((10, 250)):
  ax[i].set_title(f'n evidence = {n_evidence}')
  ax[i].set_xlim(0, 2.5); ax[i].set_ylim(0, 3.5)
  @tfd.JointDistributionCoroutine
  def model():
    Root = tfd.JointDistributionCoroutine.Root
    c0 = yield Root(tfd.Gamma(2, 2, name='c0'))
    c1 = yield Root(tfd.Gamma(2, 2, name='c1'))
    counts = yield tfd.Sample(tfd.BetaBinomial(23, c1, c0), n_evidence, name='counts')
  s = model.sample(seed=[20, 30])
  print(s)
  jd = model.experimental_pin(counts=s.counts)
  states, trace = tf.function(tfp.experimental.mcmc.windowed_adaptive_hmc)(
      100, jd, num_leapfrog_steps=5, seed=[100, 200])
  ax[i].scatter(states.c0.numpy().reshape(-1), states.c1.numpy().reshape(-1), 
                marker='+', alpha=.1)
  ax[i].scatter(s.c0, s.c1, marker='+', color='r')

StructTuple(
  c0=<tf.Tensor: shape=(), dtype=float32, numpy=0.7161876>,
  c1=<tf.Tensor: shape=(), dtype=float32, numpy=1.7696666>,
  counts=<tf.Tensor: shape=(10,), dtype=float32, numpy=array([ 6., 10., 23.,  7.,  2., 20., 14., 16., 22., 17.], dtype=float32)>
)
WARNING:tensorflow:6 out of the last 6 calls to <function windowed_adaptive_hmc at 0x7fda42bed8c0> triggered tf.function retracing. Tracing is expensive and the excessive number of tracings could be due to (1) creating @tf.function repeatedly in a loop, (2) passing tensors with different shapes, (3) passing Python objects instead of tensors. For (1), please define your @tf.function outside of the loop. For (2), @tf.function has experimental_relax_shapes=True option that relaxes argument shapes that can avoid unnecessary retracing. For (3), please refer to https://www.tensorflow.org/guide/function#controlling_retracing and https://www.tensorflow.org/api_docs/python/tf/function for  more details.
StructTuple(
  c0=<tf.Tensor: shape=(), dtype=float32, numpy=0.7161876>,
  c1=<tf.Tensor: shape=(), dtype=float32, numpy=1.7696666>,
  counts=<tf.Tensor: shape=(250,), dtype=float32, numpy=
    array([ 6., 10., 23.,  7.,  2., 20., 14., 16., 22., 17., 22., 21.,  6.,
           21., 12., 22., 23., 16., 18., 21., 16., 17., 17., 16., 21., 14.,
           23., 15., 10., 19.,  8., 23., 23., 14.,  1., 23., 16., 22., 20.,
           20., 22., 15., 16., 20., 20., 21., 23., 22., 21., 15., 18., 23.,
           12., 16., 19., 23., 18.,  5., 22., 22., 22., 18., 12., 17., 17.,
           16.,  8., 22., 20., 23.,  3., 12., 14., 18.,  7., 19., 19.,  9.,
           10., 23., 14., 22., 22., 21., 13., 23., 14., 23., 10., 17., 23.,
           17., 20., 16., 20., 19., 14.,  0., 17., 22., 12.,  2., 17., 15.,
           14., 23., 19., 15., 23.,  2., 21., 23., 21.,  7., 21., 12., 23.,
           17., 17.,  4., 22., 16., 14., 19., 19., 20.,  6., 16., 14., 18.,
           21., 12., 21., 21., 22.,  2., 19., 11.,  6., 19.,  1., 23., 23.,
           14.,  6., 23., 18.,  8., 20., 23., 13., 20., 18., 23., 17., 22.,
           23., 20., 18., 22., 16., 23.,  9., 22., 21., 16., 20., 21., 16.,
           23.,  7., 13., 23., 19.,  3., 13., 23., 23., 13., 19., 23., 20.,
           18.,  8., 19., 14., 12.,  6.,  8., 23.,  3., 13., 21., 23., 22.,
           23., 19., 22., 21., 15., 22., 21., 21., 23.,  9., 19., 20., 23.,
           11., 23., 14., 23., 14., 21., 21., 10., 23.,  9., 13.,  1.,  8.,
            8., 20., 21., 21., 21., 14., 16., 16.,  9., 23., 22., 11., 23.,
           12., 18.,  1., 23.,  9.,  3., 21., 21., 23., 22., 18., 23., 16.,
            3., 11., 16.], dtype=float32)>
)

png

Matematika, statistik

Matematika/linal
- Menambahkan tfp.math.trapz untuk integrasi trapesium.
- Menambahkan tfp.math.log_bessel_kve .
- Menambahkan no_pivot_ldl ke experimental.linalg .
- Menambahkan marginal_fn argumen untuk GaussianProcess (lihat no_pivot_ldl ).
- Ditambahkan tfp.math.atan_difference(x, y)
- Menambahkan tfp.math.erfcx , tfp.math.logerfc dan tfp.math.logerfcx
- Menambahkan tfp.math.dawsn untuk Integral Dawson.
- Menambahkan tfp.math.igammaincinv , tfp.math.igammacinv .
- Menambahkan tfp.math.sqrt1pm1 .
- Menambahkan LogitNormal.stddev_approx dan LogitNormal.variance_approx
- Menambahkan tfp.math.owens_t untuk fungsi T Owen.
- Menambahkan bracket_root metode untuk batas otomatis initialize untuk pencarian akar.
- Tambahkan metode Chandrupatla untuk menemukan akar fungsi skalar.
Statistik
- tfp.stats.windowed_mean cara efisien menghitung windowed.
- tfp.stats.windowed_variance efisien dan akurat Toedjoe menghitung berjendela varians.
- tfp.stats.cumulative_variance efisien dan akurat menghitung varians kumulatif.
- RunningCovariance dan teman-teman sekarang dapat diinisialisasi dari contoh Tensor, bukan hanya dari bentuk eksplisit dan dtype.
- Cleaner API untuk RunningCentralMoments , RunningMean , RunningPotentialScaleReduction .

Fungsi Owen's T, Erfcx, Logerfc, Logerfcx, Dawson

# Owen's T gives the probability that X > h, 0 < Y < a * X. Let's check that
# with random sampling.
h = np.array([1., 2.]).astype(np.float32)
a = np.array([10., 11.5]).astype(np.float32)
probs = tfp.math.owens_t(h, a)

x = tfd.Normal(0., 1.).sample(int(1e5), seed=(6, 245)).numpy()
y = tfd.Normal(0., 1.).sample(int(1e5), seed=(7, 245)).numpy()

true_values = (
    (x[..., np.newaxis] > h) &
    (0. < y[..., np.newaxis]) &
    (y[..., np.newaxis] < a * x[..., np.newaxis]))

print('Calculated values: {}'.format(
    np.count_nonzero(true_values, axis=0) / 1e5))

print('Expected values: {}'.format(probs))

Calculated values: [0.07896 0.01134]
Expected values: [0.07932763 0.01137507]

x = np.linspace(-3., 3., 100)
plt.plot(x, tfp.math.erfcx(x))
plt.ylabel('$erfcx(x)$')
plt.show()

plt.plot(x, tfp.math.logerfcx(x))
plt.ylabel('$logerfcx(x)$')
plt.show()

plt.plot(x, tfp.math.logerfc(x))
plt.ylabel('$logerfc(x)$')
plt.show()

plt.plot(x, tfp.math.dawsn(x))
plt.ylabel('$dawsn(x)$')
plt.show()

png

igammainv / igammacinv

# Igammainv and Igammacinv are inverses to Igamma and Igammac

x = np.linspace(1., 10., 10)
y = tf.math.igamma(0.3, x)
x_prime = tfp.math.igammainv(0.3, y)
print('x: {}'.format(x))
print('igammainv(igamma(a, x)):\n {}'.format(x_prime))

y = tf.math.igammac(0.3, x)
x_prime = tfp.math.igammacinv(0.3, y)

print('\n')
print('x: {}'.format(x))
print('igammacinv(igammac(a, x)):\n {}'.format(x_prime))

x: [ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]
igammainv(igamma(a, x)):
 [1.        1.9999992 3.000003  4.0000024 5.0000257 5.999887  7.0002484
 7.999243  8.99872   9.994673 ]


x: [ 1.  2.  3.  4.  5.  6.  7.  8.  9. 10.]
igammacinv(igammac(a, x)):
 [1.       2.       3.       4.       5.       6.       7.       8.000001

 9.       9.999999]

log-kve

x = np.linspace(0., 5., 100)
for v in [0.5, 2., 3]:
  plt.plot(x, tfp.math.log_bessel_kve(v, x).numpy())

plt.title('Log(BesselKve(v, x)')

Text(0.5, 1.0, 'Log(BesselKve(v, x)')

png

Lainnya

STS
- Mempercepat STS peramalan dan dekomposisi menggunakan internal yang tf.function pembungkus.
- Tambahkan opsi untuk mempercepat penyaringan di LinearGaussianSSM ketika hasil hanya langkah terakhir yang diperlukan.
- Variasional Inferensi dengan distribusi bersama: misalnya notebook dengan model Radon .
- Tambahkan dukungan eksperimental untuk mengubah distribusi apa pun menjadi bijektor prakondisi.
Menambahkan tfp.random.sanitize_seed .
Menambahkan tfp.random.spherical_uniform .

plt.figure(figsize=(4, 4))
seed = tfp.random.sanitize_seed(123)
seed1, seed2 = tfp.random.split_seed(seed)
samps = tfp.random.spherical_uniform([30], dimension=2, seed=seed1)
plt.scatter(*samps.numpy().T, marker='+')
samps = tfp.random.spherical_uniform([30], dimension=2, seed=seed2)
plt.scatter(*samps.numpy().T, marker='+');

png

Buku catatan Catatan Rilis TFP (0.13.0)

Pemasangan & impor

Distribusi [matematika inti]

BetaQuotient

DeterminantalPointProcess

SigmoidBeta

Zipf

NormalInverseGaussian

MatrixNormalLinearOperator

MatrixStudentTLinearOperator

Distribusi [perangkat lunak / pembungkus]

Sharded

BatchBroadcast

Masked

Bijektor

Restrukturisasi bijector

Sharded

VI

VI/MAP/MLE

MCMC

init_near_unconstrained_zero , retry_init

Sampler HMC dan NUTS adaptif berjendela

Matematika, statistik

Fungsi Owen's T, Erfcx, Logerfc, Logerfcx, Dawson

igammainv / igammacinv

log-kve

Lainnya

`BetaQuotient`

`DeterminantalPointProcess`

`SigmoidBeta`

`NormalInverseGaussian`

`MatrixNormalLinearOperator`

`MatrixStudentTLinearOperator`

`Sharded`

`BatchBroadcast`

`Masked`

`Sharded`

`init_near_unconstrained_zero` , `retry_init`