TFP 版本说明笔记本 (0.13.0)

此笔记本的目的是通过一些小片段帮助 TFP 0.13.0 “栩栩如生” - 您可以使用 TFP 实现的一些小演示。

在 TensorFlow.org 上查看

在 Google Colab 中运行

在 GitHub 上查看源代码

下载笔记本

安装和导入

!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

|████████████████████████████████| 5.4MB 8.8MB/s 
     |████████████████████████████████| 3.9MB 37.1MB/s 
     |████████████████████████████████| 296kB 31.6MB/s

分布 [核心数学]

`BetaQuotient`

两个独立的 Beta 分布随机变量的比率

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`

给定集合的子集（表示为独热）上的分布。样本遵循排斥性属性（概率与对应于所选点子集的向量所跨越的体积成正比），这倾向于对多样化的子集进行采样。[与 i.i.d. 伯努利样本进行比较。]

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`

两个伽马分布的对数几率。比 Beta 具有更稳定的数值样本空间。

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

添加了 JAX 支持。

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

png

`NormalInverseGaussian`

支持重尾、偏斜和普通正态的灵活参数族。

`MatrixNormalLinearOperator`

矩阵正态分布。

# 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`

矩阵 T 分布。

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)>

分布 [软件/包装器]

`Sharded`

跨多个处理器对分布的独立事件部分进行分片。聚合跨设备的 log_prob，与 tfp.experimental.distribute.JointDistribution* 协同处理梯度。在分布式推理笔记本中了解更多内容。

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`

隐式地将基础分布的批次维度 *与* 或 *到* 给定的批次形状进行广播。

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`

对于单程序/多数据或稀疏作为掩码密集的用例，一个分布，它掩盖了无效基础分布的 log_prob。

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)

双射器

双射器
- 添加双射器以模仿 tf.nest.flatten (tfb.tree_flatten) 和 tf.nest.pack_sequence_as (tfb.pack_sequence_as)。
- 添加 tfp.experimental.bijectors.Sharded
- 删除已弃用的 tfb.ScaleTrilL。使用 tfb.FillScaleTriL 代替。
- 为双射器添加 cls.parameter_properties() 注释。
- 将范围 tfb.Power 扩展到奇数整数幂的所有实数。
- 如果未另行指定，则使用自动微分推断标量双射器的对数度雅可比行列式。

重构双射器

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`

对数行列式的 SPMD 约简。请参阅分布中的 Sharded，如下所示。

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

将 build_split_flow_surrogate_posterior 添加到 tfp.experimental.vi 以从归一化流构建结构化 VI 替代后验。
将 build_affine_surrogate_posterior 添加到 tfp.experimental.vi 以从事件形状构建 ADVI 替代后验。
将 build_affine_surrogate_posterior_from_base_distribution 添加到 tfp.experimental.vi 以启用使用仿射变换诱导的关联结构构建 ADVI 替代后验。

VI/MAP/MLE

添加了便利方法 tfp.experimental.util.make_trainable(cls) 用于创建可训练的分布和双射实例。

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

MCMC 诊断支持任意状态结构，而不仅仅是列表。
remc_thermodynamic_integrals 添加到 tfp.experimental.mcmc
添加了 tfp.experimental.mcmc.windowed_adaptive_hmc
添加了用于从无约束空间中的近零均匀分布初始化马尔可夫链的实验性 API。 tfp.experimental.mcmc.init_near_unconstrained_zero
添加了一个实验性实用程序，用于重试马尔可夫链初始化，直到找到可接受的点。 tfp.experimental.mcmc.retry_init
将实验性流式 MCMC API 重新排列到 tfp.mcmc 中，以最大程度地减少干扰。
添加了 ThinningKernel 到 experimental.mcmc.
添加了 experimental.mcmc.run_kernel 驱动程序，作为基于流的替代 mcmc.sample_chain 的候选者。

`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>
)

窗口自适应 HMC 和 NUTS 采样器

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 reduce_retracing=True option that relaxes argument shapes that can avoid unnecessary retracing. For (3), please refer to https://tensorflowcn.cn/guide/function#controlling_retracing and https://tensorflowcn.cn/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

数学，统计

数学/线性代数
- 添加了 tfp.math.trapz 用于梯形积分。
- 添加了 tfp.math.log_bessel_kve.
- 添加了 no_pivot_ldl 到 experimental.linalg.
- 添加了 marginal_fn 参数到 GaussianProcess（参见 no_pivot_ldl）。
- 添加了 tfp.math.atan_difference(x, y)
- 添加了 tfp.math.erfcx，tfp.math.logerfc 和 tfp.math.logerfcx
- 添加了 tfp.math.dawsn 用于 Dawson 积分。
- 添加了 tfp.math.igammaincinv，tfp.math.igammacinv.
- 添加了 tfp.math.sqrt1pm1.
- 添加了 LogitNormal.stddev_approx 和 LogitNormal.variance_approx
- 添加了 tfp.math.owens_t 用于 Owen 的 T 函数。
- 添加了 bracket_root 方法，用于自动初始化根搜索的边界。
- 添加了 Chandrupatla 的方法，用于查找标量函数的根。
统计
- tfp.stats.windowed_mean 有效地计算窗口均值。
- tfp.stats.windowed_variance 有效且准确地计算窗口方差。
- tfp.stats.cumulative_variance 有效且准确地计算累积方差。
- RunningCovariance 及其相关方法现在可以从示例张量初始化，而不仅仅是从显式形状和数据类型初始化。
- 更清晰的 RunningCentralMoments、RunningMean、RunningPotentialScaleReduction API。

Owen 的 T、Erfc、Logerfc、Logerfcx、Dawson 函数

# 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

其他

STS
- 使用内部 tf.function 包装加速 STS 预测和分解。
- 添加了选项，当仅需要最后一步的结果时，可以加速 LinearGaussianSSM 中的过滤。
- 联合分布的变分推断：使用 Radon 模型的示例笔记本。
- 添加了对将任何分布转换为预处理双射的实验性支持。
添加了 tfp.random.sanitize_seed.
添加了 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

TFP 版本说明笔记本 (0.13.0)

安装和导入

分布 [核心数学]

BetaQuotient

DeterminantalPointProcess

SigmoidBeta

Zipf

NormalInverseGaussian

MatrixNormalLinearOperator

MatrixStudentTLinearOperator

分布 [软件/包装器]

Sharded

BatchBroadcast

Masked

双射器

重构双射器

Sharded

VI

VI/MAP/MLE

MCMC

init_near_unconstrained_zero, retry_init

窗口自适应 HMC 和 NUTS 采样器

数学，统计

Owen 的 T、Erfc、Logerfc、Logerfcx、Dawson 函数

igammainv / igammacinv

log-kve

其他

`BetaQuotient`

`DeterminantalPointProcess`

`SigmoidBeta`

`NormalInverseGaussian`

`MatrixNormalLinearOperator`

`MatrixStudentTLinearOperator`

`Sharded`

`BatchBroadcast`

`Masked`

`Sharded`

`init_near_unconstrained_zero`, `retry_init`