python - 如何在 TensorFlow 中设置矢量化参数的双射器？

Question

我遵循本教程的第三个示例的逻辑 GaussianProcessRegressionModel 。但是，我的设置的差异之一是我的振幅和长度比例是矢量。但是，我很难为矢量化参数设置双射器。

我尝试了官方示例教程中的一种方法(click here 并搜索关键字“Batching Bijectors”)。

他们使用

softplus = tfp.bijectors.Softplus(
  hinge_softness=[1., .5, .1])
print("Hinge softness shape:", softplus.hinge_softness.shape)

更改标量参数的 Softplus 形状。但控制台一直显示相同的错误消息。

我的compute_joint_log_prob_3只是输出给定所有数据和参数的标量对数后验概率。而且我测试过这个功能运行良好。唯一的问题是在存在矢量化内核超参数的情况下设置 unconstrained_bijectors。

# Create a list to save all variables to be iterated.
initial_chain_states = [
    tf.ones([1, num_GPs], dtype=tf.float32, name="init_amp_1"),
    tf.ones([1, num_GPs], dtype=tf.float32, name="init_scale_1"),
    tf.ones([1, num_GPs], dtype=tf.float32, name="init_amp_0"),
    tf.ones([1, num_GPs], dtype=tf.float32, name="init_scale_0"),
    tf.ones([], dtype=tf.float32, name="init_sigma_sq_1"),
    tf.ones([], dtype=tf.float32, name="init_sigma_sq_0")
]

vectorized_sp = tfb.Softplus(hinge_softness=np.ones([1, num_GPs], dtype=np.float32))

unconstrained_bijectors = [
    vectorized_sp,
    vectorized_sp,
    vectorized_sp,
    vectorized_sp,
    tfp.bijectors.Softplus(),
    tfp.bijectors.Softplus()
]

def un_normalized_log_posterior(amplitude_1, length_scale_1,
                                amplitude_0, length_scale_0,
                                noise_var_1, noise_var_0):
    return compute_joint_log_prob_3(
        para_index, delayed_signal, y_type,
        amplitude_1, length_scale_1, amplitude_0, length_scale_0,
        noise_var_1, noise_var_0
    )

num_results = 200
[
    amps_1,
    scales_1,
    amps_0,
    scales_0,
    sigma_sqs_1,
    sigma_sqs_0
], kernel_results = tfp.mcmc.sample_chain(
    num_results=num_results,
    num_burnin_steps=250,
    num_steps_between_results=3,
    current_state=initial_chain_states,
    kernel=tfp.mcmc.TransformedTransitionKernel(
        inner_kernel=tfp.mcmc.HamiltonianMonteCarlo(
            target_log_prob_fn=un_normalized_log_posterior,
            step_size=np.float32(0.1),
            num_leapfrog_steps=3,
            step_size_update_fn=tfp.mcmc.make_simple_step_size_update_policy(
                num_adaptation_steps=100)),
        bijector=unconstrained_bijectors))

它应该可以工作，并且模型将抽取该参数的样本。相反，我收到了一堆错误消息说

Traceback (most recent call last):
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/framework/ops.py", line 1659, in _create_c_op
    c_op = c_api.TF_FinishOperation(op_desc)
tensorflow.python.framework.errors_impl.InvalidArgumentError: Requires start <= limit when delta > 0: 1/0 for 'mcmc_sample_chain/transformed_kernel_bootstrap_results/mh_bootstrap_results/hmc_kernel_bootstrap_results/maybe_call_fn_and_grads/value_and_gradients/softplus_10/forward_log_det_jacobian/range' (op: 'Range') with input shapes: [], [], [] and with computed input tensors: input[0] = <1>, input[1] = <0>, input[2] = <1>.

During handling of the above exception, another exception occurred:

Traceback (most recent call last):
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/runpy.py", line 183, in _run_module_as_main
    mod_name, mod_spec, code = _get_module_details(mod_name, _Error)
  File "/Library/Frameworks/Python.framework/Versions/3.7/lib/python3.7/runpy.py", line 109, in _get_module_details
    __import__(pkg_name)
  File "/MMAR_q/MMAR_q.py", line 237, in <module>
    bijector=unconstrained_bijectors))
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/sample.py", line 235, in sample_chain
    previous_kernel_results = kernel.bootstrap_results(current_state)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/transformed_kernel.py", line 344, in bootstrap_results
    transformed_init_state))
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/hmc.py", line 518, in bootstrap_results
    kernel_results = self._impl.bootstrap_results(init_state)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/metropolis_hastings.py", line 264, in bootstrap_results
    pkr = self.inner_kernel.bootstrap_results(init_state)
  File "/MAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/hmc.py", line 687, in bootstrap_results
    ] = mcmc_util.maybe_call_fn_and_grads(self.target_log_prob_fn, init_state)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/util.py", line 237, in maybe_call_fn_and_grads
    result, grads = _value_and_gradients(fn, fn_arg_list, result, grads)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/util.py", line 185, in _value_and_gradients
    result = fn(*fn_arg_list)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/transformed_kernel.py", line 204, in new_target_log_prob
    event_ndims=event_ndims)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/transformed_kernel.py", line 51, in fn
    for b, e, sp in zip(bijector, event_ndims, transformed_state_parts)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/mcmc/transformed_kernel.py", line 51, in <listcomp>
    for b, e, sp in zip(bijector, event_ndims, transformed_state_parts)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/bijectors/bijector.py", line 1205, in forward_log_det_jacobian
    return self._call_forward_log_det_jacobian(x, event_ndims, name)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/bijectors/bijector.py", line 1177, in _call_forward_log_det_jacobian
    kwargs=kwargs)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/bijectors/bijector.py", line 982, in _compute_inverse_log_det_jacobian_with_caching
    event_ndims)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/bijectors/bijector.py", line 1272, in _reduce_jacobian_det_over_event
    axis=self._get_event_reduce_dims(min_event_ndims, event_ndims))
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow_probability/python/bijectors/bijector.py", line 1284, in _get_event_reduce_dims
    return tf.range(-reduce_ndims, 0)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/ops/math_ops.py", line 1199, in range
    return gen_math_ops._range(start, limit, delta, name=name)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/ops/gen_math_ops.py", line 6746, in _range
    "Range", start=start, limit=limit, delta=delta, name=name)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/framework/op_def_library.py", line 788, in _apply_op_helper
    op_def=op_def)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/util/deprecation.py", line 507, in new_func
    return func(*args, **kwargs)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/framework/ops.py", line 3300, in create_op
    op_def=op_def)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/framework/ops.py", line 1823, in __init__
    control_input_ops)
  File "/MMAR_q/venv/lib/python3.7/site-packages/tensorflow/python/framework/ops.py", line 1662, in _create_c_op
    raise ValueError(str(e))
ValueError: Requires start <= limit when delta > 0: 1/0 for 'mcmc_sample_chain/transformed_kernel_bootstrap_results/mh_bootstrap_results/hmc_kernel_bootstrap_results/maybe_call_fn_and_grads/value_and_gradients/softplus_10/forward_log_det_jacobian/range' (op: 'Range') with input shapes: [], [], [] and with computed input tensors: input[0] = <1>, input[1] = <0>, input[2] = <1>.

我不知道这些输入形状到底意味着什么。感谢您的时间和解释。

--------我是人工分隔线------

与Brian讨论后，我知道自己错在哪里了。该错误消息可能意味着 compute_joint_log_prob_3 的结果不是标量而是其他形状。

正如 Brian 昨天所说，Softplus() 能够根据其输入的张量自动广播。如果我想改变它的柔软度，那么我可以修改hinge_softness=...。

而我在阅读了tutorial on tensorflow distribution shape后也有了更深刻的理解。 .

再次感谢您的澄清...在我知道自己错在哪里之后，这是多么美好的一天...

Answer 1

如果您只想使用铰链软度为 1 的相同 softplus，双射器将广播，您可以编写:

vectorized_sp = tfb.Softplus(hinge_softness=np.float32(1))另请注意，默认值为 1，因此更简单:vectorized_sp = tfb.Softplus()

另外，我建议查看 SimpleStepSizeAdaptation 内核(目前可能仅位于 pip install tfp-nightly 中)。

我认为您看到的实际异常可能是由双射器参数形状与您的潜在状态形状以某种方式冲突引起的。转换后的转换内核需要减少双射器指定的事件维度上的 log_prob。每个潜在变量的 event_ndims 是使用从 target_log_prob_fn 返回的 log_prob 的排名作为目标批处理排名得出的，即尾随事件维度将通过双射器减少。

你能多说一下你想要做什么吗？看起来您正在尝试在一堆 GP 内核 hparam 上运行单条 MCMC 链。如果不了解 compute_joint_log_prob_3 的内部结构，就很难提供太多帮助。