為什么我的 pymc3 采樣器在 Jupyter 筆記本中使用 C 代碼？

Question

我在 Anaconda Jupyter 筆記本中遇到問題，我在其中運行 pymc3 采樣器從正態分布的后部進行采樣。

import autograd.numpy as np
import pymc3 as pm
from pymc3 import Model
import theano.tensor as Th
from scipy.special import softmax


def pymc3_sampling_test(out_last_hidden_layer, output_dim, y, D, mu_wanted=0, tau_wanted=1, samples_wanted=100,
                       number_chains=2):
        """
        :param out_last_hidden_layer: the feature map after the trained Neural network
        :param output_dim: the output dimension (= number of classes)
        :param y: your training labels
        :param D: the number of hidden nodes (is also the dimensionnality of the output of the feature map)
        :param mu_wanted: mu of the normal prior
        :param tau_wanted: precision of the normal prior
        :param samples_wanted: number of samples generated
        :param number_chains: number of chains ran
        :return: samples from the posterior of the Bayesian Logistic regression
        """
        initialization_pymc3 = nlm.get_feature_map_weights()
        with pm.Model() as replacing_HMC:
            w = pm.Normal('w', mu=0, tau=tau_wanted, shape=(D * output_dim + output_dim))
            linear_combinations = []
            for j in range(output_dim):
                dot = pm.math.dot(out_last_hidden_layer[0].T, w[j * D:j * D + D]) + w[-output_dim+j]
                linear_combi = pm.Deterministic('s' + str(j), dot)
                linear_combinations.append(linear_combi)
            thetas = pm.Deterministic('theta', Th.nnet.softmax(linear_combinations))
            y_obs = pm.Categorical('y_obs', p=thetas.T, observed=y)
            trace = pm.sample(samples_wanted, chains=number_chains)
        return trace
    
    
traces=pymc3_sampling_test( nlm.forward(nlm.weights,X_train.T,partial=True), 4, y_train.T,5)

我的采樣器運行速度非常慢，我按照這個網站上的說明安裝了模塊 theano 和 pip 以及編譯器 clang_osx-64 和 clangxx_osx-64。

這似乎使我的采樣器運行 C 代碼，我在 Mac OSX 10.15.7 上運行 Python 3.8。 這是我的錯誤信息：

You can find the C code in this temporary file: /var/folders/72/7tyqmpr158x1ps3r1z7591pw0000gp/T/theano_compilation_error_rx998tv5
---------------------------------------------------------------------------
Exception                                 Traceback (most recent call last)
<ipython-input-19-5bcc6da39369> in <module>
     33 
     34 
---> 35 traces=pymc3_sampling_test( nlm.forward(nlm.weights,X_train.T,partial=True), 4, y_train.T,5)

<ipython-input-19-5bcc6da39369> in pymc3_sampling_test(out_last_hidden_layer, output_dim, y, D, mu_wanted, tau_wanted, samples_wanted, number_chains)
     27                 linear_combi = pm.Deterministic('s' + str(j), dot)
     28                 linear_combinations.append(linear_combi)
---> 29             thetas = pm.Deterministic('theta', Th.nnet.softmax(linear_combinations))
     30             y_obs = pm.Categorical('y_obs', p=thetas.T, observed=y)
     31             trace = pm.sample(samples_wanted, chains=number_chains)

~/opt/anaconda3/lib/python3.8/site-packages/theano/tensor/nnet/nnet.py in softmax(c)
    813     if c.broadcastable[-1]:
    814         warnings.warn("The softmax is applied on a dimension of shape 1, which does not have a semantic meaning.")
--> 815     return softmax_op(c)
    816 
    817 

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/op.py in __call__(self, *inputs, **kwargs)
    667 
    668                 # compute output value once with test inputs to validate graph
--> 669                 thunk = node.op.make_thunk(node, storage_map, compute_map,
    670                                            no_recycling=[])
    671                 thunk.inputs = [storage_map[v] for v in node.inputs]

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/op.py in make_thunk(self, node, storage_map, compute_map, no_recycling, impl)
    952                               compute_map=compute_map, impl='c')
    953             try:
--> 954                 return self.make_c_thunk(node, storage_map, compute_map,
    955                                          no_recycling)
    956             except (NotImplementedError, utils.MethodNotDefined):

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/op.py in make_c_thunk(self, node, storage_map, compute_map, no_recycling)
    855                 raise NotImplementedError("float16")
    856         _logger.debug('Trying CLinker.make_thunk')
--> 857         outputs = cl.make_thunk(input_storage=node_input_storage,
    858                                 output_storage=node_output_storage)
    859         thunk, node_input_filters, node_output_filters = outputs

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cc.py in make_thunk(self, input_storage, output_storage, storage_map, keep_lock)
   1213         """
   1214         init_tasks, tasks = self.get_init_tasks()
-> 1215         cthunk, module, in_storage, out_storage, error_storage = self.__compile__(
   1216             input_storage, output_storage, storage_map,
   1217             keep_lock=keep_lock)

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cc.py in __compile__(self, input_storage, output_storage, storage_map, keep_lock)
   1151         input_storage = tuple(input_storage)
   1152         output_storage = tuple(output_storage)
-> 1153         thunk, module = self.cthunk_factory(error_storage,
   1154                                             input_storage,
   1155                                             output_storage,

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cc.py in cthunk_factory(self, error_storage, in_storage, out_storage, storage_map, keep_lock)
   1621             for node in self.node_order:
   1622                 node.op.prepare_node(node, storage_map, None, 'c')
-> 1623             module = get_module_cache().module_from_key(
   1624                 key=key, lnk=self, keep_lock=keep_lock)
   1625 

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cmodule.py in module_from_key(self, key, lnk, keep_lock)
   1187             try:
   1188                 location = dlimport_workdir(self.dirname)
-> 1189                 module = lnk.compile_cmodule(location)
   1190                 name = module.__file__
   1191                 assert name.startswith(location)

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cc.py in compile_cmodule(self, location)
   1518         try:
   1519             _logger.debug("LOCATION %s", str(location))
-> 1520             module = c_compiler.compile_str(
   1521                 module_name=mod.code_hash,
   1522                 src_code=src_code,

~/opt/anaconda3/lib/python3.8/site-packages/theano/gof/cmodule.py in compile_str(module_name, src_code, location, include_dirs, lib_dirs, libs, preargs, py_module, hide_symbols)
   2396             # prints the exception, having '\n' in the text makes it more
   2397             # difficult to read.
-> 2398             raise Exception('Compilation failed (return status=%s): %s' %
   2399                             (status, compile_stderr.replace('\n', '. ')))
   2400         elif config.cmodule.compilation_warning and compile_stderr:

Exception: ('Compilation failed (return status=1): In file included from /Users/gaelancel/.theano/compiledir_macOS-10.15.7-x86_64-i386-64bit-i386-3.8.5-64/tmp03mtegep/mod.cpp:1:. In file included from /Users/gaelancel/opt/anaconda3/include/python3.8/Python.h:25:. In file included from /usr/local/include/stdio.h:64:. /usr/local/include/_stdio.h:93:16: warning: pointer is missing a nullability type specifier (_Nonnull, _Nullable, or _Null_unspecified) [-Wnullability-completeness].         unsigned char   *_base;.                         ^. /usr/local/include/_stdio.h:93:16: note: insert \'_Nullable\' if the pointer may be null.         unsigned char   *_base;.

````

Answer 1

Theano 生成和編譯語言代碼（主要是 C）以提高其評估速度（s. https://en.wikipedia.org/wiki/Theano_(software) ）。 PyMC3 依賴於 theano，它的數學運算不能與非 theano 的運算混合（例如scipy.special.softmax ）。

示例代碼崩潰，因為 thenao 操作Th.nnet.softmax只使用至少二維的張量。 在示例中，改為傳遞列表linear_combinations 。

您可以將列表中的張量組合成一個張量，例如，通過

Th.concatenate(linear_combinations, axis=0)

注意： Th.nnet.softmax沿軸 1 運行（s. https://github.com/pymc-devs/Theano-PyMC/issues/183 ）。 因此，您可能希望在將linear_combinations附加到linear_combi之前對其進行轉置。

我運行以下代碼沒有錯誤：

import pymc3 as pm
from pymc3 import Model
import theano.tensor as Th
import numpy as np


def pymc3_sampling_test(out_last_hidden_layer, output_dim, y, D, mu_wanted=0, tau_wanted=1, samples_wanted=100,
                       number_chains=2):
        with pm.Model() as replacing_HMC:
            w = pm.Normal('w', mu=0, tau=tau_wanted, shape=(D * output_dim + output_dim))
            linear_combinations = []
            for j in range(output_dim):
                dot = pm.math.dot(out_last_hidden_layer[0].T, w[j * D:j * D + D]) + w[-output_dim+j]
                linear_combi = pm.Deterministic('s' + str(j), Th.shape_padleft(dot, n_ones=1))
                linear_combinations.append(linear_combi)
            lc = Th.concatenate(linear_combinations, axis=0)
            thetas = pm.Deterministic('theta', Th.nnet.softmax(lc))
            y_obs = pm.Categorical('y_obs', p=thetas.T, observed=y)
            trace = pm.sample(samples_wanted, chains=number_chains)
        return trace

pymc3_sampling_test(np.array([[1,2,3],[4,5,6],[7,8,9]]), 4, [0], 3)

我在 macOS 11.0.1 上使用了 PyMC3 3.9.3。 我安裝了 PyMC3 及其所有依賴項

conda install -c conda-forge pymc3