特定于都会区的TypeError：此操作的输入的可广播模式不正确

Question

我正在尝试在PyMC3中建立一个多层，多维贝叶斯模型。对于这个问题，我将使用具有以下图形结构的较小的玩具模型：

其中G代表基因，K细胞类型和C_k细胞类型的k细胞。总体而言，该模型表示从不同细胞类型的细胞集合中采样的基因转录本，其中存在一些通过细胞类型平均表达水平mu_gk和特定于细胞的捕获效率{{1} }。

当我使用NUTS对该玩具模型进行采样时，它可以正常工作并恢复合理的后验分布：

p_kc

但是，当我尝试通过Metropolis进行采样时，例如

import numpy as np
import pymc3 as pm
import theano.tensor as tt


# Generative model for data simulation
def sample_data(G=1, K=2, C_k=100):
    mu_gk = np.random.randint(1, 1000, size=(G, K))
    p_kc = np.random.beta(5, 95, (K, C_k))
    N_gkc = np.random.binomial(mu_gk[:, :, np.newaxis], p_kc[np.newaxis, :, :])

    return N_gkc


G = 10    # genes
K = 5     # cell types
C_k = 20  # cells per type

data = sample_data(G, K, C_k)

with pm.Model() as capture_efficiency:

    # Genes expression levels per cell type
    mu_gk = pm.Uniform('mu_gk', 1, 1000, shape=(G, K, 1))

    # Cell capture efficiencies
    p_kc = pm.Beta('p_kc', shape=(1, K, C_k), alpha=5, beta=95)

    # Captured transcripts
    N_gkc = pm.Binomial('N_gkc', shape=(G, K, C_k),
                        n=tt.tensordot(mu_gk, np.ones((C_k, 1)), [[2], [1]]),
                        p=tt.tensordot(np.ones((G, 1)), p_kc, [[1], [0]]),
                        observed=data)

    trace = pm.sample(5000, tune=10000, target_accept=0.99)

我收到以下堆栈跟踪和错误消息：

    trace = pm.sample(5000, tune=10000, step=pm.Metropolis())

我确实找到了a GitHub issue filed for something along these lines，但是我不清楚在我的情况下有人针对他们的特定模型提出的“解决方法”会如何转化。

我怀疑该模型与遇到的错误最相关的方面是在实例化二项式随机变量时手动广播参数：

Traceback (most recent call last):
  File "/Applications/PyCharm.app/Contents/helpers/pydev/pydev_run_in_console.py", line 52, in run_file
    pydev_imports.execfile(file, globals, locals)  # execute the script
  File "/Applications/PyCharm.app/Contents/helpers/pydev/_pydev_imps/_pydev_execfile.py", line 18, in execfile
    exec(compile(contents+"\n", file, 'exec'), glob, loc)
  File "/Users/mfansler/Projects/pymc3/intro/capture-efficiency-celltypes.py", line 46, in <module>
    trace = pm.sample(5000, tune=10000,  step=pm.Metropolis(),
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/pymc3/step_methods/arraystep.py", line 65, in __new__
    step.__init__([var], *args, **kwargs)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/pymc3/step_methods/metropolis.py", line 136, in __init__
    self.delta_logp = delta_logp(model.logpt, vars, shared)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/pymc3/step_methods/metropolis.py", line 624, in delta_logp
    [logp0], inarray0 = pm.join_nonshared_inputs([logp], vars, shared)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/pymc3/theanof.py", line 245, in join_nonshared_inputs
    xs_special = [theano.clone(x, replace, strict=False) for x in xs]
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/pymc3/theanof.py", line 245, in <listcomp>
    xs_special = [theano.clone(x, replace, strict=False) for x in xs]
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/scan_module/scan_utils.py", line 247, in clone
    share_inputs)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/compile/pfunc.py", line 232, in rebuild_collect_shared
    cloned_v = clone_v_get_shared_updates(outputs, copy_inputs_over)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/compile/pfunc.py", line 93, in clone_v_get_shared_updates
    clone_v_get_shared_updates(i, copy_inputs_over)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/compile/pfunc.py", line 93, in clone_v_get_shared_updates
    clone_v_get_shared_updates(i, copy_inputs_over)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/compile/pfunc.py", line 93, in clone_v_get_shared_updates
    clone_v_get_shared_updates(i, copy_inputs_over)
  [Previous line repeated 9 more times]
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/compile/pfunc.py", line 96, in clone_v_get_shared_updates
    [clone_d[i] for i in owner.inputs], strict=rebuild_strict)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/gof/graph.py", line 246, in clone_with_new_inputs
    new_node = self.op.make_node(*new_inputs)
  File "/Users/mfansler/anaconda/envs/pymc3/lib/python3.6/site-packages/theano/tensor/elemwise.py", line 230, in make_node
    % (self.input_broadcastable, ib)))
TypeError: The broadcastable pattern of the input is incorrect for this op. Expected (False, False, True), got (False, False, False).

将2D张量“拉伸”为与所需输出形状匹配的3D张量。

在运行Metropolis时应如何实现此模型以避免错误？

Answer 1

对于该玩具模型，使所有参数采样步骤保持平坦似乎已足够：

with pm.Model() as capture_efficiency:

    # Genes expression levels per cell type
    mu_gk_flat = pm.Uniform('mu_gk', 1, 1000, shape=G*K)
    mu_gk = mu_gk_flat.reshape((G, K, 1))

    # Cell capture efficiencies
    p_kc_flat = pm.Beta('p_kc', shape=K*C_k, alpha=5, beta=95)
    p_kc = p_kc_flat.reshape((1, K, C_k))

    # Captured transcripts
    N_gkc = pm.Binomial('N_gkc', shape=(G, K, C_k),
                        n=tt.tensordot(mu_gk, np.ones((C_k, 1)), [[2], [1]]),
                        p=tt.tensordot(np.ones((G, 1)), p_kc, [[1], [0]]),
                        observed=data)

    trace = pm.sample(5000, tune=10000, step=pm.Metropolis())

N_gkc似乎在张量形式上很好，也许是因为它仅涉及似然计算而不是实际的采样步骤。

仅从这个玩具示例来看，尚不清楚是否还需要将其他层次结构层次化。