I am trying to run the following model, but it fails during compilation:

import numpy as np
import pymc3 as pm


def sample_data(G=1, K=2):
    # mean proportion ([0,1]) for each g
    p_g = np.random.beta(2, 2, size=G)

    # concentration around each p_g
    c_g = np.random.lognormal(mean=0.5, sigma=1, size=G)

    # reparameterization for standard Beta(a,b)
    a_g = c_g * p_g / np.sqrt(p_g**2 + (1.-p_g)**2)
    b_g = c_g*(1.-p_g) / np.sqrt(p_g**2 + (1.-p_g)**2)

    # for each p_g, sample K proportions
    p_gk = np.random.beta(a_g[:, np.newaxis], b_g[:, np.newaxis], size=(G, K))

    return p_gk

# Data size
G = 3
K = 5

# obtain a G x K array of proportions p_gk in [0,1]
data = sample_data(G, K) 

with pm.Model() as m:

    # Parameters
    p_g = pm.Beta('p_g', 1., 1., shape=G)
    sd_g = pm.HalfNormal('sd_g', sd=1., shape=G)

    # Observed proportions
    p_gk = pm.Beta('p_gk', mu=p_g, sd=sd_g, shape=(G, K), observed=data)

    trace = pm.sample(2000)

with these errors:

Exception: ("Compilation failed (return status=1):

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:400:27: 
  error: non-constant-expression cannot be narrowed from type 'npy_intp' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
     int init_totals[2] = {V3_n0, V3_n1};.
                           ^~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:400:27:
  note: insert an explicit cast to silence this issue.
     int init_totals[2] = {V3_n0, V3_n1};.
                           ^~~~~.
                           static_cast<int>( ).

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:400:34: 
  error: non-constant-expression cannot be narrowed from type 'npy_intp' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
     int init_totals[2] = {V3_n0, V3_n1};.
                                  ^~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:400:34: 
  note: insert an explicit cast to silence this issue.
     int init_totals[2] = {V3_n0, V3_n1};.
                                  ^~~~~.
                                  static_cast<int>( ).

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:412:9: 
  error: non-constant-expression cannot be narrowed from type 'ssize_t' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
         V3_stride0, V3_stride1, .
         ^~~~~~~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:412:9: 
  note: insert an explicit cast to silence this issue.
         V3_stride0, V3_stride1, .
         ^~~~~~~~~~.
         static_cast<int>( ).

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:412:21: 
  error: non-constant-expression cannot be narrowed from type 'ssize_t' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
         V3_stride0, V3_stride1, .
                     ^~~~~~~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:412:21:
  note: insert an explicit cast to silence this issue.
         V3_stride0, V3_stride1, .
                     ^~~~~~~~~~.
                     static_cast<int>( ).

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:413:1: 
  error: non-constant-expression cannot be narrowed from type 'ssize_t' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
 V1_stride0, V1_stride1.
 ^~~~~~~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:413:1: 
  note: insert an explicit cast to silence this issue.
 V1_stride0, V1_stride1.
 ^~~~~~~~~~.
 static_cast<int>( ).

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:413:13:
  error: non-constant-expression cannot be narrowed from type 'ssize_t' (aka 'long') to 'int' in initializer list [-Wc++11-narrowing].
 V1_stride0, V1_stride1.
             ^~~~~~~~~~.

/Users/mfansler/.theano/compiledir_Darwin-17.6.0-x86_64-i386-64bit-i386-3.6.3-64/tmpr58gulp2/mod.cpp:413:13:
  note: insert an explicit cast to silence this issue.
 V1_stride0, V1_stride1.
             ^~~~~~~~~~.
             static_cast<int>( ).

6 errors generated.. ", '[Elemwise{log,no_inplace}(TensorConstant{[[0.297343..76841722]]})]')

I'm new to PyMC3. I don't see these errors when running existing PyMC3 examples. I suspect that I'm seeing these because I'm using a multidimensional format (i.e., (G,K)), since I haven't seen others using this format (I might be imposing my familiarity with Stan).

Generally, I'm having trouble getting a sense of how to implement multilevel models that have multiple dimensions.

Any idea what is causing the errors I'm seeing?

Versions

python 3.6.3
numpy 1.14.5
Theano 1.0.2
pymc3 3.4.1
Mac OS 10.13.5

Update

I installed the same package versions (via conda) on an HPC node (CentOS 7), and was able to run the modified version of the model suggested by @colcarroll. However, on my OS X machine, I still see the Theano compilation errors indicated above, even with the model changes. Is this possibly a clang problem? Can one specify the compiler for Theano to use?

回答1:

One workaround is to suppress the compilation errors:

import theano

theano.config.gcc.cxxflags = "-Wno-c++11-narrowing"

The extent to which these errors matter for program correctness is unclear. They do not arise when I compile on CentOS 7 (even when explicitly checking for them with -Wc++11-narrowing). The sampling results on Mac OS X with suppressed errors and CentOS without were comparable.

I would still prefer to see an answer that explains the underlying issue.

回答2:

Yes - You do have to be a bit more explicit about shapes for higher dimensions. The library does a little to be "clever", but if you provide the shape argument, it will use that.

Your example here is syntactically fixed by setting

with pm.Model() as m:

    # Parameters
    p_g = pm.Beta('p_g', 1., 1., shape=(G, 1))
    sd_g = pm.HalfNormal('sd_g', sd=1, shape=(G, 1))

    # Observed proportions
    p_gk = pm.Beta('p_gk', mu=p_g.dot(np.ones((1,K))), sd=sd_g.dot(np.ones((1, K))), shape=(G, K), observed=data)
    trace = pm.sample()

Note that running m.check_test_point() wil show that p_gk has 0 probability. This is because sd_g is too wide, and PyMC3 tries to initialize that at 0.8, which is out of the support of a mu, sd parametrized beta distribution.

Setting sd_g = pm.HalfNormal('sd_g', sd=0.1, shape=(G, 1)) allows you to also sample from the model, though this may not be the prior you intended!