Ошибка оптимизации для pymc3

Question

Я пытаюсь создать относительно простую иерархическую байесовскую модель, используя pymc3. Тем не менее, я все-таки получаю сообщение об ошибке. Код:

import numpy as np 
import pymc3 as pm 

# Example data. 
ncond = 4 
nSubj = 40 
trials = 64 

N = np.repeat([trials], (ncond * nSubj)) 
z = np.array([45, 63, 58, 64, 58, 63, 51, 60, 59, 47, 63, 61, 60, 51, 59, 45, 
61, 59, 60, 58, 63, 56, 63, 64, 64, 60, 64, 62, 49, 64, 64, 58, 64, 52, 64, 64, 
64, 62, 64, 61, 59, 59, 55, 62, 51, 58, 55, 54, 59, 57, 58, 60, 54, 42, 59, 57, 
59, 53, 53, 42, 59, 57, 29, 36, 51, 64, 60, 54, 54, 38, 61, 60, 61, 60, 62, 55, 
38, 43, 58, 60, 44, 44, 32, 56, 43, 36, 38, 48, 32, 40, 40, 34, 45, 42, 41, 32, 
48, 36, 29, 37, 53, 55, 50, 47, 46, 44, 50, 56, 58, 42, 58, 54, 57, 54, 51, 49, 
52, 51, 49, 51, 46, 46, 42, 49, 46, 56, 42, 53, 55, 51, 55, 49, 53, 55, 40, 46, 
56, 47, 54, 54, 42, 34, 35, 41, 48, 46, 39, 55, 30, 49, 27, 51, 41, 36, 45, 41, 
53, 32, 43, 33]) 
condition = np.repeat([0,1,2,3], nSubj) 


# Specify the model in PyMC 
with pm.Model() as model: 
    # define the hyperparameters 
    kappa = pm.Gamma('kappa', 1, 0.1) 
    mu = pm.Beta('mu', 1, 1, shape=ncond) 
    # define the prior 
    theta = pm.Beta('theta', mu[condition] * kappa, (1 - mu[condition]) * kappa, shape=len(z)) 
    # define the likelihood 
    y = pm.Binomial('y', p=theta, n=N, observed=z) 
    start = pm.find_MAP() 
    step1 = pm.Metropolis([mu]) 
    step2 = pm.Metropolis([theta]) 
    step3 = pm.NUTS([kappa]) 
# samplers = [pm.Metropolis([rv]) for rv in model.unobserved_RVs] 
    trace = pm.sample(10000, [step1, step2, step3], start=start, progressbar=False) 

Но я все время получаю сообщение об ошибке в отношении функции find_MAP(). Может ли кто-нибудь объяснить эту ошибку мне?

--------------------------------------------------------------------------- 
ValueError        Traceback (most recent call last) 
<ipython-input-2-c4e40b20fd5c> in <module>() 
    38  # define the likelihood 
    39  y = pm.Binomial('y', p=theta, n=N, observed=z) 
---> 40  start = pm.find_MAP() 
    41  step1 = pm.Metropolis([mu]) 
    42  step2 = pm.Metropolis([theta]) 

/Library/Python/2.7/site-packages/pymc3/tuning/starting.pyc in find_MAP(start, vars, fmin, return_raw, disp, model, *args, **kwargs) 
    124       "density. 2) your distribution logp's are " + 
    125       "properly specified. Specific issues: \n" + 
--> 126       specific_errors) 
    127  mx = {v.name: np.floor(mx[v.name]) if v.dtype in discrete_types else 
    128   mx[v.name] for v in model.vars} 

ValueError: Optimization error: max, logp or dlogp at max have non-finite values. Some values may be outside of distribution support. max: {'mu': array([ 14.66440283, 67.64627608, 36.73991444, -2.27146408]), 'theta': array([ -3.28858534e+02, 1.49945045e+02, -7.02150417e+01, 
     9.97352990e-01, -7.02150417e+01, 1.49945045e+02, 
     -1.50195789e+02, 5.63428376e+00, -9.29002815e+01, 
     -2.70445580e+02, 1.49945045e+02, 1.03986058e+02, 
     5.63428376e+00, -1.50195789e+02, -9.29002815e+01, 
     -3.28858534e+02, 1.03986058e+02, -9.29002815e+01, 
     5.63428376e+00, -7.02150417e+01, 1.49945045e+02, 
     -5.57301509e+01, 1.49945045e+02, 1.01682005e+00, 
     9.62368437e-01, 5.63428376e+00, 9.95206871e-01, 
     5.88827819e+01, -2.08511670e+02, -7.51688112e+00, 
     9.54524715e+00, -7.02150417e+01, 1.02401342e+00, 
     -1.24386722e+02, 1.00553699e+00, 1.00113792e+00, 
     1.05862921e+00, 5.88827819e+01, 9.96530636e-01, 
     1.03986058e+02, -1.66473577e+02, -1.66473577e+02, 
     1.21070195e+02, 7.06961277e+01, 1.51469750e+02, 
     -1.01158381e+02, 1.21070195e+02, 1.47085125e+02, 
     -1.66473577e+02, -5.55202522e-01, -1.01158381e+02, 
     5.37160225e+01, 1.47085125e+02, -3.00112781e+01, 
     -1.66473577e+02, -5.55202522e-01, -1.66473577e+02, 
     1.58340576e+02, 1.58340575e+02, -3.00112781e+01, 
     -1.66473577e+02, -5.55202521e-01, -1.87830813e+01, 
     -7.63325604e+01, 1.51469750e+02, 6.56687525e+02, 
     5.37160224e+01, 1.47085125e+02, 1.47085125e+02, 
     -7.30815598e+01, 5.20052822e+02, 5.37160224e+01, 
     5.20052822e+02, 5.37160224e+01, 7.06961278e+01, 
     1.21070195e+02, -7.30815598e+01, -1.20799887e+01, 
     -1.01158381e+02, 5.37160224e+01, 2.55349034e+01, 
     2.55349034e+01, -1.42715299e+02, 3.77924839e+01, 
     4.84747986e+00, -1.07962425e+02, -8.33028412e+01, 
     1.00157336e+02, -1.42715299e+02, -5.22680519e+01, 
     -5.22680519e+01, -1.27123074e+02, 4.61912845e+01, 
     -1.52905863e+01, -3.44347435e+01, -1.42715299e+02, 
     1.00157336e+02, -1.07962425e+02, -1.65836239e+02, 
     -9.64018880e+01, 1.06636770e+02, 6.59333401e+01, 
     1.19873182e+02, 8.44063494e+01, 6.60981540e+01, 
     2.55349034e+01, 1.19873182e+02, 3.77924839e+01, 
     -3.45990714e+01, -1.52905863e+01, -3.45990714e+01, 
     8.91977361e+01, 5.07494024e+00, 8.91977361e+01, 
     1.21864768e+02, 1.12323534e+02, 1.17572851e+02, 
     1.21864768e+02, 1.12323534e+02, 1.21864768e+02, 
     6.29159569e+01, 6.29159569e+01, -1.64948241e+01, 
     1.05932671e+02, 6.29159569e+01, 1.85689051e+01, 
     -1.64948241e+01, 9.30151996e+01, 4.81456147e+01, 
     1.12276366e+02, 4.81456147e+01, 1.05932671e+02, 
     9.30151996e+01, 4.81456147e+01, -5.32061084e+01, 
     6.29159569e+01, 1.85689051e+01, 8.03463229e+01, 
     7.34110211e+01, 7.34110211e+01, -1.64948241e+01, 
     -1.29160807e+02, -1.19831995e+02, -3.54559256e+01, 
     9.50334978e+01, 6.29159569e+01, -6.95343458e+01, 
     4.81456147e+01, -1.61402820e+02, 1.05932671e+02, 
     -1.92150490e+02, 1.12276366e+02, -3.54559256e+01, 
     -1.09378401e+02, 4.37180227e+01, -3.54559256e+01, 
     9.30151996e+01, -1.45569868e+02, 3.34881430e+00, 
     -1.37632194e+02]), 'kappa': array(1399.2675885517883)} logp: array(-inf) dlogp: array([   nan,   nan,   nan,   nan, 
       nan, -0.  , 0.  , -0.  , 
     64.16985826, -0.  , 0.  , -0.  , 
     0.  , -0.  , -0.  , 0.  , 
     0.  , 0.  , -0.  , -0.  , 
     -0.  , 0.  , -0.  , 0.  , 
     -0.  , 0.  , -0.  , 0.  , 
     0.  , 66.50259666, 0.  , 64.30823767, 
     0.  , -0.  , -0.  , 0.  , 
     -0.  , 0.  , -0.  , 0.  , 
     0.  , 0.  , 0.  , 64.22281229, 
     0.  , -0.  , -0.  , 0.  , 
     0.  , 0.  , -0.  , 0.  , 
     0.  , -0.  , -0.  , -0.  , 
     0.  , 0.  , -0.  , -0.  , 
     -0.  , -0.  , 0.  , 0.  , 
     -0.  , -0.  , -0.  , -0.  , 
     -0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , -0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , -0.  , -0.  , -0.  , 
     0.  , 0.  , 0.  , -0.  , 
     0.  , 0.  , -0.  , -0.  , 
     0.  , -0.  , -0.  , -0.  , 
     -0.  , 0.  , -0.  , -0.  , 
     -0.  , 0.  , -0.  , -0.  , 
     -0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , -0.  , -0.  , -0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 
     0.  , 0.  , 0.  , 0.  , 0.  ])Check that 1) you don't have hierarchical parameters, these will lead to points with infinite density. 2) your distribution logp's are properly specified. Specific issues: 
mu.logp bad: -inf 
theta.dlogp bad at idx: (array([160, 161, 162, 163, 164]),) with values: [ nan nan nan nan nan] 
theta.logp bad: -inf 

Answer 1

Ошибка означает, что алгоритм оптимизации закончен, но возвратил значения, которые не имеют никакого смысла. Обычно это происходит потому, что максимум не определен.

Однако это действительно сработало для меня. Какие у вас версии?

У меня есть python 2.7, последний pymc3, theano 0.7.0, scipy 0.13