NAN log_prob_sum in Poisson model?

Hello Pyro community! I’m a Pyro noob, just getting my feet wet with some simple models, and ran into a warning that I could use some help understanding.

I’m attempting to use NUTS to draw from the posterior of a simple Poisson GLM with one covariate and n observations:

y_i ~ Poisson(exp(a + b * x_i)) for i = 1, …, n
a ~ Normal(0, 2)
b ~ Normal(0, 1)

Here’s the code I have so far:

import numpy as np
import torch
import pyro
import pyro.distributions as dist
from pyro.infer.mcmc import MCMC, NUTS
from pyro.infer import EmpiricalMarginal

def simulate_data(n, alpha, beta1):
    Simulate data from a Poisson GLM
    n: number of observations
    alpha: intercept
    beta1: slope
    x = np.linspace(start=0, stop=1, num=n)
    log_lam = alpha + beta1 * x
    lam = np.exp(log_lam)
    counts = np.random.poisson(lam)
    out = {'n': n,
           'alpha': alpha, 
           'beta1': beta1, 
           'x': x.astype('float32'), 
           'lambda': lam,
           'counts': counts.astype('float32')}
    return out

data = simulate_data(n=40, alpha=3, beta1=-1.5)
x = torch.tensor(data['x'])
counts = torch.tensor(data['counts'])

def model():
    alpha = pyro.sample('alpha', dist.Normal(loc=0, scale=2))
    beta1 = pyro.sample('beta1', dist.Normal(loc=0, scale=1))
    log_lam = alpha + beta1 * x
    lam = torch.exp(log_lam)
    with pyro.iarange('observe_data'):
        pyro.sample('obs', dist.Poisson(rate=lam), obs=counts)

kernel = NUTS(model, adapt_step_size=True)
num_samples = 1000
warmup_steps = 1000
mcmc = MCMC(kernel, num_samples, warmup_steps).run()

This last line returns the following warning:

/home/max/anaconda3/lib/python3.6/site-packages/pyro/poutine/ UserWarning: Encountered NAN log_prob_sum at site 'obs'
  warnings.warn("Encountered NAN log_prob_sum at site '{}'".format(name))

I’m not sure why the joint log probability of the observed counts would be NAN, but any insight into what’s causing this warning, and whether there’s a fix would be much appreciated. Apologies if this is obvious to others, I’m coming mainly from R and Stan so I’m doubly out of my depth here.

Thanks in advance.

Hi, that warning occurs during MCMC adaptation and should have no effect on your results. If you look at the samples in mcmc you shouldn’t see any NaNs.

Thanks - I see that there are no NaN values in the posterior samples, which is great! Any insight into why this occurs during adaptation? Is it an issue of parameter initialization, either for the model or for NUTS?

Any insight into why this occurs during adaptation? Is it an issue of parameter initialization, either for the model or for NUTS?

During the adaptation phase, NUTS tries step sizes based on an exponential schedule. When sites are constrained and we use a large step size, it is easy for the integrator to generate samples which result in a NaN when transformed back to the constrained support of the original sample site. This isn’t a problem as it will try out a smaller value for the step size when this happens, though I agree that the warning can be confusing. Thanks for reporting this - I will look into silencing these warnings for the adaptation period.

Great - this makes sense @neerajprad. Thanks for the explanation!