I am trying to estimate a model in tensorflow using NUTS by providing it a likelihood function. I have checked the likelihood function is returning reasonable values. I am following the setup here for setting up NUTS: https://rlhick.people.wm.edu/posts/custom-likes-tensorflow.html
and some of the examples here for setting up priors, etc.: https://github.com/tensorflow/probability/blob/master/tensorflow_probability/examples/jupyter_notebooks/Multilevel_Modeling_Primer.ipynb
My code is in a colab notebook here: https://drive.google.com/file/d/1L9JQPLO57g3OhxaRCB29do2m808ZUeex/view?usp=sharing
I get the error: OperatorNotAllowedInGraphError: iterating over
tf.Tensoris not allowed: AutoGraph did not convert this function. Try decorating it directly with @tf.function.
This is my first time using tensorflow and I am quite lost interpreting this error. It would also be ideal if I could pass the starting parameter values as a single input (example I am working off doesn't do it, but I assume it is possible).
Update It looks like I had to change the position of the @tf.function decorator. The sampler now runs, but it gives me the same value for all samples for each of the parameters. Is it a requirement that I pass a joint distribution through the log_prob() function? I am clearly missing something. I can run the likelihood through bfgs optimization and get reasonable results (I've estimated the model via maximum likelihood with fixed parameters in other software). It looks like I need to define the function to return a joint distribution and call log_prob(). I can do this if I set it up as a logistic regression (logit choice model is logistically distributed in differences). However, I lose the standard closed form.
My function is as follows:
@tf.function
def mmnl_log_prob(init_mu_b_time,init_sigma_b_time,init_a_car,init_a_train,init_b_cost,init_scale):
# Create priors for hyperparameters
mu_b_time = tfd.Sample(tfd.Normal(loc=init_mu_b_time, scale=init_scale),sample_shape=1).sample()
# HalfCauchy distributions are too wide for logit discrete choice
sigma_b_time = tfd.Sample(tfd.Normal(loc=init_sigma_b_time, scale=init_scale),sample_shape=1).sample()
# Create priors for parameters
a_car = tfd.Sample(tfd.Normal(loc=init_a_car, scale=init_scale),sample_shape=1).sample()
a_train = tfd.Sample(tfd.Normal(loc=init_a_train, scale=init_scale),sample_shape=1).sample()
# a_sm = tfd.Sample(tfd.Normal(loc=init_a_sm, scale=init_scale),sample_shape=1).sample()
b_cost = tfd.Sample(tfd.Normal(loc=init_b_cost, scale=init_scale),sample_shape=1).sample()
# Define a heterogeneous random parameter model with MultivariateNormalDiag()
# Use MultivariateNormalDiagPlusLowRank() to define nests, etc.
b_time = tfd.Sample(tfd.MultivariateNormalDiag( # b_time
loc=mu_b_time,
scale_diag=sigma_b_time),sample_shape=num_idx).sample()
# Definition of the utility functions
V1 = a_train + tfm.multiply(b_time,TRAIN_TT_SCALED) + b_cost * TRAIN_COST_SCALED
V2 = tfm.multiply(b_time,SM_TT_SCALED) + b_cost * SM_COST_SCALED
V3 = a_car + tfm.multiply(b_time,CAR_TT_SCALED) + b_cost * CAR_CO_SCALED
print("Vs",V1,V2,V3)
# Definition of loglikelihood
eV1 = tfm.multiply(tfm.exp(V1),TRAIN_AV_SP)
eV2 = tfm.multiply(tfm.exp(V2),SM_AV_SP)
eV3 = tfm.multiply(tfm.exp(V3),CAR_AV_SP)
eVD = eV1 + eV2 +
eV3
print("eVs",eV1,eV2,eV3,eVD)
l1 = tfm.multiply(tfm.truediv(eV1,eVD),tf.cast(tfm.equal(CHOICE,1),tf.float32))
l2 = tfm.multiply(tfm.truediv(eV2,eVD),tf.cast(tfm.equal(CHOICE,2),tf.float32))
l3 = tfm.multiply(tfm.truediv(eV3,eVD),tf.cast(tfm.equal(CHOICE,3),tf.float32))
ll = tfm.reduce_sum(tfm.log(l1+l2+l3))
print("ll",ll)
return ll
The function is called as follows:
nuts_samples = 1000
nuts_burnin = 500
chains = 4
## Initial step size
init_step_size=.3
init = [0.,0.,0.,0.,0.,.5]
##
## NUTS (using inner step size averaging step)
##
@tf.function
def nuts_sampler(init):
nuts_kernel = tfp.mcmc.NoUTurnSampler(
target_log_prob_fn=mmnl_log_prob,
step_size=init_step_size,
)
adapt_nuts_kernel = tfp.mcmc.DualAveragingStepSizeAdaptation(
inner_kernel=nuts_kernel,
num_adaptation_steps=nuts_burnin,
step_size_getter_fn=lambda pkr: pkr.step_size,
log_accept_prob_getter_fn=lambda pkr: pkr.log_accept_ratio,
step_size_setter_fn=lambda pkr, new_step_size: pkr._replace(step_size=new_step_size)
)
samples_nuts_, stats_nuts_ = tfp.mcmc.sample_chain(
num_results=nuts_samples,
current_state=init,
kernel=adapt_nuts_kernel,
num_burnin_steps=100,
parallel_iterations=5)
return samples_nuts_, stats_nuts_
samples_nuts, stats_nuts = nuts_sampler(init)