Thanks, @fritzo. Actually, I had not made that particular connection. Good to know though. So with to_event(1) the variables are considered dependent, while with plate, they are independent. Is it that simple?
So the only time neither plate or to_event is required is when we are dealing with a scalar global variable?
So let me ask both @fritzo and Jeffmax:
If it is a choice between to_event(1) and plate, why not choose plate since the individual questions are independent of each other. Would the code not run faster? Could you please explain? Thanks.
Gordon
I am still confused on how to do inference in this model. I have inferred guess_probs using SVI and retrieved the skill sets using infer_discrete on the model. Given the model, the skill_set can only be 0 or 1, correct? However, in Chapter 2 of Winn & Bishop, Figure 2.7 suggests that the skills are real numbers between 0 and 1. I do not understand how to achieve that using the model they are using, or with the model and guide below. Does this sound confusing?
def complete_model_tensor():
alpha0 = torch.ones(48) * 2.5
beta0 = torch.ones(48) * 7.5
guess_probs = pyro.sample('guess_prob',
dist.Beta(alpha0, beta0).independent(1))
with pyro.plate("participants", 22):
skills = []
for i in pyro.plate("skills", 7):
skills.append(pyro.sample("skill_{}".format(i),
dist.Bernoulli(0.5),
infer={"enumerate": "parallel"}))
for q in pyro.plate("questions", 48):
has_skills = reduce(operator.mul,
[skills[i] for i in skills_needed[q]]).float()
prob_correct = has_skills * (1 - prob_mistake) + (1 - has_skills) * guess_probs[q]
pyro.sample("isCorrect{}".format(q),
dist.Bernoulli(prob_correct))
def complete_model_tensor_guide():
guess_prob_a = pyro.param('guess_prob_a', torch.ones(48) * 4,
constraint=constraints.positive)
guess_prob_b = pyro.param('guess_prob_b', torch.ones(48) * 4,
constraint=constraints.positive)
guess_probs = pyro.sample('guess_prob',
dist.Beta(guess_prob_a , guess_prob_b).independent(1))My understanding of this (which could be wrong) is the following. I welcome any corrections!
Some algorithms that are able to take advantage of the independence assumptions could run slower if .to_event is used in a place where there is actual independence., but the answers shouldn’t be wrong. Sometimes I suspect .to_event is used because it is simpler to type in the code and may not be meaningfully different in a particular situation than using plate. I think, while not necessarily called out that often in the docs, especially if you turn on validation, Pyro wants all the sites to be annotated with plate or to_event, so you have to do one of them.
In my case, I use .to_event() for a variable x to specify that event_shape of the distribution which generates x is x.shape. I’ll use plate to denote the independence.
Sometimes, when they are equivalent and x.dim() >= 2 then I’ll use .to_event() to simply the code as @jeffmax pointed out. But I don’t recommend doing that way. Two plate statements are more explicit IMO.
In the following enumerated model, skills are enumerated. I count 2^(22*7) terms, which is huge, and yet it works. What is the real count? Thanks.
with pyro.plate("participants", 22):
skills = []
# Enumerate over skills (2 values for each skill)
for i in pyro.plate("skills", 7):
# skills: 0 or 1
skills.append(pyro.sample("skill_{}".format(i),
dist.Bernoulli(0.5),
infer={"enumerate": "parallel"}))
for q in pyro.plate("questions", 48):
# skills_needed[q] is a list of skills need for qth question
has_skills = reduce(operator.mul,
[skills[i] for i in skills_needed[q]]).float()
prob_correct = has_skills * (1 - prob_mistake) + (1 - has_skills) * guess_probs[q]
# Conditioned on the data. Done outside the routine
is_correct = pyro.sample("isCorrect{}".format(q),
dist.Bernoulli(prob_correct))I am currently trying to wrap my head around the pyro plate system and try to get my pyro notebook for chapter 2 up and running.
Therefore, I wondered if you can recommend resources next to the official tutorials?
Maybe you have your latest notebooks also somewhere online?
I wonder if you can use “a more vectorized” approach for the model in this chapter?
Any help would be greatly appreciated. 
@MicPie did you try using the code in the post above? That mostly worked for me, however I ended up needing to use MCMC to get answers close to the book in a reasonable amount of time.