Is H(rule) really necessary?

[lihuiliullh]

Hi, it is really a nice paper. But I have a question.

May I know why you need to use Eq. (7) and (8) to approximate the posterior?
My idea is that in the E-step, you need to identify k rules with the best quality.
Since
you can simply calculate prior x likelihood for each rule in z_hat, and choose the top-k rules.

But what you do is to calculate the H(rule) for each rule and choose the top-k rules.
Since H(rule) is a approximate of the posterior distribution which is proportion to prior x likelihood, it will have the same effect as using prior x likelihood.

It seems to me that all the proof and proposition in Section 3.3 E-step is unnecessary.

@mnqu

[mnqu]

Thanks for your interests, and this is a good question.

The reason is that z_I here is a set of logic rules, so the prior and posterior are defined on a set of logic rules, rather than a single logic rule. Therefore, we propose to use approximation inference to infer the posterior, where H(rule) is calculated.

Does it make sense to you?