Example of ordinal regression with ImproperDistribution

[vanAmsterdam]

as requested here #612 (comment)

can someone help out with updating the docs? Haven't done that before

[fehiepsi]

Hi @vanAmsterdam , the content looks great. Thanks for contributing your example! Please don't worry about the doc format, we'll check it again.

Could you add an introductory paragraph talking a bit about ordinal regression? That would be helpful for users to get an overview on what is the purpose of the tutorial.

Also, might I add a section on the usage of

c_y = sample("c_y", dist.TransformedDistribution(dist.Normal(0, 1).expand([nclasses]),
                                                 OrderedTransform()))

to put a weak prior on the intercepts, instead of the cutpoints c_y? I can make a separate PR or add commits to your PR, depending on which one you prefer.

[vanAmsterdam]

Thanks; yes I'll write something;

Do you mean adding the TransformedDistribution method as model3, another way of getting the same result?
I'm not sure I follow what you mean with intercepts as opposed to cutpoints. What intercepts do you mean?

[fehiepsi]

Sorry, I used the language in Statistical Rethinking book. It seems that that terminology is not common.

What I meant is the models in the tutorial use improper priors for cutpoints. In my last comment, we use a "proper" prior for those cutpoints. The motivation is:

• assume that predictor is 0, cutpoints c orderly lie in the log-odds space (y-axis of this figure) and each c_i corresponds to a cumulative probability p_i of ordered categories (i.e. if the outputs are scores of students, then p_i is the probability that the score <= i)
• We can put positive-support priors on the differences (c_{i + 1} - c_{i}) of those cutpoints. In my last comment, I used LogNormal(0, 1) priors. That also means that log(c_{i+1} - c_{i}) (which belongs to the real domain of OrderedTransform - they are called intercepts in the above book IIRC) has Normal(0,1) prior.

Does that make sense to you? Do you want to write some words about it in the tutorial?

[fehiepsi]

@vanAmsterdam Feel free to ignore my comment on the usage of TransformedDistribution. We can improve the content in a follow-up PR. :)

[vanAmsterdam]

I’m a bit slow to respond due to a deadline, are you in a hurry to close the issue or can it linger for a few weeks?

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On 19 Jun 2020, at 06:59, Du Phan ***@***.***> wrote:  @vanAmsterdam Feel free to ignore my comment on the usage of TransformedDistribution. We can improve the content in a follow-up PR. :) — You are receiving this because you were mentioned. Reply to this email directly, view it on GitHub, or unsubscribe.

[fehiepsi]

Absolutely no! I just worried that you found the usage of TransformedDistribution a bit counterintuitively to address. Please take your time! I hope you enjoy doing open-source contribution so I don't want something like 'hurry' take away such pleasure. ;)