How to model outside option?

[kdzhang]

First, thank you for this great package!

I wonder if there is a way to model outside option in the package? For example, it is possible that the user buys nothing in a visit. One hacky solution I have is to force all item_obs and user_item_obs to be zero for the outside option. But this approach cannot handle session_obs unless we make every session_obs to be session_item_obs.

According to the following comment in this issue, it seems that there is a way to formally model outside option. I am good with normalizing it to 0 in each category. I very much appreciate it if you can give me some guidance on how to do this. Thank you!

there needs to be a discussion on how the outside option is modeled. How does the model choose that the user buys nothing from a given category? Can we change the value of the outside option in each category or is normalized to 0 for each category?

[kdzhang]

I managed to modify the conditional_logit_model.py a little bit to allow for outside option. I share it here in case others have a similar need.

First, make the item_index for outside option to be -1. Recall that the item_index for actual choices start from 0.

Then I modify the __init__ to add an option called outside and register it as a field.

Modify forward function by adding this at the end:

        if self.outside:
            util_zero = torch.zeros(total_utility.size(0), 1, device=batch.device)
            total_utility = torch.cat((util_zero, total_utility), dim=1)

And modify the negative_log_likelihood function by adding this before the total_utility calculation:

        # if outside option exists, need to adjust y to match the dimension of total_utility
        y_new = y.clone()
        if self.outside:
            # move all actual choices starting from 1
            # empty index (outside option) is 0
            y_new[y_new<0] = -1
            y_new+=1

Then you can get point estimates by estimating as usual. Remember to set outside=True in model initiation.

To get proper std, we need to change the run function in run_helper_lightning.py

    if isinstance(model, ConditionalLogitModel):
        def nll_loss(model):
            y_pred = model(dataset_for_std)

            # modify item_index to accomodate the outside option
            if model.outside:
                item_index_new = dataset_for_std.item_index + 1
            else:
                item_index_new = dataset_for_std.item_index
            return F.cross_entropy(y_pred, item_index_new, reduction='sum')

Then you should be able to get the std as well.

This is a hacky solution of course. I would very much appreciate it if the author has a better solution.

[TianyuDu]

Hey Kaida, thank you for your question and awesome solution to it! Your solution looks pretty elegant to me; for other users to utilize what you implemented, shall we make a pull request to integrate your implementation into the main branch? I could make the PR and acknowledge you in the PR, or you could do it if you prefer to have your contribution shown on GitHub.

Thank you for your contribution!

[kdzhang]

Hi Tianyu, thank you for your kinds words! Feel free to make the PR, I think you are the best person to do it as you know the edges of this package better. I am more than happy to contribute wherever I can. Regarding the feature, I think there is a bit more work left:

1. Expand this implementation to nested logit;
2. Probably need some consistency checking. E.g., if outside option is on, then item_index must start from -1.
3. Add some examples on outside option in the documentation. I can certainly help with this one.

Again, thank you for writing this great package!

[TianyuDu]

I have attached a new branch to this thread to implement the outside option for conditional logit models. Kaida's preliminary solution was awesome, and I made a couple of modifications:

1. In the solution Kaida proposed, the outside option zero utility was prepended to the total_utility so that total_utility[:, 0] = 0. Since the outside option is indicated by item_index = -1, I have appended the outside option zero utility so that total_utility[:, -1] = 0 in the current implementation. This would make the indexing easier. For example, suppose total_utility has the shape N*(num_items+1), in which the last column corresponds to the zero utility of the outside option. Suppose item_index has shape N with some -1 value in it to indicate outside option was chosen; then total_utility[range(item_index), item_index] could retrieve the utility for both real items and the outside option without modifying the item_index.

I am currently testing the implementation, and @kanodiaayush you can find the latest progress in the pull request here: https://github.com/gsbDBI/torch-choice/pull/42

@kanodiaayush Does this make sense to you?

[TianyuDu]

Here is a demonstration of using the outside option for condition logit models: https://github.com/gsbDBI/torch-choice/blob/41-how-to-model-outside-option/tutorials/outside_option.ipynb

I am working on testing if this works for nested regressions.

[TianyuDu]

I have implemented the outside option for nested logit model as well (see the updated pull request), @kanodiaayush could you please review it?