add double ml notebook and fix a minor typo in dml doc #24
Conversation
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I would change how we plot the cross price elasticities in the final cells and write some more comments in the way that you process the data to fit cross price. For how to depict: can we do something like: we have 3x3 subplots and each subplot contains the cross price elasticity as a function income. This way we can visualize it as a matrix and each matrix contains a plot. Also I would like to have an example that uses the FistaRegressor from here: |
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@vasilismsr From an economist's point of view, is the nuclear norm the right regularization? Low rank is nice, but it seems like they'd be more likely to try to apply a mixed effects model of some sort (e.g. shrink all individual own-price elasticities towards one value and all cross-price elasticities towards another). |
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Yeap. Low rank is the right way for high dimensional product spaces. Such latent factor models have been studied in pricing (see athey and blei, or the paper we wrote with taddy). |
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@vasilismsr But here we aren't in a high-dimensional regime; we're regressing the three log quantites on the three prices interacted with income (plus an intercept), so there are only 18 coefficients total. Maybe we should see if we can find (or generate) a high-dimensional example as well, so that we can demonstrate using the trace norm in a more appropriate setting. |
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I know. But the notebook is more for expository purposes, i.e. you could even do this. And we can say in the cell above that this would be more appropriate when you have many products and you believe they interact in a latent space. I think its an important special case and we could show we can handle it. We could in principle have a simulated data example too where we have many products. |
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As we discussed over lunch, see what happens if you add |
please take a look at my notebook, especially the last part (multi treatment and multi output). Let me know if I am doing anything wrong or anything I need to add.