Documentation for explainable for model with continuous variables

[PoorvaGarg]

This pull request adds a tutorial for the module explainable in the context of a model with continuous variables and dynamical systems.

[SamWitty]

See above comment for requested changes.

[rfl-urbaniak]

It seems like Python 3.8 is no longer available, I am removing it from CI, using 3.9 and 3.10.

[rfl-urbaniak]

Possibly this is because ubuntu-latest is dynamic. Python v3.8.2 is supported for ubuntu 20.04 (at the latest) and not for later versions.

[rfl-urbaniak]

Thanks @SamWitty for such detailed feedback! I have reacted to all the suggestions, here is a rundown of the changes.

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1. The notebook appears to be missing a clear and obvious explanatory question to motivate the analysis, written in plain English at first and then translated into specific operations later when mathematical terms are introduced. My suggestion would be to expand the text after “only one of them is responsible, and we are interested in being able to identify which one”, and move this earlier and more prominently in the tutorial.

Modified the discussion in the outline to already bring this up.

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The notebook is missing a clear and obvious conclusion we should draw from this analysis. This conclusion should be emphasized strongly visually (e.g. text in bold or a small subsection), and point to specific visual evidence and concrete numeric quantities. Once the conclusion is made clear, it would be nice to talk a bit about the policy or scientific implications. In the conclusion the notebook states the following: “It is evident from the plot above that the counterfactual for lockdown has more probability mass in the top right quadrant (low overshoot in the necessity world and high overshoot in the sufficient world). This gives us a clearer picture into why lockdown has higher causal role in the overshoot being too high as compared to masking.” It does not give me a clear picture into why lockdown has higher causal role.

Added a conclusions section. Brought up also policy-making a bit, but am not sure what other thoughts at that level of abstraction are worth being brought up.

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The notebook doesn’t discuss assumptions, possible violations of those assumptions, and their implications. This is particularly important because the model implicitly assumes that the structural functions (in this case, the SIR model) are known except for the specific parameters. As explanations in this notebook are derived from counterfactuals requiring strong assumptions like those found in this tutorial, there are many models where this kind of analysis would not be appropriate, or would otherwise need to be modified to account for more uncertainty in the structural functions.

Added an assumptions subsection.

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“Now we incorporate the Bayesian SIR model into a larger model that includes the effect of two different policies, lockdown and masking, where each can be implemented with 50 probability (these probabilities won't really matter, as we will be intervening on these, the sampling is mainly used to register the parameters with Pyro).” Why do we need pyro.sample sites rather pyro.deterministic sites here?

Why do we need the MaskedStaticIntervention?

Added a comment about this, Interestingly, this is a solution that you yourself suggested. :)

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I separated the policy_model into policy_model and overshoot_query, which is emphasizing that there’s some repeated code that could be refactored out further. Specifically, the get_overshoot function in the introduction could be vectorized when introduced, and then reused later in the actual definition of the model.

Yup, thanks!

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“Trajectories and overshoot distribution in the but-for analysis” requests:

    Add axis labels to all plots
    Make it clear that the rows correspond to the same intervention configuration. Currently it’s implied by them being next to each other, but the intervention configuration label is only on the leftmost plot.
    Fix the range of the histograms to be shared across all. Currently, it’s hard to visually compare.
    Show the mean as a vline on each histogram, and show the overshoot threshold as a vline on each histogram. Once this is done, you’ll need a single histogram legend.

Done!

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importance_infer: This is important enough that I think it justifies a little more explanation. As is, an unfamiliar audience may be left wondering a few things:

    Is importance sampling essential to the solution of this notebook, or is it just one of many plausible inference strategies from Pyro one could use?
    What do the return values represent?
    How do I get away with sampling importance weights a single time and then using them to answer many different questions downstream? (I believe the answer here is because we’ve broadcast the entire importance sampling procedure over all counterfactual worlds.)

Added an explanation of the inference strategy.

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Why do we need alternatives? Shouldn’t this always be equal to supports setminus antecedents?

Added an explanation.

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Can we add some citations justifying “degree of responsibility”?

Added reference to a particular chapter in Halpern's book - unless you had something else in mind?

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“The reader might have the impression that the numbers are relatively low: …” Could we suggest a more intuitive description of what these probabilities are? If they shouldn’t be interpreted as any conceptually meaningful probabilities, then we should emphasize that explicitly or consider removing.

So I think those one-number summaries are important, but also that the user needs to understand what they are and how to go beyond them. Tried to explain this in more detail in the current version.

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“Counterfactual - necessity world” figure (and all following similar plots) requests:

The overlapping histogram plots is a bit difficult to interpret. Something about the way colors blend together is hard to read. Could you change this to multiple subplots with shared axes or change the color overlap somehow?

Fixed.

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“Filter for the relevant context” -> Something about conditioning on the context nodes. I don’t like the word “filter” here.

Sure, fixed.

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“Comparing how necessity interventions for the two antecedents affect the overshoot” I don’t know what this means. I think the terminology of “necessity world” and “sufficiency world” is a little confusing. Is there a way we could reuse the mathematical notation introduced earlier to denote which counterfactual world we’re considering at any given point in the narrative?

I think the terminology is quite natural, but I can see how it wasn't introduced. So I added an explanation of these notions now. As for explaining in terms of notation, this is done in the current version of the categorical variables tutorial so I refer the reader to it. At this point I think doing something analogous here would overburden the reader as it wouldn't be too straightforward: the notation is for particular interventional settings and values under settings, whereas possible worlds cut through those.

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14. Heatmap suggestions/questions:

    We need a colorbar showing how the colors correspond to probability density.
    How should I interpret the vertical and horizontal lines? I think I get that “mean overshoot” is the point at the intersection, but I don’t know how to interpret “overshoot too high”. Is this saying that any configuration above and to the right of that intersection is too high?
    

Revised the heatmap and added more extensive explanation thereof.