The Mythos of Model Interpretability in Machine Learning
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Re: The Mythos of Model Interpretability in Machine Learning
#2You may prefer this link: https://arxiv.org/abs/1606.03490
Re: The Mythos of Model Interpretability in Machine Learning
#3You may prefer this link: https://arxiv.org/abs/1606.03490
extra points for linking to abstract, not pdf :)
Re: The Mythos of Model Interpretability in Machine Learning
#4Its funny, and characteristic of that part of the field, that mathematical provability in not even mentioned explicitly.
A model (and a learning algorithm) should be interpretable if we can clearly state the assumptions, and prove that under these assumptions, we get what we state we get.
We can predict the movement of the planets (short term). This is interpretable, because we only assume a model of 3d space, and Newton's laws(1). The rest is mathematics, which gives us elliptic trajectories, etc. The resulting predictions may be wrong, due to wrong assumptions, but the model is still interpretable.
Linear regressions, histograms, decision trees(2) are all interpretable. We know exactly what they do, under proper assumptions. Yes, these models can be sometimes manipulated. But we know this precisely because we know exactly what they do. Whether we should use these models, or statistics in general, in courts etc, is an ethical decision, and perhaps practical decision, similar to whether we should use the death penalty. Has nothing to do with interpretability.
With CNNs, at the moment we have very vague understanding of both the assumptions and the models. When we do have this understanding, we will likely also have better and simpler models.
Mathematics was always a tool for understanding reality. Proving is understanding. And it was pretty successful so far.
(1) and some other things -- the rest of the planets are far enough, etc. (2) given enough data wrt the size of the tree, under proper distributional assumptions.
Re: The Mythos of Model Interpretability in Machine Learning
#5Its funny, and characteristic of that part of the field, that mathematical provability in not even mentioned explicitly. A model (and a learning algorithm) should be interpretable if we can clearly state the assumptions, and prove that under these assumptions, we get what we state we get. We can predict the movement of the planets (short term). This is interpretable, because we only assume a model of 3d space, and Ne…
Along the same lines, convergence is mentioned as a candidate for interpretability but convexity is not mentioned even once.
Re: The Mythos of Model Interpretability in Machine Learning
#6Anyone have other good references for this topic?
Re: The Mythos of Model Interpretability in Machine Learning
#7Its funny, and characteristic of that part of the field, that mathematical provability in not even mentioned explicitly. A model (and a learning algorithm) should be interpretable if we can clearly state the assumptions, and prove that under these assumptions, we get what we state we get. We can predict the movement of the planets (short term). This is interpretable, because we only assume a model of 3d space, and Ne…
I don’t agree with this. For example, you can set up a collection of assumptions to underpin frequentist statistics, and then create a set of theorems about consistent or unbiased estimators, and develop a theory like that of p-values.
But then in a practical setting, the model doesn’t correspond to something physical or to the inference goal of a practitioner. The p-value tells you something about the relative extremity of a certain statistic that, under certain assumptions, will have a particular distribution.
The practitioner wants to know the posterior probability of a particular model or hypothesis given the data, and the frequentist outcome literally can’t comment on it.
In this sense I think being able to state assumptions and connect them to outcomes with theorems is good, but not always necessary or even sufficient for applied work.
And there can creep in nasty subjective aspects of the problem that are uniquely defined by the specific inference goals at hand. Proofs about how a model would behave under assumptions are often totally useless in these cases. Practitioners don’t use linear regression for complex financial models because the assumptions hold or because of nice properties if the assumptions held. They use them because it’s simple and easy and sort of “just works” despite glaring flaws.
Re: The Mythos of Model Interpretability in Machine Learning
#8Anyone have other good references for this topic?
Interpretable ML [1] is a small online book on interpretable methods. Even if the content itself is rather shallow, it has links to a lot of more focused papers on the topic. Towards A Rigorous Science of Interpretable Machine Learning is one of the most thorough papers on interpretable ML that I have come across. The main author, Finale Doshi-Velez, has a done a lot of interesting work on interpretability [3].
[1] https://christophm.github.io/interpretable-ml-book/
Re: The Mythos of Model Interpretability in Machine Learning
#9I think interpretability is much more correlated with model size than model type.
Small neural net is much more interpretable than decision trees with thousands of nodes.
Re: The Mythos of Model Interpretability in Machine Learning
#10Its funny, and characteristic of that part of the field, that mathematical provability in not even mentioned explicitly. A model (and a learning algorithm) should be interpretable if we can clearly state the assumptions, and prove that under these assumptions, we get what we state we get. We can predict the movement of the planets (short term). This is interpretable, because we only assume a model of 3d space, and Ne…
Along the same lines, convergence is mentioned as a candidate for interpretability but convexity is not mentioned even once.
This is a very interesting notion, could you elaborate why convexity would be a candidate? Convexity defining a class is clear, but as a proxy for interpretability I have not heard this before. I would assume this would need some measure of degree of convexity - different than strong > strict > convex