Thread by @ShalitUri

Happy to share that our paper “On Calibration and Out-of-domain Generalization” is accepted to #NeurIPS2021!

Congratulations to the wonderful students who came up with the idea and led the work on this paper:
@wald_yoav @amir_feder @d_greenfeld

arxiv.org/abs/2102.10395

1/15

tl;dr: Making a classifier calibrated over multiple training domains is an easy and powerful way for better generalization to unseen domains
2/15

Say you have patient data from several hospitals which differ in their demographics, imaging machines etc, and you want to learn a classifier that generalizes to new unseen hospitals. This is the problem of out-of-domain (OOD) generalization, ubiquitous in NLP, vision & more
3/15

This fig is based on Camelyon17, a dataset of pathology slides from multiple hospitals.
Naive/Robust/CLOvE are methods to re-calibrate trained classifiers.
For each model, reducing in-domain avg. calibration error (x-axis, ECE) also improves OOD accuracy (y-axis).
How come?
4/15

Generally there are multiple different ways to formalize the goals of OOD generalization, e.g. see this recent thread

https://twitter.com/roydanroy/status/1444623015191400451?s=20

5/15

We formalize the problem using the causal graph below, assuming that at test time we see data from a previously unobserved domain E=e.
Important: we assume we’re *not* told which of the features are causal, anti-causal spurious, or anti-causal non-spurious
(ac=anti-causal)
6/15

Any model using the ac-spurious features from the graph above is carrying the risk of making arbitrarily large mistakes if the domain (E) changes. Thus, bounding max risk means we must avoid these features

7/15

Speaking more generally, we (and others) claim a good property for a classifier f(X) expected to generalize to new domains E is:
Y⫫E | f(X)

"Y is independent of E conditioned on f(X)"

8/15

Optimizing for Y⫫E | f(X) looks a bit nasty, as cond. indep. is often hard + we’re conditioning on a continuous variable, which is ALSO the target of our optimization problem.
We show this problem is almost equivalent to a more approachable 𝘤𝘢𝘭𝘪𝘣𝘳𝘢𝘵𝘪𝘰𝘯 problem
9/15

Reminder:
For binary Y and classifier f(X), f is calibrated if
𝔼[Y | f(X)] = f(X)
We add that this should happen for every training domain:
𝔼[Y | f(X),E=eᵢ] = f(X) for all train eᵢ

10/15

In linear-Gaussian settings we prove that if a model is simultaneously calibrated over diverse domains, it is guaranteed to be free of spurious correlations and generalize well OOD

11/15

We further prove that multi-domain calibration leads to learning the correct invariances even in cases where IRM(v1) fails to do so
(figure inspired by Kamath et al. AISTATS 2021 paper arxiv.org/abs/2101.01134)
12/15

Our theory shows multi-domain calibration works in linear-Gaussian settings with infinite samples.
We were gratified to see that multi-domain calibration also works in practical, finite-sample, not-at-all-linear settings, getting great results on the WILDS benchmark
13/15

We experimented with successively more sophisticated ways to encourage multi-domain calibration: model selection, post-processing with a robust version of isotonic regression, and a new objective we call CLOvE based on work by Kumar et al (ICML 2018) proceedings.mlr.press/v80/kumar18a.h…
14/15

Many more results in the paper - main takeaway: make your classifier calibrated across training domains, and get better out-of-domain generalization. It’s easy :)
Still many open q's, both theory and practice - looking forward to discussing them here and at #NeurIPS2021
15/15