Out-of-Distribution Generalization via Risk Extrapolation (REx)

David Krueger, Ethan Caballero, Joern-Henrik Jacobsen, Amy Zhang, Jonathan Binas, Remi Le Priol, Aaron Courville

​

Notes on OOD reading group presentation

• Started out a bit weak
• Can use Yoshua’s kind of OOD story? (“you go to another country….”)
• Can use the canonical cow photos
• IRM story for “not paying attention to color” is unclear… shouldn’t gradients on the training envs want you to pay attention to color??
• Unclear: distributions vs. Risk functions
• Probabilistic view + Leon’s talk
• Picture before equations!
• 2 Goals of REx should maybe come earlier (where/how?)
• Need frequencies = 1,2,3 for sine wave example!
• Also an equation saying “test risk != ½(risk1 + risk2)”
• Gradient vector fields still don’t have a good place…
• It’s a LOT of content overall; needs to be pared down
• Double check RL spurious feature construction
• Experiments should focus on TAKE-AWAYS! (write those down on the slides!)

The problem of spurious features

Real world example:

Background=grass �vs. �Background=water

​

​

​

​

​

​

​

​

​

Synthetic example:

Color=green

Vs.

Color=red

environments

The problem of spurious features

Real world example:

Background=grass �vs. �Background=water

​

​

​

​

​

​

​

​

​

Synthetic example:

Color=green

Vs.

Color=red

The Invariant Risk Minimization (IRM) solution:

• IRM says: “If the classifier wants to pay more attention to a feature in some environments than others, then that feature is spurious”

features

classifier

ERM term regularizer

​

Leon Bottou, in a talk about IRM:

​

Why we need IRM

Training environments:

P1,P2,P3,P4

The Risk Extrapolation (REx) solution:

The “robust approach” Leon was just talking about:

​

​

​

Our generalization, MM-REx:

​

​

​

​

A simpler variant, V-REx:

Good performance

​

Consistent performance

The Risk Extrapolation (REx) solution:

Convex �combination

Affine combination

Why does REx work?

​

Goals of Risk Extrapolation:

1. Lower average risk
2. Similarity of risks across environments

�

​

Training environments

Test environment

Why does REx work?

​

Goals of Risk Extrapolation:

• Lower average risk
• Similarity of risks across environments

�

​

Training environments

Test environment

Why does REx work?

​

Goals of Risk Extrapolation:

• Lower average risk
• Similarity of risks across environments

�

​

Training environments

Test environment

Someone should have a question around now….

Why does REx work?

​

Goals of Risk Extrapolation:

• Lower average risk
• Similarity of risks across environments

�

​

Training environments

Test environment

Someone should have a question around now….

​

Are these extrapolations Correct??

Why does REx work?

​

Goals of Risk Extrapolation:

• Lower average risk
• Similarity of risks across environments

�

​

Training environments

Test environment

Someone should have a question around now….

​

Are these extrapolations Correct??

Answer: No.

Counterexample: sine wave regression

​

Train1

​

​

Test

​

​

​

Train 2

​

Suppose my model predicts Y=sin(x)...

​

Risk > 0

​

​

​

Risk = 0

​

​

​

Risk > 0

A Probabilistic view on REx:

Negative

Probabilities!?!?�

...or positive probabilities with a different loss function?

Results: CMNIST

Results: CMNIST

A note on methodology…

​

OOD is mostly about unknown unknowns ⇒ No tuning allowed on test distribution!

​

Solution:

• Use development tasks for tuning.
• “pre-register” evaluation experiments.

​

​

MM-REx vs. V-REx

​

​

​

​

​

Our generalization, MM-REx:

​

​

​

​

A simpler variant, V-REx:

​

​

​

​

Goals of Risk Extrapolation:

1. Lower average risk
2. Similarity of risks across environments

Results: CMNIST

A note on methodology…

​

OOD is mostly about unknown unknowns ⇒ No tuning allowed on test distribution!

​

Solution:

• Use development tasks for tuning.
• “pre-register” evaluation experiments.

​

​

Results: VLCS and PACS

VLCS: V(VOC2007), L(LabelMe), S(SUN09), C(Caltech).

PACS: P(photo), A(art), C(cartoon), S(sketch).

Results: VLCS and PACS

Results: RL

​

​

​

Spurious feature construction:

• Copy part of the original state
• Add (environment -dependent) noise to the original state

�Result:

• ERM wants to use copied state
• REx doesn’t
• IRM fails for some reason

�

Structural equation models (from IRM paper)

Good:

​

​

​

Bad:

OMG more results! Financial prediction task

Why is IRM difficult to train?

Memorization minimizes �IRM and REx penalties!

Timing is everything:

Hypothesis: �To train IRM/REx:�1) learn predictive features�2) throw out spurious ones

​

​

Remaining Questions/Directions:

• Can REx deal with changing levels of label noise?
• When is linearly extrapolating risks valid/sensible?
• Is there a causal interpretation of REx?
• Improving OOD evaluation
• Better benchmarks
• Better methodology
• How relevant are spurious features in practice?

What are YOUR questions?�