Robustly Disentangled Causal Mechanisms: Validating Deep - PowerPoint PPT Presentation

Robustly Disentangled Causal Mechanisms: Validating Deep Representations for Interventional Robustness Raphael Suter 1 , Ðor¯ c 1 , Bernhard Schölkopf 2 , Stefan Bauer 2 de Miladinovi´ 1 ETH Zurich, 2 MPI for Intelligent Systems ICML 2019 1

Contributions • Causal Model for Representation Learning • Interventional Robustness Score • Visualising Robustness 2

Disentangled Representations Observation: X ∈ R n Feature encoding: Z = E ( X ) ∈ R K , n ≫ K Disentanglement ⇐ ⇒ components Z i represent different sources of variation in X 3

Definition: Disentangled Causal Process C · · · G 1 G 2 G K − 1 G K X Disentangled Causal Mechanisms: � � ∀ g △ p ( g i | do ( G j ← g △ � = p ( g i | g △ j )) = p ( g i ) j ) j 4

Unified Causal Model Generative Factors · · · G 1 G 2 G K − 1 G K X · · · Z 1 Z 2 Z K ′ − 1 Z K ′ Feature Representation 5

Robust Representation relevant factors: G 1 , G 2 nuisance factor: G K selected features: Z 1 , Z 2 6

Interventional Robustness Post Interventional Disagreement � � E [ Z sel | g rel )] , E [ Z sel | g rel , do ( G nuis ← g △ nuis )] d Interventional Robustness Score normalised score ∈ [ 0 , 1 ] 7

Theoretical Results • Properties of a disentangled causal process • IRS estimation from observational data D = { ( g ( i ) , x ( i ) ) } N i = 1 • Handles confounding G i ← C → G j • Efficient O ( N ) algorithm 8

Conclusion • disentanglement_lib by Locatello et al. (2019): github.com/google-research/disentanglement_lib • Poster: Thurs 06:30 – 09:00 PM at Pacific Ballroom #29 9