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Main Authors: Chaudhuri, Abhra, Georgescu, Serban, Dutta, Anjan
Format: Preprint
Published: 2024
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Online Access:https://arxiv.org/abs/2402.11682
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author Chaudhuri, Abhra
Georgescu, Serban
Dutta, Anjan
author_facet Chaudhuri, Abhra
Georgescu, Serban
Dutta, Anjan
contents Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder $φ^*$ that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder $Φ^*_τ$. We prove that non-commutativity steers the optimization towards $Φ^*_τ$ instead of $φ^*$, bringing the $\mathcal{H}$-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning $Φ^*_τ$, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over $2\%$, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.
format Preprint
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publishDate 2024
record_format arxiv
spellingShingle Learning Conditional Invariances through Non-Commutativity
Chaudhuri, Abhra
Georgescu, Serban
Dutta, Anjan
Machine Learning
Computer Vision and Pattern Recognition
Invariance learning algorithms that conditionally filter out domain-specific random variables as distractors, do so based only on the data semantics, and not the target domain under evaluation. We show that a provably optimal and sample-efficient way of learning conditional invariances is by relaxing the invariance criterion to be non-commutatively directed towards the target domain. Under domain asymmetry, i.e., when the target domain contains semantically relevant information absent in the source, the risk of the encoder $φ^*$ that is optimal on average across domains is strictly lower-bounded by the risk of the target-specific optimal encoder $Φ^*_τ$. We prove that non-commutativity steers the optimization towards $Φ^*_τ$ instead of $φ^*$, bringing the $\mathcal{H}$-divergence between domains down to zero, leading to a stricter bound on the target risk. Both our theory and experiments demonstrate that non-commutative invariance (NCI) can leverage source domain samples to meet the sample complexity needs of learning $Φ^*_τ$, surpassing SOTA invariance learning algorithms for domain adaptation, at times by over $2\%$, approaching the performance of an oracle. Implementation is available at https://github.com/abhrac/nci.
title Learning Conditional Invariances through Non-Commutativity
topic Machine Learning
Computer Vision and Pattern Recognition
url https://arxiv.org/abs/2402.11682