On the Fundamental Trade-offs in Learning Invariant Representations

• URL: http://arxiv.org/abs/2109.03386v1
• Date: Wed, 8 Sep 2021 01:26:46 GMT
• Title: On the Fundamental Trade-offs in Learning Invariant Representations
• Authors: Bashir Sadeghi and Vishnu Boddeti
• Abstract summary: We identify and determine two fundamental trade-offs between utility and semantic dependence induced by the statistical dependencies between the data and its corresponding target and semantic attributes. We numerically quantify the trade-offs on representative problems and compare to the solutions achieved by baseline representation learning algorithms.
• Score: 7.868449549351487
• License: http://creativecommons.org/licenses/by-sa/4.0/
• Abstract: Many applications of representation learning, such as privacy-preservation, algorithmic fairness and domain adaptation, desire explicit control over semantic information being discarded. This goal is often formulated as satisfying two potentially competing objectives: maximizing utility for predicting a target attribute while simultaneously being independent or invariant with respect to a known semantic attribute. In this paper, we \emph{identify and determine} two fundamental trade-offs between utility and semantic dependence induced by the statistical dependencies between the data and its corresponding target and semantic attributes. We derive closed-form solutions for the global optima of the underlying optimization problems under mild assumptions, which in turn yields closed formulae for the exact trade-offs. We also derive empirical estimates of the trade-offs and show their convergence to the corresponding population counterparts. Finally, we numerically quantify the trade-offs on representative problems and compare to the solutions achieved by baseline representation learning algorithms.

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