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arXiv 2109.03386cs.LG
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关于不变表示学习中权衡的刻画

On Characterizing the Trade-off in Invariant Representation Learning

Michigan State University(密歇根州立大学)

Bashir Sadeghi, Sepehr Dehdashtian, Vishnu Boddeti

摘要:

表示学习的许多应用,如隐私保护、算法公平性和领域自适应,都需要对被丢弃的语义信息进行显式控制。该目标被制定为满足两个目标:最大化预测目标属性的效用,同时对已知的语义属性是不变的(独立的)。不变表示学习(IRepL)问题的解决方案导致效用和不变性之间的权衡时,他们是竞争。虽然现有的作品研究这种权衡的界限,两个问题仍然悬而未决:1)效用和不变性之间的确切权衡是什么?以及2)什么是编码器(将数据映射到表示)来实现权衡,以及我们如何从训练数据估计它?本文讨论了再生核希尔伯特空间(RKHS)中的IRepLs的这些问题。在假设高维数据的低维投影的分布近似正态分布的情况下,我们推导出RKHS编码器的底层优化问题的全局最优解的封闭形式的解决方案。这产生了接近最优折衷、对应的最优表示维度和对应的编码器的封闭公式。我们还对代表性问题的权衡进行了数字量化,并将其与基线IRepL算法实现的权衡进行了比较。

英文摘要:

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 formulated as satisfying two objectives: maximizing utility for predicting a target attribute while simultaneously being invariant (independent) to a known semantic attribute. Solutions to invariant representation learning (IRepL) problems lead to a trade-off between utility and invariance when they are competing. While existing works study bounds on this trade-off, two questions remain outstanding: 1) What is the exact trade-off between utility and invariance? and 2) What are the encoders (mapping the data to a representation) that achieve the trade-off, and how can we estimate it from training data? This paper addresses these questions for IRepLs in reproducing kernel Hilbert spaces (RKHS)s. Under the assumption that the distribution of a low-dimensional projection of high-dimensional data is approximately normal, we derive a closed-form solution for the global optima of the underlying optimization problem for encoders in RKHSs. This yields closed formulae for a near-optimal trade-off, corresponding optimal representation dimensionality, and the corresponding encoder(s). We also numerically quantify the trade-off on representative problems and compare them to those achieved by baseline IRepL algorithms.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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