We derive analytic bounds on the noise invariance of majority vote classifiers operating on compressed inputs. Specifically, starting from recent bounds on the true risk of majority vote classifiers, we extend the applicability of PAC-Bayesian theory to quantify the resilience of majority votes to input noise stemming from compression. The derived bounds are intuitive in binary classification settings, where they can be measured as expressions of voter differentials and voter pair agreement. By combining measures of input distortion with analytic guarantees on noise invariance, we prescribe rate-efficient machines to compress inputs without affecting subsequent classification. Our validation shows how bounding noise invariance can inform the compression stage for any majority vote classifier such that worst-case implications of bad input reconstructions are known, and inputs can be compressed to the minimum amount of information needed prior to inference.翻译

我们推导出多数投票分类器在处理压缩输入时的噪声不变性的解析界限。具体来说，从最近关于多数投票分类器真实风险的界限出发，我们扩展了PAC-Bayesian理论的适用性，以量化多数投票对来自压缩的输入噪声的抵抗能力。这些导出的界限在二元分类设置中具有直观性，可以通过选民差异和选民对一致性的表达式来衡量。通过将输入失真度量与噪声不变性的解析保证相结合，我们可以指定有效率的机器来压缩输入，而不影响后续的分类。我们的验证表明，通过界定噪声不变性，可以为任何多数投票分类器的压缩阶段提供信息，以便在知道恶劣输入重构的最坏情况下，将输入压缩到推理所需的最小信息量。