Kolchinsky Artemy
ICREA-Complex Systems Lab, Universitat Pompeu Fabra, 08003 Barcelona, Spain.
Universal Biology Institute, The University of Tokyo, Tokyo 113-0033, Japan.
Entropy (Basel). 2024 Jun 26;26(7):546. doi: 10.3390/e26070546.
The partial information decomposition (PID) aims to quantify the amount of redundant information that a set of sources provides about a target. Here, we show that this goal can be formulated as a type of information bottleneck (IB) problem, termed the "redundancy bottleneck" (RB). The RB formalizes a tradeoff between prediction and compression: it extracts information from the sources that best predict the target, without revealing which source provided the information. It can be understood as a generalization of "Blackwell redundancy", which we previously proposed as a principled measure of PID redundancy. The "RB curve" quantifies the prediction-compression tradeoff at multiple scales. This curve can also be quantified for individual sources, allowing subsets of redundant sources to be identified without combinatorial optimization. We provide an efficient iterative algorithm for computing the RB curve.
部分信息分解（PID）旨在量化一组源关于一个目标所提供的冗余信息量。在此，我们表明这个目标可以被表述为一种信息瓶颈（IB）问题，称为“冗余瓶颈”（RB）。RB 将预测与压缩之间的权衡形式化：它从最能预测目标的源中提取信息，而不揭示是哪个源提供了该信息。它可以被理解为“布莱克威尔冗余”的一种推广，我们之前将其作为 PID 冗余的一种有原则的度量提出。“RB 曲线”在多个尺度上量化预测 - 压缩权衡。这条曲线也可以针对单个源进行量化，从而无需组合优化就能识别冗余源的子集。我们提供了一种用于计算 RB 曲线的高效迭代算法。
