In the classical source coding problem, the compressed source is reconstructed at the decoder with respect to some distortion metric. Motivated by settings in which we are interested in more than simply reconstructing the compressed source, we investigate a single-shot compression problem where the decoder is tasked with reconstructing the original data as well as making inferences from it. Quality of inference and reconstruction is determined by a distortion criteria for each task. Given allowable distortion levels, we are interested in characterizing the probability of excess distortion. Modeling the joint inference and reconstruction problem as direct-indirect source coding one, we obtain lower and upper bounds for excess distortion probability. We specialize the converse bound and present a new easily computable achievability bound for the case where the distortion metric for reconstruction is logarithmic loss.

翻译：在经典信源编码问题中，压缩后的信源在解码端依据某种失真度量进行重建。受我们不仅关注压缩信源重建这一简单目标的场景启发，本文研究了一种单次压缩问题，其中解码器需同时完成原始数据的重建与推理任务。推理与重建的质量由各自任务的失真准则决定。在给定容许失真水平的前提下，我们致力于刻画超额失真的概率。通过将联合推理与重建问题建模为直接-间接信源编码问题，我们获得了超额失真概率的上下界。针对重建失真度量为对数损失的情形，我们对对偶界进行了专门化，并提出了一种新的易于计算的可达性界。