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：在经典的信源编码问题中，压缩后的信源在解码端根据某种失真度量进行重构。受限于我们对压缩信源的需求不仅限于简单重构的场景，本文研究了一种单次压缩问题，其中解码器需同时重构原始数据并对其进行推理。推理与重构的质量分别由各自任务的失真准则决定。在给定允许失真等级的情况下，我们致力于刻画过量失真的概率。通过将联合推理与重构问题建模为直接-间接信源编码问题，我们获得了过量失真概率的上下界。针对重构失真度量为对数损失的特殊情形，我们对逆界进行了具体化，并提出了一种易于计算的新可达性界。