For several styles of fidelity constraints -- guaranteed distortion, conditional excess distortion, excess distortion -- we show mutual information upper bounds on the minimum expected description length needed to represent a random variable. Coupled with the corresponding converses, these results attest that as long as the information content in the data is not too low, minimizing the mutual information under an appropriate fidelity constraint serves as a reasonable proxy for the minimum description length of the data. We provide alternative characterizations of all three convex proxies, shedding light on the structure of their solutions.

翻译：针对多种保真度约束类型——包括保证失真、条件超额失真及超额失真——我们给出了表示随机变量所需最小期望描述长度的互信息上界。结合相应的逆定理，这些结果表明：只要数据中的信息含量不过低，在适当的保真度约束下最小化互信息即可作为数据最小描述长度的合理代理。我们提供了三种凸代理的替代表征，从而揭示其解的结构特性。