Given data generated from multiple factors of variation that cooperatively transform their appearance, disentangled representations aim at reversing the process by mapping data to multiple random variables that individually capture distinct generative factors. As the concept is intuitive but abstract, one needs to quantify it with disentanglement metrics to evaluate and compare the quality of disentangled representations between different models. Current disentanglement metrics are designed to measure the concentration, e.g., absolute deviation, variance, or entropy, of each variable conditioned by each generative factor, optionally offset by the concentration of its marginal distribution, and compare it among different variables. When representations consist of more than two variables, such metrics may fail to detect the interplay between them as they only measure pairwise interactions. In this work, we use the Partial Information Decomposition framework to evaluate information sharing between more than two variables, and build a framework, including a new disentanglement metric, for analyzing how the representations encode the generative factors distinctly, redundantly, and cooperatively. We establish an experimental protocol to assess how each metric evaluates increasingly entangled representations and confirm through artificial and realistic settings that the proposed metric correctly responds to entanglement. Our results are expected to promote information theoretic understanding of disentanglement and lead to further development of metrics as well as learning methods.

提出了一种分析多元表示如何解开基础生成因素的框架，通过部分信息分解方法分析多元表示中的信息共享并提出了新的分离度量，实验发现分离度量对纠缠反应正确，发现分离度量相似的自编码器模型在纠缠方面有不同的特征，需要采用不同的策略来获得分离表示。

利用部分信息分解进行解缠分析