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The total correlation(TC) is a crucial index to measure the correlationbetween marginal distribution in multidimensional random variables, and it isfrequently applied as an inductive bias in representation learning. Previousresearch has shown that the TC value can be estimated using mutual informationboundaries through decomposition. However, we found through theoreticalderivation and qualitative experiments that due to the use of importancesampling in the decomposition process, the bias of TC value estimated based onMI bounds will be amplified when the proposal distribution in the samplingdiffers significantly from the target distribution. To reduce estimation biasissues, we propose a TC estimation correction model based on supervisedlearning, which uses the training iteration loss sequence of the TC estimatorbased on MI bounds as input features to output the true TC value. Experimentsshow that our proposed method can improve the accuracy of TC estimation andeliminate the variance generated by the TC estimation process.

Understanding the limitation of Total Correlation Estimation Based on Mutual Information Bounds