  The total correlation(TC) is a crucial index to measure the correlation
between marginal distribution in multidimensional random variables, and it is
frequently applied as an inductive bias in representation learning. Previous
research has shown that the TC value can be estimated using mutual information
boundaries through decomposition. However, we found through theoretical
derivation and qualitative experiments that due to the use of importance
sampling in the decomposition process, the bias of TC value estimated based on
MI bounds will be amplified when the proposal distribution in the sampling
differs significantly from the target distribution. To reduce estimation bias
issues, we propose a TC estimation correction model based on supervised
learning, which uses the training iteration loss sequence of the TC estimator
based on MI bounds as input features to output the true TC value. Experiments
show that our proposed method can improve the accuracy of TC estimation and
eliminate the variance generated by the TC estimation process.
