Abstract: The pointwise mutual information profile, or simply profile, is the distribution of pointwise mutual information for a given pair of random variables. One of its important properties is that its expected value is precisely the mutual information between these random variables. In this paper, we analytically describe the profiles of multivariate normal distributions and show that for an expressive family of distributions, termed Bend and Mix Models, the profile can be accurately estimated using Monte Carlo methods. We then show how Bend and Mix Models can be used to study the limitations of existing mutual information estimators, investigate the behavior of neural critics used in variational estimators, and understand the effect of experimental outliers on mutual information estimation. Finally, we show how Bend and Mix Models can be used to obtain model-based Bayesian estimates of mutual information, suitable for problems with available domain expertise in which uncertainty quantification is necessary. The accompanying code is available at https://github.com/cbg-ethz/bmi.
Submission Length: Regular submission (no more than 12 pages of main content)
Changes Since Last Submission: This is the camera-ready version of the manuscript. It has been deanonymized and includes the following minor changes:
- Completed additional proofreading to eliminate typographical errors.
- Improved the clarity of figures in Appendix C.5.3.
Code: https://github.com/cbg-ethz/bmi
Assigned Action Editor: ~Taylor_W._Killian1
Submission Number: 3233
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