# Bounds on mutual information of mixture data for classification tasks

arXiv: https://arxiv.org/abs/2101.11670 · HTML: https://mlsanity.com/paper/2101.11670/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2021.

## Built on by (most cited first, 1 of 1)

- [End-to-End Optimization of Incoherent Imaging for Classification Under Detector-Limited Readout](https://mlsanity.com/paper/2606.09792/) (2026)

## Abstract (arXiv)

The data for many classification problems, such as pattern and speech recognition, follow mixture distributions. To quantify the optimum performance for classification tasks, the Shannon mutual information is a natural information-theoretic metric, as it is directly related to the probability of error. The mutual information between mixture data and the class label does not have an analytical expression, nor any efficient computational algorithms. We introduce a variational upper bound, a lower bound, and three estimators, all employing pair-wise divergences between mixture components. We compare the new bounds and estimators with Monte Carlo stochastic sampling and bounds derived from entropy bounds. To conclude, we evaluate the performance of the bounds and estimators through numerical simulations.