  With the exponential growth in data volume and the emergence of
data-intensive applications, particularly in the field of machine learning,
concerns related to resource utilization, privacy, and fairness have become
paramount. This paper focuses on the textual domain of data and addresses
challenges regarding encoding sentences to their optimized representations
through the lens of information-theory. In particular, we use empirical
estimates of mutual information, using the Donsker-Varadhan definition of
Kullback-Leibler divergence. Our approach leverages this estimation to train an
information-theoretic sentence embedding, called TexShape, for (task-based)
data compression or for filtering out sensitive information, enhancing privacy
and fairness. In this study, we employ a benchmark language model for initial
text representation, complemented by neural networks for information-theoretic
compression and mutual information estimations. Our experiments demonstrate
significant advancements in preserving maximal targeted information and minimal
sensitive information over adverse compression ratios, in terms of predictive
accuracy of downstream models that are trained using the compressed data.
