A New Information Theory of Certainty for Machine Learning
This work addresses the need for certainty quantification in machine learning, offering a novel theoretical framework with practical applications, though it appears incremental as an extension of entropy concepts.
The authors introduced 'troenpy' as a dual concept to entropy to quantify certainty in distributions, applying it to document classification and neural language models, achieving dramatic perplexity reduction.
Claude Shannon coined entropy to quantify the uncertainty of a random distribution for communication coding theory. We observe that the uncertainty nature of entropy also limits its direct usage in mathematical modeling. Therefore we propose a new concept troenpy,as the canonical dual of entropy, to quantify the certainty of the underlying distribution. We demonstrate two applications in machine learning. The first is for the classical document classification, we develop a troenpy based weighting scheme to leverage the document class label. The second is a self-troenpy weighting scheme for sequential data and show that it can be easily included in neural network based language models and achieve dramatic perplexity reduction. We also define quantum troenpy as the dual of the Von Neumann entropy to quantify the certainty of quantum systems.