| Paper ID | D3-S7-T3.4 |
| Paper Title |
t-Entropy: A New Measure of Uncertainty with Some Applications |
| Authors |
Saptarshi Chakraborty, University of California, Berkeley, United States; Debolina Paul, Swagatam Das, Indian Statistical Institute, India |
| Session |
D3-S7-T3: Topics in Learning II |
| Chaired Session: |
Thursday, 15 July, 00:00 - 00:20 |
| Engagement Session: |
Thursday, 15 July, 00:20 - 00:40 |
| Abstract |
The concept of Entropy plays a key role in Information Theory, Statistics, and Machine Learning. This paper introduces a new entropy measure, called the \textit{t}-entropy, which exploits the concavity of the inverse-tan function. We analytically show that the proposed \textit{t}-entropy satisfies the prominent axiomatic properties of an entropy measure. We demonstrate an application of the proposed entropy measure for multi-level thresholding of images. We also propose the entropic-loss as a measure of the divergence between two probability distributions, which leads to robust estimators in the context of parametric statistical inference. The consistency and asymptotic breakdown point of the proposed estimator are mathematically analysed. Finally, we also show an application of the \textit{t}-entropy to feature weighted data clustering.
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