On robustness of Spectral R\'{e}nyi divergence

Tetsuya Takabatake; Keisuke Yano

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arXiv · 2310.06902

On robustness of Spectral R\'{e}nyi divergence

Tetsuya Takabatake·Keisuke Yano

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Abstract

This paper studies a specific class of statistical divergences for spectral densities of time series: the spectral $\alpha$-R\'{e}nyi divergences, which include the Itakura-Saito divergence as a limiting case. The aim of this paper is to highlight both information-theoretic and statistical properties of spectral $\alpha$-R\'{e}nyi divergences. We reveal the connection between the spectral $\alpha$-R\'{e}nyi divergence and the $\gamma$-divergence in robust statistics, and a variational representation of the spectral $\alpha$-R\'{e}nyi divergence. Inspired by these results suggesting "robustness" of spectral $\alpha$-R\'{e}nyi divergence, we show that the minimum spectral R\'{e}nyi divergence estimate has a stable optimization path with respect to outliers in the frequency domain, unlike the minimum Itakura-Saito divergence estimator, and thus it delivers more stable estimates, reducing the need for intricate pre-processing.

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Tetsuya Takabatake, Keisuke Yano. 2023-10-10. On robustness of Spectral R\'{e}nyi divergence. https://arxiv.org/abs/2310.06902

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