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Estimation of Spectral Risk Measures

Authors

Ajay Kumar Pandey

Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India


Prashanth L.A.

Department of Computer Science and Engineering, Indian Institute of Technology Madras, Chennai, India


Sanjay P. Bhat

TCS Research, Hyderabad, India, and Department of Electrical Engineering, Indian Institute of Technology Madras, Chennai, India


Proceedings:

No. 13: AAAI-21 Technical Tracks 13

Volume

Issue:

Proceedings of the AAAI Conference on Artificial Intelligence, 35

Track:

AAAI Technical Track on Reasoning under Uncertainty

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Abstract:

We consider the problem of estimating a spectral risk measure (SRM) from i.i.d. samples, and propose a novel method that is based on numerical integration. We show that our SRM estimate concentrates exponentially, when the underlying distribution has bounded support. Further, we also consider the case when the underlying distribution satisfies an exponential moment bound, which includes sub-Gaussian and subexponential distributions. For these distributions, we derive a concentration bound for our estimation scheme. We validate the theoretical findings on a synthetic setup, and in a vehicular traffic routing application.

DOI:

10.1609/aaai.v35i13.17444


AAAI

Proceedings of the AAAI Conference on Artificial Intelligence, 35