- arXivOnline Estimation and Optimization of Utility-Based Shortfall RiskMenon, Arvind S., A., Prashanth L., and Jagannathan, Krishna2021
Utility-Based Shortfall Risk (UBSR) is a risk metric that is increasingly popular in financial applications, owing to certain desirable properties that it enjoys. We consider the problem of estimating UBSR in a recursive setting, where samples from the underlying loss distribution are available one-at-a-time. We cast the UBSR estimation problem as a root finding problem, and propose stochastic approximation-based estimations schemes. We derive non-asymptotic bounds on the estimation error in the number of samples. We also consider the problem of UBSR optimization within a parameterized class of random variables. We propose a stochastic gradient descent based algorithm for UBSR optimization, and derive non-asymptotic bounds on its convergence.
- arXivQ-means using variational quantum feature embeddingMenon, Arvind S, and Puri, Nikaash2021
This paper proposes a hybrid quantum-classical algorithm that learns a suitable quantum feature map that separates unlabelled data that is originally non linearly separable in the classical space using a Variational quantum feature map and q-means as a subroutine for unsupervised learning. The objective of the Variational circuit is to maximally separate the clusters in the quantum feature Hilbert space. First part of the circuit embeds the classical data into quantum states. Second part performs unsupervised learning on the quantum states in the quantum feature Hilbert space using the q-means quantum circuit. The output of the quantum circuit are characteristic cluster quantum states that represent a superposition of all quantum states belonging to a particular cluster. The final part of the quantum circuit performs measurements on the characteristic cluster quantum states to output the inter-cluster overlap based on fidelity. The output of the complete quantum circuit is used to compute the value of the cost function that is based on the Hilbert-Schmidt distance between the density matrices of the characteristic cluster quantum states. The gradient of the expectation value is used to optimize the parameters of the variational circuit to learn a better quantum feature map.