Nonparametric Regression Quantum Neural Networks

TL;DR

This paper extends quantum neural networks to nonparametric regression methods, implementing and analyzing nonparametric tests like LNR-QNN and PNR-QNN using Gauss-Jordan Elimination quantum neural networks with confidence interval training.

Contribution

It introduces nonparametric regression quantum neural networks and demonstrates their implementation with Gauss-Jordan Elimination quantum neural networks, expanding the applicability of QNNs.

Findings

Nonparametric QNNs are effective for regression tasks.

Implementation via GJE-QNN is feasible.

Confidence intervals guide training in nonparametric QNNs.

Abstract

In two pervious papers \cite{dndiep3}, \cite{dndiep4}, the first author constructed the least square quantum neural networks (LS-QNN), and ploynomial interpolation quantum neural networks ( PI-QNN), parametrico-stattistical QNN like: leanr regrassion quantum neural networks (LR-QNN), polynomial regression quantum neural networks (PR-QNN), chi-squared quantum neural netowrks ($\chi^2$-QNN). We observed that the method works also in the cases by using nonparametric statistics. In this paper we analyze and implement the nonparametric tests on QNN such as: linear nonparametric regression quantum neural networks (LNR-QNN), polynomial nonparametric regression quantum neural networks (PNR-QNN). The implementation is constructed through the Gauss-Jordan Elimination quantum neural networks (GJE-QNN).The training rule is to use the high probability confidence regions or intervals.