Nonparametric Regression Quantum Neural Networks
This work is incremental, applying nonparametric statistical techniques to quantum neural networks for potential improvements in regression tasks.
The authors extended their previous quantum neural network (QNN) frameworks to incorporate nonparametric regression methods, specifically implementing linear and polynomial nonparametric regression QNNs using Gauss-Jordan Elimination QNNs and training with high-probability confidence regions.
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 ($χ^2$-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.