Problem
Research questions and friction points this paper is trying to address.
Regularized Least Squares
Quadratic Neural Networks
System Identification
Regularized Least Squares Training of Quadratic Neural Networks with Applications to System Identification
🤖 AI Summary
本文提出了一种正则化最小二乘法来训练二次神经网络，提供了权重及其对数据误差敏感性的解析表达式，减少了计算时间，并成功应用于非线性系统辨识。
📝 Abstract
This paper proposes a least squares approach for the training of quadratic neural networks with regularization. The proposed methodology yields a lower bound on the solution of the training optimization problem for the case where the regularization coefficient is positive. Moreover, it yields closed-form expressions for the approximate solution and its sensitivity The lower bound is tight and the approximate solution is the optimal solution when the regularization coefficient is zero. Having a closed-form expression for the weights reduces considerably the computational time when compared with iterative numerical methods such as backpropagation that can get stuck in local minima. The proposed approach has three main contributions, namely, (i) it yields an analytical expression for the weights, (ii) an analytical expression for the sensitivity of the weights to errors in the data is also provided, (iii) it establishes a connection between the optimization to compute a lower bound and nuclear norm minimization. The proposed least squares training is successfully applied to a nonlinear system identification example where the proposed lower bound is compared with the optimal value.
Innovation
Methods, ideas, or system contributions that make the work stand out.
least squares
quadratic neural networks
regularization
closed-form solution
sensitivity analysis
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