二次神经网络的正则化最小二乘训练及其在系统辨识中的应用
Regularized Least Squares Training of Quadratic Neural Networks with Applications to System Identification
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中文总结 AI 辅助
本文提出一种带正则化的二次神经网络最小二乘训练方法，给出权重及灵敏度的闭式解，并建立与核范数最小化的联系，在系统辨识中验证了其有效性。
中文摘要 AI 辅助
本文提出了一种带正则化的二次神经网络训练的最小二乘方法。所提出的方法在正则化系数为正的情况下，给出了训练优化问题解的一个下界。此外，它还给出了近似解及其灵敏度的闭式表达式。当正则化系数为零时，该下界是紧的，且近似解即为最优解。与诸如反向传播等可能陷入局部最小值的迭代数值方法相比，权重的闭式表达式显著减少了计算时间。所提出的方法有三个主要贡献，即：（i）它给出了权重的解析表达式；（ii）还提供了权重对数据误差的灵敏度的解析表达式；（iii）它建立了计算下界的优化与核范数最小化之间的联系。所提出的最小二乘训练成功应用于一个非线性系统辨识实例，其中将所提出的下界与最优值进行了比较。
英文摘要
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.
发表机构
- Concordia University（康考迪亚大学）
机构由 AI 辅助整理，请以论文原文为准。
