Why a Model Produced by Training a Neural Network is Often More Computationally Efficient than a Nonlinear Regression Model: A Theoretical Explanation

Jaime Nava; Vladik Kreinovich

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Why a Model Produced by Training a Neural Network is Often More Computationally Efficient than a Nonlinear Regression Model: A Theoretical Explanation

机译：为什么通过训练神经网络生成的模型通常比非线性回归模型在计算上更有效：一个理论解释

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摘要

Many real-life dependencies can be reasonably accurately described by linear functions. If we want a more accurate description, we need to take non-linear terms into account. To take nonlinear terms into account, we can either explicitly add quadratic terms to the regression equation, or, alternatively, we can train a neural network with a non-linear activation function. At first glance, regression algorithms lead to simpler expressions, but in practice, often, a trained neural network turns out to be a more computationally efficient way of predicting the corresponding dependence. In this paper, we provide a reasonable explanation for this empirical fact.

机译：线性函数可以合理准确地描述许多现实生活中的依赖性。如果我们想要更准确的描述，则需要考虑非线性项。为了考虑非线性项，我们可以将二次项显式添加到回归方程中，或者可以训练带有非线性激活函数的神经网络。乍一看，回归算法可以简化表达式，但实际上，训练有素的神经网络通常是预测相应依赖关系的更有效的计算方法。在本文中，我们为这一经验事实提供了合理的解释。

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《Journal of uncertain systems》 |2014年第3期|193-204|共12页
作者
Jaime Nava; Vladik Kreinovich;
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作者单位

Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA;

Department of Computer Science, University of Texas at El Paso, El Paso, TX 79968, USA;

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原文格式 PDF
正文语种 eng
中图分类
关键词
neural networks; linear regression; nonlinear regression;

机译：神经网络;线性回归非线性回归;

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5. Computationally complex, nonlinear systems modeling using neural networks. [D] . Hu, Xiao. 2004

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Why a Model Produced by Training a Neural Network is Often More Computationally Efficient than a Nonlinear Regression Model: A Theoretical Explanation

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