关键词: 神经网络, 数据包络, 效率估计

Abstract: As a non-parametric model which is suitable for multi input and multi output set, Data Envelopment Analysis(DEA) and its extended models can avoid the reliance on the specific form of the production efficiency function, making them more universal and practical in solving practical problems. However, DEA computes the production frontier on the basis of deterministic assumptions which ignore the uncertain factors such as noise, random errors or environmental variables in the model while the data of actual production sets is composed of non-theoretical data which often include errors and other interference factors. Therefore, using DEA to estimate the efficiency of actual production sets would result in production frontier bias, which is easily influenced by specific data.
Machine learning algorithm, having advantages in handling uncertainty problems, have become the mainstream method for data processing. In this paper, we consider combining DEA with machine learning algorithms to form an extensible integrated model with wider applicability to analyze multi-feature and uncertain data of actual production sets, reducing reliance on specific parameters or probability distributions of production efficiency function. As neural network algorithms have advantages in handling multidimensional and complex data, this paper develops a stochastic hybrid production frontier based on BP neural network algorithm (BP_SHPF), which can evaluate the efficiency of decision-making units on uncertain frontiers. The BP_SHPF includes the following four steps: (1)Using DEA to determine the production frontier. (2)Assuming that decision-making units located near the production frontier still have a certain probability of being effective, mix these decision-making units with the effective decision-making units to generate a new production frontier. (3)Constructing a three layer structure neural network, training the dataset, and determining the new position of the production frontier. (4)Estimating the decision-making unit efficiency value with the newly established production frontier, where the distance between the actual output value of the decision-making units and the output value on the production frontier represents the units' ineffective part.
This paper uses Monte Carlo method to verify the BP_SHPF in single output single input sets and multi output multi input sets. The results show that the BP_SHPF model's MSE and BIAS values are lower than those of the control group experiment, and that these values decrease as the sample size increases and increase as the data dimension increases. Through Spearman rank correlation analysis, the efficiencies of the decision-making units computed by BP_SHPF are consistent with those of the original DEA, indicating that the efficiency rankings of the BP_SHPF is reliable. Additionally, this paper uses BP_SHPF to evaluate the efficiency of 107 China rural commercial banks between 2014 and 2018, and finds that rural commercial banks in the eastern region has the best efficiency average during this period. The efficiency standard deviation obtained by empirical analysis shows that the efficiency values' standard deviation of decision-making units processed by BP_SHPF is higher than that obtained by DEA in the same region, highlighting a greater variation in efficiency values in the same region and better reflecting the efficiency gap between rural commercial banks.
In all, BP_ SHPF can not only avoid the limitations of non-machine learning methods, but also preserve the positional relationship between decision-making units and production frontiers as it corrects the problem of production frontiers. It obtains more easily distinguishable and reasonable decision-making unit efficiency values and efficiency rankings in evaluating the efficiency of actual production sets.

Key words: neural network, Data Envelopment Analysis, estimate efficiency