The support vector machine (SVM) is a machine learning approach rooted in statistical learning theory [19]. It hinges on VC dimensional theory, the principle of structural risk minimization [20,21], and represents the pioneering algorithm grounded in geometric distance [22]. Serving as a small-sample learning technique with a robust theoretical foundation, an SVM’s final decision function is influenced by only a handful of support vectors. Its computational complexity hinges on these vectors rather than the sample space’s dimensionality, sidestepping the so-called “dimensional disaster”. Wang et al. [23] harnessed SVM to predict the nonlinear facet of garlic prices, coupling it with ARIMA for linear price prediction, yielding accurate results. Nevertheless, SVM does have drawbacks, including diminished performance when data features (dimensions) surpass the sample size, sensitivity to parameters and kernel functions. Consequently, approaches like parameter optimization are frequently employed to enhance SVM prediction performance. Duan et al. [24] employed a genetic algorithm to identify optimal parameter combinations for a support vector regression model. With these optimized parameters, they constructed a support vector regression model for predicting fish prices, yielding precise outcomes with minor errors. SVR’s remarkable ability to manage high-dimensional, nonlinear, and small-sample data positions is a vital technique in agricultural price prediction.

贝叶斯网络本质上是一个有向无环图，它使用概率网络进行不确定性推断。贝叶斯网络在解决农产品价格预测和其他农业问题方面的卓越表现主要源于以下主要特点：（A Bayesian network is essentially a directed acyclic graph that uses probabilistic networks to make uncertainty inferences. The excellence of Bayesian networks in solving agricultural price forecasting as well as other agricultural problems stems mainly from the following key features: (1）贝叶斯网络可以处理不完整的数据集;（2）贝叶斯网络允许人们理解变量之间的关系并量化这些关系的强度;（3）定量和定性数据相结合的能力;（4）将专业知识和数据结合到贝叶斯网络中的能力;（5）贝叶斯方法可以相对容易地避免学习过程中的数据过度拟合。) Bayesian networks can handle incomplete datasets; (2) Bayesian networks allow one to understand the relationships between variables and quantify the strength of these relationships; (3) the ability to combine quantitative and qualitative data; (4) the ability to combine expert knowledge and data into Bayesian network; and (5) Bayesian methods can relatively easily avoid data overfitting during the learning process. Putri [25]使用贝叶斯网络算法作为数据挖掘分类方法，根据天气信息预测万隆地区的胡椒商品价格。贝叶斯网络的一个缺点是它们不支持环形网络 used Bayesian network algorithms as a data mining classification method to predict pepper commodity prices in Bandung region based on weather information. One disadvantage of Bayesian networks is that they do not support ring networks [26]，这会削弱网络的鲁棒推理能力，并且这种限制对静态贝叶斯网络并不友好。动态贝叶斯网络（, which would weaken the robust inference capability of the network, and this limitation is not friendly to static Bayesian networks. Dynamic Bayesian network (DBN）是一个融合概率论和影响图的动态模型。它将时变隐马尔可夫模型与传统的静态贝叶斯网络相结合，从两者中获益，同时通过随时间推移的动态适应性和新状态的合并来避开它们的局限性) is a dynamic model amalgamating probability theory and influence diagram. It combines a time-varying hidden Markov model with a traditional static Bayesian network, capturing benefits from both while sidestepping their limitations through dynamic adaptability over time and the incorporation of new states [27]。马再兴. Ma Zaixing [28]利用 used the PC算法从数据中学习，根据专家知识进行构造，并将专家知识和PC算法相结合进行结构学习。得到初始结构后，他调整得到的初始结构得到模型的网络结构，然后用EM算法进行参数学习。此外，他获得了用于价格预测的完整动态贝叶斯网络模型，并根据预测结果选择最佳模型来预测生猪的价格和产量。结果表明，预测效果优于对照组的ARIMA、SVM和BP神经网络模型。 algorithm to learn from data, construct according to expert knowledge, and combine expert knowledge and PC algorithm to perform structural learning. After obtaining the initial structure, he adjusted the obtained initial structure to obtain the network structure of the model, and then used the EM algorithm to perform parameter learning. Moreover, he obtained a complete dynamic Bayesian network model for price prediction, and selected the best model based on the prediction results to predict the price and output of live pigs. The results show that the prediction effect is better than the control group’s ARIMA, SVM, and BP neural network models.

神经网络通常被称为人工神经网络Neural networks are commonly referred to as artificial neural networks （ANN）。它们构成了一个复杂的非线性网络系统，由许多以类似于生物神经元的方式相互连接的处理单元组成。神经网络表现出强大的非线性拟合能力，使它们能够映射复杂的非线性关系。此外，他们的学习规则很简单，可以在计算机上轻松实现。它们具有较强的鲁棒性、记忆力、非线性映射能力和强大的自学习能力，在应对农产品价格预测挑战方面具有独特的优势。1987年，(ANN). They constitute a complex nonlinear network system composed of numerous processing units interconnected in a manner resembling biological neurons. Neural networks exhibit robust nonlinear fitting capabilities, enabling them to map intricate nonlinear relationships. Furthermore, their learning rules are simple, making them easily implementable on computers. They possess strong robustness, memory, nonlinear mapping abilities, and powerful self-learning capabilities, showcasing unique advantages in addressing agricultural commodity price prediction challenges. In 1987, Lapedes和 and Farber [29]率先将神经网络应用于预测，标志着神经网络预测的开始。 pioneered the application of neural networks to forecasting, marking the inception of neural network predictions. In 1993年，, Kohzadi等人 et al. [30]是最早使用前馈神经网络来预测美国小麦和牛价格的人之一。他们将预测结果与 were among the first to employ feed-forward neural networks for predicting US wheat and cattle prices. They compared the predictive results with those from ARIMA的结果进行了比较，得出的结论是神经网络表现出卓越的转折点预测能力，并实现了更准确的价格预测。, concluding that neural networks exhibited superior turning point prediction capabilities and achieved more accurate price forecasting.

随着大数据和人工智能技术的进步，神经网络在农业领域的应用越来越广泛As big data and artificial intelligence technology advance, neural networks find increasingly wide application in the agricultural domain [31]。在价格预测领域，流行的神经网络模型如下（表. In the realm of price prediction, prevalent neural network models are as follows (Table 2和示例总结了神经网络在农产品价格预测中的应用）：, along with examples, summarizes the applications of neural networks in agricultural commodity price prediction):

• 反向传播（Backpropagation (BP）网络) Networks [32，,33，,34]：: BP网络易于实现和理解。但是，很容易陷入局部最优解，训练速度相对较慢。 networks are easy to implement and understand. However, it is easy to fall into local optimal solutions and the training speed is relatively slow.

• 径向基函数神经网络（Radial Basis Function Neural Networks (RBFNN）) [35，,36]：: A BP网络是非线性映射的全局近似，而RBF网络是非线性映射的局部近似，训练速度更快。RBF可以处理复杂的非线性关系，具有良好的泛化能力。但是，它对网络结构和超参数敏感，训练和调优相对复杂。当问题涉及复杂的非线性关系并且有足够的训练数据时，您可以尝试使用 RBF 神经网络。 network is a global approximation of a nonlinear mapping, whereas an RBF network is a local approximation of a nonlinear mapping and is faster to train. RBF can handle complex nonlinear relationships and has good generalization ability. However, it is sensitive to the network structure and hyperparameters, and the training and tuning are relatively complicated. When the problem involves complex nonlinear relationships and there is enough training data, you can try to use RBF neural network.
• 长短期记忆网络（Long Short-Term Memory Networks (LSTM）) [37，,38]：: LSTM神经网络是一种特殊的递归神经网络，它通过引入遗忘门、输入门和输出门等结构来控制通过单元状态的信息流，从而解决长期依赖性和梯度消失的问题。LSTM 神经网络具有记忆和捕获长期依赖关系的能力。因此，当预测问题涉及时间序列数据时，LSTM 是一个不错的选择，尤其是具有长期依赖关系的数据。 neural network is a special kind of recurrent neural network that solves the problems of long-term dependency and gradient vanishing by introducing structures, such as forgetting gates, input gates, and output gates, to control the flow of information through the unit states. LSTM neural networks have the ability to memorize and capture long-term dependencies. Therefore, LSTM is a good choice when the prediction problem involves time series data, especially with long-term dependencies.
• 卷积神经网络（Convolutional Neural Networks (CNN）) [39]：: CNN是一个多层前馈神经网络，通过卷积层、池化层和全连接层等结构从数据中提取局部和全局特征，以实现自动特征学习和抽象。在价格预测任务中，CNN 可以学习和捕获输入数据中的重要特征，例如时间序列、数据趋势、周期性等。市场价格通常受到多种因素的组合影响，CNN可以更好地处理这些复杂的非线性关系。 is a multi-layer feed-forward neural network that extracts local and global features from data through structures, such as convolutional, pooling, and fully connected layers to enable automatic feature learning and abstraction. In price prediction tasks, CNNs can learn and capture important features, such as time series, data trends, periodicity, etc., in the input data. Market prices are usually affected by a combination of several factors, and CNNs can better handle these complex nonlinear relationships.
• 混沌神经网络（Chaos Neural Networks (CNN）) [40，,41]：混沌神经网络（: Chaos neural network (CNN）是一种结合混沌理论和神经网络的智能信息处理系统。混沌神经网络利用混沌现象的敏感性和不可预测性，增强神经网络的学习和泛化能力，从而提高预测和建模的准确性。通过引入混沌噪声或逻辑图等方法，混沌神经网络能够在一定程度上避免神经网络陷入局部极小值，从而加快训练过程并提高收敛率。) is a kind of intelligent information processing system that combines chaos theory and neural network. Chaotic neural networks exploit the sensitivity and unpredictability of chaotic phenomena to enhance the learning and generalization capabilities of neural networks, thus improving the accuracy of prediction and modeling. By introducing methods, such as chaotic noise or logistic maps, chaotic neural networks are able to avoid neural networks from falling into local minima to a certain extent, thus speeding up the training process and increasing the convergence rate.
• 极限学习机（Extreme Learning Machines (ELM）) [42]：极限学习机是一种前馈神经网络，由新加坡南洋理工大学的黄广斌教授于: The extreme learning machine is a feed-forward neural network that was first proposed by Professor Huang Guangbin of Nanyang Technological University in Singapore in 2006年首次提出。ELM具有训练快、泛化能力强、实现简单等优点。. ELM has the advantages of fast training, high generalization ability, and simple implementation.
• 小波神经网络（Wavelet Neural Networks (WNN）) [43，,44]：小波神经网络（: Wavelet neural network (WNN）是一种基于小波变换和神经网络的方法。通过将原始数据分解为不同尺度的小波系数，能够有效地提取数据中的各种特征，如趋势、周期、季节性等，WNN结合了神经网络强大的拟合能力，能够进行非线性映射，从而实现对未来价格的准确预测。然而，高复杂性和高数据要求是该方法不可避免的缺点。) is a method based on wavelet transform and neural network. By decomposing the original data into wavelet coefficients at different scales, it is able to effectively extract a variety of features in the data, such as trend, cycle, seasonality, etc. WNN combines the powerful fitting ability of neural networks, which is capable of nonlinear mapping, thus achieving accurate prediction of future prices. However, high complexity and high data requirements are the unavoidable drawbacks of this method.