# Research on Named Entity Recognition Based on Gated Interaction Mechanisms
## 2 Materials and Methods
### Feature Extraction Layer
Specifically, Bayesian optimization assumes that i is the collection of hyperparameters U and e in the proposed algorithm, and f(i) is the corresponding model effect. The goal is to solve the distribution of the posterior probability P(f*i*,i,f), where f* refers to the untried model effect, and i* refers to the corresponding untried hyperparameters. By fitting this posterior probability distribution, the estimated model effects corresponding to different hyperparameter sets ii are obtained. In the process of Bayesian optimization, Gaussian process regression is employed as the prior function, and the upper bound of the confidence interval is used as the acquisition function. This method fully utilizes historical evaluation results and continuously updates the model. In the parameter optimization stage, a Gaussian process regression (GPR) strategy is adopted, aiming to fit the posterior probability distribution using historical evaluation data. As a non-parametric Bayesian method, GPR assumes that the posterior distribution of the target function (i.e., model performance metric) can be regarded as a Gaussian process, given the training dataset. Specifically, the Gaussian process assumes that the joint probability distribution of any set of random variables and their corresponding process states follows an N-dimensional Gaussian distribution. This distribution is completely characterized by its mean function and covariance function. The mean function reflects the overall trend of the process, while the covariance function describes the degree of association between different data points. Under the framework of Bayesian optimization, we use Gaussian process regression as the prior function and update the posterior probability distribution based on the observed experimental data. Based on the updated posterior distribution, we select the next evaluation point, usually choosing those expected to bring the greatest performance improvement. This process will iterate until it meets the predetermined stopping criteria, reaches the specified number of iterations, or observes that the improvement in model performance has saturated. The key equations are as follows:  
\[f*i,y,i*\sim N(Q*,\mathrm{cov}(f*)) \tag{3}\]  
\[Q*=k(i*,i){(k(i,i^{\prime})+\sigma_{n}^{2}I)}^{-1}y \tag{4}\]  
\[\mathrm{cov}(f*)=k(i*,i*)-k(i*,i){(k(i,i^{\prime})+\sigma_{n}^{2}I)}^{-1}k(i, i*) \tag{5}\]  
In the equations: i \(\in\mathrm{R^{Nrd}}\) represents the input data matrix; y \(\in\mathrm{R^{N}}\) represents the output data matrix; I \(\in\mathrm{R^{NN}}\) is the N-dimensional identity matrix; k(i,i*) is the symmetric positive definite covariance matrix; k(i,i*) \(\in\mathrm{R^{NN}}\) is the covariance matrix between the test point i and the training set inputs i; k(i*,i*) \(\in\mathrm{R^{NN}}\) is the covariance of the test point i itself; Q* is the mean corresponding to the test point i*; cov(f*) is the covariance corresponding to the test point i*. In the above formulas: The input data matrix i contains N observation samples, each with d-dimensional features; the output data matrix y contains the corresponding target values; and I is an N-dimensional identity matrix, used to ensure the positive definiteness of the covariance matrix. Bayesian optimization is a sequential model-based optimization method that, as the sampling of the parameter space increases, yields a distribution increasingly closer to the true distribution, thereby improving the accuracy of optimization. However, since model training consumes a large amount of computational resources, there is a need to balance the number of samples and computational cost in practice. To assess the quality of sampling in Bayesian optimization, we introduce the acquisition function, which measures the computational value of the current model's covariance function and mean function. The task of the acquisition function is to guide the algorithm in a targeted exploration of the parameter space in order to find the optimal solution more quickly.