ReRecent studies in machine learning are based on models in which parameters or state variables are bounded restricted. These restrictions are from prior information to ensure the validity of scientific theories or structural consistency based on physical phenomena. The valuable information contained in the restrictions must be considered during the estimation process to improve estimation accuracy. Many researchers have focused on linear regression models subject to linear inequality restrictions, but generalized linear models have received little attention. In this paper, the parameters of beta Bayesian regression models subjected to linear inequality restrictions are estimated. The proposed Bayesian restricted estimator, which is demonstrated by simulated studies, outperforms ordinary estimators. Even in the presence of multicollinearity, it outperforms the ridge estimator in terms of the standard deviation and the mean squared error. The results confirm that the proposed Bayesian restricted estimator makes sparsity in parameter estimating without using the regularization penalty. Finally, a real data set is analyzed by the new proposed Bayesian estimation method.

翻译：近期机器学习研究多采用参数或状态变量受有界约束的模型。这些约束源于先验信息，旨在确保科学理论的有效性或基于物理现象的结构一致性。为提升估计精度，必须在估计过程中充分考虑约束中包含的宝贵信息。众多研究者聚焦于受线性不等式约束的线性回归模型，但广义线性模型却鲜受关注。本文针对受线性不等式约束的Beta贝叶斯回归模型参数进行估计。经仿真研究验证，所提出的贝叶斯受限估计量优于常规估计量。即便存在多重共线性时，该估计量在标准差与均方误差方面仍优于岭估计量。研究结果证实，所提出的贝叶斯受限估计量无需正则化惩罚即可实现参数估计的稀疏性。最后，采用新提出的贝叶斯估计方法对真实数据集进行了分析。