论文标题
奇异的伍德伯里和伪确定的矩阵身份，并应用于高斯流程回归
A Singular Woodbury and Pseudo-Determinant Matrix Identities and Application to Gaussian Process Regression
论文作者
论文摘要
我们研究了由伍德伯里基质身份的单数形式产生的矩阵。我们为该矩阵提供了广义的逆和伪确定身份，这些身份直接应用于高斯过程回归，特别是其可能性表示和精度矩阵。我们将精度矩阵的定义扩展到协方差矩阵的Bott-Duffin倒数，并保留与条件独立性，条件精度和边际精度有关的属性。我们还为提出的确定性身份提供了有效的算法和数值分析，并在特定条件下证明了它们的优势，该条件与计算对数确定术语相关的特定条件可能会以高斯过程回归的可能性功能。
We study a matrix that arises from a singular form of the Woodbury matrix identity. We present generalized inverse and pseudo-determinant identities for this matrix, which have direct applications for Gaussian process regression, specifically its likelihood representation and precision matrix. We extend the definition of the precision matrix to the Bott-Duffin inverse of the covariance matrix, preserving properties related to conditional independence, conditional precision, and marginal precision. We also provide an efficient algorithm and numerical analysis for the presented determinant identities and demonstrate their advantages under specific conditions relevant to computing log-determinant terms in likelihood functions of Gaussian process regression.
