标题： VBALD - 变分贝叶斯对数行列式的近似 显示英文标题

标题： VBALD - Variational Bayesian Approximation of Log Determinants

摘要： 评估正定矩阵的对数行列式在机器学习中非常普遍。 应用范围从高斯过程、最小体积椭球、度量学习、核学习、贝叶斯神经网络、确定点过程、马尔可夫随机场到离散图模型的划分函数。 为了避免经典的但代价高昂的Cholesky$\mathcal{O}(n^{3})$计算成本，我们提出了一种新方法，复杂度为$\mathcal{O}(n^{2})$，该方法基于约束变分贝叶斯算法。 我们将我们的方法与泰勒、切比雪夫和兰佐斯方法进行比较，并在合成和现实世界数据集上展示了最先进的性能。 显示英文摘要

摘要： Evaluating the log determinant of a positive definite matrix is ubiquitous in machine learning. Applications thereof range from Gaussian processes, minimum-volume ellipsoids, metric learning, kernel learning, Bayesian neural networks, Determinental Point Processes, Markov random fields to partition functions of discrete graphical models. In order to avoid the canonical, yet prohibitive, Cholesky $\mathcal{O}(n^{3})$ computational cost, we propose a novel approach, with complexity $\mathcal{O}(n^{2})$, based on a constrained variational Bayes algorithm. We compare our method to Taylor, Chebyshev and Lanczos approaches and show state of the art performance on both synthetic and real-world datasets.