The paper "Information-Theoretic Metric Learning" by Jason Davis, Brian Kulis, Suvrit Sra, and Inderjit Dhillon formulates the metric learning problem as minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. The authors show that this problem can be solved as a low-rank kernel learning problem, specifically by minimizing the Burg divergence of a low-rank kernel to an input kernel, subject to pairwise distance constraints. This approach offers several advantages over existing methods, including a natural information-theoretic formulation, faster running time due to the avoidance of eigenvector computation, and insights into the connections between metric learning and kernel learning. The paper also discusses extensions to the basic framework, such as handling different baseline distances and incorporating more complex constraints. The authors compare their method with related work, highlighting its efficiency and flexibility in enforcing interpoint constraints.The paper "Information-Theoretic Metric Learning" by Jason Davis, Brian Kulis, Suvrit Sra, and Inderjit Dhillon formulates the metric learning problem as minimizing the differential relative entropy between two multivariate Gaussians under constraints on the Mahalanobis distance function. The authors show that this problem can be solved as a low-rank kernel learning problem, specifically by minimizing the Burg divergence of a low-rank kernel to an input kernel, subject to pairwise distance constraints. This approach offers several advantages over existing methods, including a natural information-theoretic formulation, faster running time due to the avoidance of eigenvector computation, and insights into the connections between metric learning and kernel learning. The paper also discusses extensions to the basic framework, such as handling different baseline distances and incorporating more complex constraints. The authors compare their method with related work, highlighting its efficiency and flexibility in enforcing interpoint constraints.