Deep Mutual Density Ratio Estimation with Bregman Divergence and Its Applications

发布时间：2025-07-05 作者：浏览次数：

Speaker:	孙六全	DateTime:	2025年7月7日（周一）下午14:00-15:00
Brief Introduction to Speaker: 孙六全 ,中国科学院数学与系统科学研究院		Place:	国交2号楼315
Abstract:This talk introduces a unified approach to estimating the mutual density ratio, defined as the ratio between the joint density function and the product of the individual marginal density functions of two random vectors. It serves as a fundamental measure for quantifying the relationship between two random vectors. Our method uses Bregman divergence to construct the objective function and leverages deep neural networks to approximate the logarithm of the mutual density ratio. We establish a non-asymptotic error bound for our estimator, achieving the optimal minimax rate of convergence under a bounded support condition. Additionally, our estimator mitigates the curse of dimensionality when the distribution is supported on a lower-dimensional manifold. We extend our results to overparameterized neural networks and the case with unbounded support. Applications of our method include conditional probability density estimation, mutual information estimation, and independence testing. Simul...