Mutual information is widely used, in a descriptive way, to measure the stochastic dependence of categorical random variables. In order to address questions such as the reliability of the descriptive value, one must consider sample-to-population inferential approaches. This paper deals with the posterior distribution of mutual information, as obtained in a Bayesian framework by a second-order Dirichlet prior distribution. The exact analytical expression for the mean, and analytical approximations for the variance, skewness and kurtosis are derived. These approximations have a guaranteed accuracy level of the order O(1/n^3), where n is the sample size. Leading order approximations for the mean and the variance are derived in the case of incomplete samples. The derived analytical expressions allow the distribution of mutual information to be approximated reliably and quickly. In fact, the derived expressions can be computed with the same order of complexity needed for descriptive mutual information. This makes the distribution of mutual information become a concrete alternative to descriptive mutual information in many applications which would benefit from moving to the inductive side. Some of these prospective applications are discussed, and one of them, namely feature selection, is shown to perform significantly better when inductive mutual information is used.
ImputeECG: Deep Learning Reconstruction of Complete 12-Lead Electrocardiograms from Incomplete Recordings for Cardiac Assessment
National Institute of Health Data Science, Peking University（北京大学健康医疗大数据国家研究院）；School of Intelligence Science and Technology, Peking University（北京大学智能科学与技术学院）；Institute of Medical Technology, Peking University Health Science Center（北京大学医学部医学技术研究所）；University of the Chinese Academy of Sciences（中国科学院大学）；Department of Cardiology, Peking University People’s Hospital（北京大学人民医院心内科）；Department of Computer Science, Tianjin University of Technology（天津理工大学计算机科学与工程学院）
Choosing the number of factors in factor analysis with incomplete data via a hierarchical Bayesian information criterion
Yunnan University of Finance and Economics（云南财经大学）；Guilin University of Technology（桂林理工大学）；BNU-HKBU United International College（北京师范大学-香港浸会大学联合国际学院）；The Education University of Hong Kong（香港教育大学）
CyIN: Cyclic Informative Latent Space for Bridging Complete and Incomplete Multimodal Learning
School of Electronics and Information Technology, Sun Yat-Sen University（中山大学电子与信息学院）；School of Electrical and Electronic Engineering, Nanyang Technological University（南洋理工大学电气与电子工程学院）；School of Computer Science, South China Normal University（华南师范大学计算机科学学院）；Desay SV Automotive Co., Ltd（德赛股份有限公司）；Pazhou Laboratory（琶洲实验室）
Revisiting Initializing Then Refining: An Incomplete and Missing Graph Imputation Network
National University of Defense Technology（国防科技大学）；Chongqing University of Posts and Telecommunications（重庆邮电大学）；Hainan University（海南大学）；Hainan blockchain technology engineering research center（海南区块链技术工程研究中心）
