手法を比較

	MICE	EMアルゴリズム	行列補完
分野	統計学	統計学	機械学習
系統	Process / pipeline	Machine learning	Machine learning
提唱年	2011	1977	2009
提唱者	Stef van Buuren & Karin Groothuis-Oudshoorn	Dempster, Laird & Rubin	Emmanuel Candès & Benjamin Recht
種類	Iterative multiple imputation algorithm	Iterative optimization algorithm	Convex low-rank recovery
原典	van Buuren, S., & Groothuis-Oudshoorn, K. (2011). mice: Multivariate imputation by chained equations in R. Journal of Statistical Software, 45(3), 1–67.	Dempster, A. P., Laird, N. M., & Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. Journal of the Royal Statistical Society: Series B, 39(1), 1–38.	Candès, E. J., & Recht, B. (2009). Exact matrix completion via convex optimization. Foundations of Computational Mathematics, 9(6), 717–772.
別名	Fully Conditional Specification, Sequential Regression Multivariate Imputation, Chained Equations Imputation, Zincirleme Denklemlerle Çoklu Atama	EM, Expectation-Maximization, Maximum Likelihood via Incomplete Data, BM Algoritması	Nuclear Norm Minimization, Collaborative Filtering via Low-Rank Recovery, Inductive Matrix Completion, Matris Tamamlama
関連	3	2	2
概要	Multivariate Imputation by Chained Equations (MICE) is an iterative procedure for handling missing data in multivariate datasets. Introduced by Stef van Buuren and Karin Groothuis-Oudshoorn through the R package mice (2011), the algorithm fills each missing variable using a separate regression model conditioned on all other variables, cycling through variables repeatedly until the imputed values converge. The result is m completed datasets that are analysed separately and combined using Rubin's rules.	The Expectation-Maximization (EM) algorithm is an iterative optimization procedure for finding maximum likelihood or maximum a posteriori estimates of parameters in statistical models with latent variables or missing data. Introduced by Dempster, Laird, and Rubin in their landmark 1977 paper, EM alternates between computing the expected complete-data log-likelihood (E-step) and maximizing it with respect to the parameters (M-step), guaranteeing monotone non-decreasing likelihood at each iteration.	Matrix Completion is a technique for recovering a low-rank matrix from a small, possibly random subset of its entries. Introduced by Emmanuel Candès and Benjamin Recht in 2009, it reformulates the problem as nuclear norm minimization — a convex surrogate for rank minimization — and provides theoretical guarantees that exact recovery is achievable when entries are observed uniformly at random and the matrix satisfies an incoherence condition.