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Multiple imputation can be used in cases where the data are missing completely at random, missing at random, and missing not at random, though it can be biased in the latter case. [14] One approach is multiple imputation by chained equations (MICE), also known as "fully conditional specification" and "sequential regression multiple imputation."
Predictive mean matching (PMM) [1] is a widely used [2] statistical imputation method for missing values, first proposed by Donald B. Rubin in 1986 [3] and R. J. A. Little in 1988. [ 4 ] It aims to reduce the bias introduced in a dataset through imputation, by drawing real values sampled from the data. [ 5 ]
Missing at random (MAR) occurs when the missingness is not random, but where missingness can be fully accounted for by variables where there is complete information. [7] Since MAR is an assumption that is impossible to verify statistically, we must rely on its substantive reasonableness. [ 8 ]
If all the vertices in the domain are visited, then terminate. Else, go to step 3. The sequence of the visited vertices is the output of the algorithm. The nearest neighbour algorithm is easy to implement and executes quickly, but it can sometimes miss shorter routes which are easily noticed with human insight, due to its "greedy" nature.
Candès and Recht [3] proved that with assumptions on the sampling of the observed entries and sufficiently many sampled entries this problem has a unique solution with high probability. An equivalent formulation, given that the matrix M {\displaystyle M} to be recovered is known to be of rank r {\displaystyle r} , is to solve for X ...
This simple example for the case of mean estimation is just to illustrate the construction of a jackknife estimator, while the real subtleties (and the usefulness) emerge for the case of estimating other parameters, such as higher moments than the mean or other functionals of the distribution.
GPR is a Bayesian non-linear regression method. A Gaussian process (GP) is a collection of random variables, any finite number of which have a joint Gaussian (normal) distribution. A GP is defined by a mean function and a covariance function, which specify the mean vectors and covariance matrices for each finite collection of the random variables.
The data imputation procedure with NMF can be composed of two steps. First, when the NMF components are known, Ren et al. (2020) proved that impact from missing data during data imputation ("target modeling" in their study) is a second order effect.