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Statistical analysis of massive datasets very often implies expensive linearalgebra operations with large dense matrices. Typical tasks are an estimationof unknown parameters of the underlying statistical model and prediction ofmissing values. We developed the H-MLE procedure, which solves these tasks. Theunknown parameters can be estimated by maximizing the joint Gaussianlog-likelihood function, which depends on a covariance matrix. To decrease highcomputational cost, we approximate the covariance matrix in the hierarchical(H-) matrix format. The H-matrix technique allows us to work with inhomogeneouscovariance matrices and almost arbitrary locations. Especially, H-matrices canbe applied in cases when the matrices under consideration are dense andunstructured.  For validation purposes, we implemented three machine learning methods: thek-nearest neighbors (kNN), random forest, and deep neural network. The bestresults (for the given datasets) were obtained by the kNN method with three orseven neighbors depending on the dataset. The results computed with the H-MLEmethod were compared with the results obtained by the kNN method.  The developed H-matrix code and all datasets are freely available online.

Identification of unknown parameters and prediction with hierarchical matrices