We consider the problem of inductive matrix completion under the assumption that many features are non-informative, which leads to row- and column-sparse structure of coefficient matrix. Under the additional assumption on the low rank of coefficient matrix we propose the matrix factorization framework with group-lasso regularization on parameter matrices. We suggest efficient optimization algorithm for the solution of the obtained problem. From theoretical point of view, we prove the oracle generalization bound on the expected error of matrix completion. Corresponding sample complexity bounds show the benefits of the proposed approach compared to competitors in the sparse problems. The experiments on synthetic and real-world datasets show the state-of-the-art efficiency of the proposed method.

This paper considers the problem of brain disease classification based on connectome data. A connectome is a network representation of a human brain. The typical connectome classification problem is very challenging because of the small sample size and high dimensionality of the data. We propose to use simultaneous approximate diagonalization of adjacency matrices in order to compute their eigenstructures in more stable way. The obtained approximate eigenvalues are further used as features for classification. The proposed approach is demonstrated to be efficient for detection of Alzheimer's disease, outperforming simple baselines and competing with state-of-the-art approaches to brain disease classification.

We describe GTApprox - a new tool for medium-scale surrogate modeling in industrial design. Compared to existing software, GTApprox brings several innovations: a few novel approximation algorithms, several advanced methods of automated model selection, novel options in the form of hints. We demonstrate the efficiency of GTApprox on a large collection of test problems. In addition, we describe several applications of GTApprox to real engineering problems.