Séminaire Shuyu Dong

Matrix and tensor decomposition plays a crucial role in addressing various real-world problems related to topics such as statistical inference, data acquisition, and data restoration. In this talk, we start with low-rank matrix/tensor models for the data completion problem [1,2]. We tackle this problem in the framework of low-rank matrix/tensor decomposition with a least-squares model. These rank-constrained problems are known not only for their low computational complexity but also the capability of extracting the most important information in the data. We discuss a type of Riemannian gradient-based algorithms that exploit the structure of these rank-constrained models. Secondly, we present a novel application of low-rank matrix methods in the context of causal structure learning. We will show how low-rank matrix decomposition, in combination with a sparse mask operator, can be used to efficiently find directed acyclic graphs (DAGs) proximal to a given graph (with cycles). Furthermore, for learning causal DAGs from observational data, we present a sparse matrix decomposition method [4] and discuss its efficiency through experiments on synthetic and real-world data.
[1] S. Dong, P.-A. Absil, and K. A. Gallivan, Riemannian gradient descent methods for graph-regularized matrix completion. Linear Algebra and its Applications 623 (2021), 193-235
[2] S. Dong, B. Gao, Y. Guan, and F. Glineur, New Riemannian preconditioned algorithms for tensor completion via polyadic decomposition, SIAM Journal on Matrix Analysis and Applications 43 (2) (2022), 840-866
[3] S. Dong and M. Sebag, From graphs to DAGs: a low-complexity model and a scalable algorithm, European Conference on Machine Learning and Principles and Practice of Knowledge Discovery in Databases (ECML-PKDD), 2022
[4] S. Dong, K. Uemura, A. Fujii, S. Chang, Y. Koyanagi, K. Maruhashi, and M. Sebag, Learning large causal structures from inverse covariance matrix via matrix decomposition, arXiv preprint arXiv:2211.14221, 2023