3 papers
math.ST2025
Dimension-free Bounds for Covariance Estimation with Tensor-Train Structure
Artsiom Patarusau, Nikita Puchkin, Maxim Rakhuba +1
We consider a problem of covariance estimation from a sample of i.i.d. high-dimensional random vectors. To avoid the curse of dimensionality, we impose an additional assumption on…
math.NA2025
Optimization on the Extended Tensor-Train Manifold with Shared Factors
Alexander Molozhavenko, Maxim Rakhuba
This paper studies tensors that admit decomposition in the Extended Tensor Train (ETT) format, with a key focus on the case where some decomposition factors are constrained to be e…
math.NA2022
Tensor rank bounds and explicit QTT representations for the inverses of circulant matrices
Lev Vysotsky, Maxim Rakhuba
In this paper, we are concerned with the inversion of circulant matrices and their quantized tensor-train (QTT) structure. In particular, we show that the inverse of a complex circ…