Related papers: Long Random Matrices and Tensor Unfolding
We propose a generative model for robust tensor factorization in the presence of both missing data and outliers. The objective is to explicitly infer the underlying low-CP-rank tensor capturing the global information and a sparse tensor…
Estimating the rank of a corrupted data matrix is an important task in data analysis, most notably for choosing the number of components in PCA. Significant progress on this task was achieved using random matrix theory by characterizing the…
It recently has been found that methods of the statistical theories of spectra can be a useful tool in the analysis of spectra far from levels of Hamiltonian systems. Several examples originate from areas, such as quantitative linguistics…
This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models---including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation---which…
In this paper, we focus on developing randomized algorithms for the computation of low multilinear rank approximations of tensors based on the random projection and the singular value decomposition. Following the theory of the singular…
In tensor completion tasks, the traditional low-rank tensor decomposition models suffer from the laborious model selection problem due to their high model sensitivity. In particular, for tensor ring (TR) decomposition, the number of model…
In this paper, we study a nonlinear spiked random matrix model where a nonlinear function is applied element-wise to a noise matrix perturbed by a rank-one signal. We establish a signal-plus-noise decomposition for this model and identify…
In this paper, we study the power iteration algorithm for the spiked tensor model, as introduced in [44]. We give necessary and sufficient conditions for the convergence of the power iteration algorithm. When the power iteration algorithm…
We further explore the connection between holographic $O(n)$ tensor models and random matrices. First, we consider the simplest non-trivial uncolored tensor model and show that the results for the density of states, level spacing and…
In this paper, we investigate the limiting empirical spectral distribution (LSD) of sums of independent rank-one $k$-fold tensor products of $n$-dimensional vectors as $k,n \to \infty$. Assuming that the base vectors are complex random…
Learning relies on coordinated synaptic changes in recurrently connected populations of neurons. Therefore, understanding the collective evolution of synaptic connectivity over learning is a key challenge in neuroscience and machine…
In this paper, we study the perturbation of the extreme singular values of a matrix in the particular case where it is obtained after appending an arbitrary column vector. Such results have many applications in bifurcation theory, signal…
Low rank matrix and tensor completion problems are to recover the incomplete two and higher order data by using their low rank structures. The essential problem in the matrix and tensor completion problems is how to improve the efficiency.…
The so-called block-term decomposition (BTD) tensor model, especially in its rank-$(L_r,L_r,1)$ version, has been recently receiving increasing attention due to its enhanced ability of representing systems and signals that are composed of…
The singular values squared of the random matrix product $Y = G_r G_{r-1} \cdots G_1 (G_0 + A)$, where each $G_j$ is a rectangular standard complex Gaussian matrix while $A$ is non-random, are shown to be a determinantal point process with…
We study the problem of approximate ranking from observations of pairwise interactions. The goal is to estimate the underlying ranks of $n$ objects from data through interactions of comparison or collaboration. Under a general framework of…
In this paper, we study the problem of low-rank tensor learning, where only a few of training samples are observed and the underlying tensor has a low-rank structure. The existing methods are based on the sum of nuclear norms of unfolding…
This paper studies inference in linear models with a high-dimensional parameter matrix that can be well-approximated by a ``spiked low-rank matrix.'' A spiked low-rank matrix has rank that grows slowly compared to its dimensions and nonzero…
Factor model is an appealing and effective analytic tool for high-dimensional time series, with a wide range of applications in economics, finance and statistics. This paper develops two criteria for the determination of the number of…
We define in this paper a class of three indices tensor models, endowed with $O(N)^{\otimes 3}$ invariance ($N$ being the size of the tensor). This allows to generate, via the usual QFT perturbative expansion, a class of Feynman tensor…