Related papers: A QR Decomposition Approach to Factor Modelling: A…
Quantile regression (QR) is becoming increasingly popular due to its relevance in many scientific investigations. There is a great amount of work about linear and nonlinear QR models. Specifically, nonparametric estimation of the…
The concepts of sparsity, and regularised estimation, have proven useful in many high-dimensional statistical applications. Dynamic factor models (DFMs) provide a parsimonious approach to modelling high-dimensional time series, however, it…
Topologically ordered states are fundamentally important in theoretical physics, which are also suggested as promising candidates to build fault-tolerant quantum devices. However, it is still elusive how topological orders can be affected…
Tensor decomposition is a fundamental tool for analyzing multi-dimensional data by learning low-rank factors to represent high-order interactions. While recent works on temporal tensor decomposition have made significant progress by…
Many multivariate data analysis techniques for an $m\times n$ matrix $\m Y$ are related to the model $\m Y = \m M +\m E$, where $\m Y$ is an $m\times n$ matrix of full rank and $\m M$ is an unobserved mean matrix of rank $K< (m\wedge n)$.…
Factor Analysis is a popular method for modeling dependence in multivariate data. However, determining the number of factors and obtaining a sparse orientation of the loadings are still major challenges. In this paper, we propose a…
Adaptive algorithms based on sample matrix inversion belong to an important class of algorithms used in radar target detection to overcome prior uncertainty of interference covariance. Sample matrix inversion problem is generally ill…
Standard noise radars, as well as noise-type radars such as quantum two-mode squeezing radar, are characterized by a covariance matrix with a very specific structure. This matrix has four independent parameters: the amplitude of the…
In this article the notion of the nondecreasing (ND) rank of a matrix or tensor is introduced. A tensor has an ND rank of r if it can be represented as a sum of r outer products of vectors, with each vector satisfying a monotonicity…
To distinguish Markov equivalent graphs in causal discovery, it is necessary to restrict the structural causal model. Crucially, we need to be able to distinguish cause $X$ from effect $Y$ in bivariate models, that is, distinguish the two…
The matrix factor model has drawn growing attention for its advantage in achieving two-directional dimension reduction simultaneously for matrix-structured observations. In this paper, we propose a simple iterative least squares algorithm…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
This paper studies the inference problem in quantile regression (QR) for a large sample size $n$ but under a limited memory constraint, where the memory can only store a small batch of data of size $m$. A natural method is the na\"ive…
This paper investigates the signal detection problem in colored noise with an unknown covariance matrix. In particular, we focus on detecting a non-random signal by capitalizing on the leading eigenvalue (a.k.a. Roy's largest root) of the…
We consider the factorization of a rectangular matrix $X $ into a positive linear combination of rank-one factors of the form $u v^\top$, where $u$ and $v$ belongs to certain sets $\mathcal{U}$ and $\mathcal{V}$, that may encode specific…
Quantile is an important measure in finance and quality assessment in service industry. In this paper, we model the temporal and cross-sectional interactive effect of the quantiles of large-dimensional time series by a latent quantile…
The proposed article aims at offering a comprehensive tutorial for the computational aspects of structured matrix and tensor factorization. Unlike existing tutorials that mainly focus on {\it algorithmic procedures} for a small set of…
We consider functional data which are measured on a discrete set of observation points. Often such data are measured with additional noise. We explore in this paper the factor structure underlying this type of data. We show that the latent…
Quantum Machine Learning (QML) offers significant potential for complex tasks like genome sequence classification, but quantum noise on Noisy Intermediate-Scale Quantum (NISQ) devices poses practical challenges. This study systematically…
Quantile regression (QR) is a principal regression method for analyzing the impact of covariates on outcomes. The impact is described by the conditional quantile function and its functionals. In this paper we develop the nonparametric…