Related papers: Statistical Inference for Low-Rank Tensor Models
High-dimensional tensors or multi-way data are becoming prevalent in areas such as biomedical imaging, chemometrics, networking and bibliometrics. Traditional approaches to finding lower dimensional representations of tensor data include…
Uncertainty quantification based on stochastic spectral methods suffers from the curse of dimensionality. This issue was mitigated recently by low-rank tensor methods. However, there exist two fundamental challenges in low-rank tensor-based…
Time series prediction has been a long-standing research topic and an essential application in many domains. Modern time series collected from sensor networks (e.g., energy consumption and traffic flow) are often large-scale and incomplete…
In the Tensor PCA problem introduced by Richard and Montanari (2014), one is given a dataset consisting of $n$ samples $\mathbf{T}_{1:n}$ of i.i.d. Gaussian tensors of order $k$ with the promise that $\mathbb{E}\mathbf{T}_1$ is a rank-1…
In many applications, such as classification of images or videos, it is of interest to develop a framework for tensor data instead of an ad-hoc way of transforming data to vectors due to the computational and under-sampling issues. In this…
We establish non-asymptotic efficiency guarantees for tensor decomposition-based inference in count data models. Under a Poisson framework, we consider two related goals: (i) parametric inference, the estimation of the full distributional…
We study a noisy tensor completion problem of broad practical interest, namely, the reconstruction of a low-rank tensor from highly incomplete and randomly corrupted observations of its entries. While a variety of prior work has been…
Regression analysis is a key area of interest in the field of data analysis and machine learning which is devoted to exploring the dependencies between variables, often using vectors. The emergence of high dimensional data in technologies…
We introduce two nonlinear sufficient dimension reduction methods for regressions with tensor-valued predictors. Our goal is two-fold: the first is to preserve the tensor structure when performing dimension reduction, particularly the…
Most regularized tensor regression research focuses on tensors predictors with scalars responses or vectors predictors to tensors responses. We consider the sparse low rank tensor on tensor regression where predictors $\mathcal{X}$ and…
The paper considers function-valued tensors, viewed as multidimensional arrays with entries in an abstract Hilbert space. Despite the absence of the algebraic structure of a field, the geometric inner-product structure suffices to introduce…
This paper concerns statistical inference for the components of a high-dimensional regression parameter despite possible endogeneity of each regressor. Given a first-stage linear model for the endogenous regressors and a second-stage linear…
We consider functional linear regression models where functional outcomes are associated with scalar predictors by coefficient functions with shape constraints, such as monotonicity and convexity, that apply to sub-domains of interest. To…
The tensorial principal component analysis is a generalization of ordinary principal component analysis, focusing on data which are suitably described by tensors rather than matrices. This paper aims at giving the nonperturbative…
Extracting latent low-dimensional structure from high-dimensional data is of paramount importance in timely inference tasks encountered with `Big Data' analytics. However, increasingly noisy, heterogeneous, and incomplete datasets as well…
This paper provides a unified framework for analyzing tensor estimation problems that allow for nonlinear observations, heteroskedastic noise, and covariate information. We study a general class of high-dimensional models where each…
Many statistical estimation techniques for high-dimensional or functional data are based on a preliminary dimension reduction step, which consists in projecting the sample $\bX_1, \hdots, \bX_n$ onto the first $D$ eigenvectors of the…
This paper proposes a novel formulation of the tensor completion problem to impute missing entries of data represented by tensors. The formulation is introduced in terms of tensor train (TT) rank which can effectively capture global…
During the last years, low-rank tensor approximation has been established as a new tool in scientific computing to address large-scale linear and multilinear algebra problems, which would be intractable by classical techniques. This survey…
This paper proposes a novel diffusion-index model for forecasting when predictors are high-dimensional matrix-valued time series. We apply an $\alpha$-PCA method to extract low-dimensional matrix factors and build a bilinear regression…