Related papers: High-dimensional Tensor Response Regression using …

Tensor train (TT) decomposition provides a space-efficient representation for higher-order tensors. Despite its advantage, we face two crucial limitations when we apply the TT decomposition to machine learning problems: the lack of…

In this paper, we investigate the statistical convergence rate of a Bayesian low-rank tensor estimator. Our problem setting is the regression problem where a tensor structure underlying the data is estimated. This problem setting occurs in…

Reduced Rank Regression (RRR) is a widely used method for multi-response regression. However, RRR assumes a linear relationship between features and responses. While linear models are useful and often provide a good approximation, many…

We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…

We propose dimension reduction methods for sparse, high-dimensional multivariate response regression models. Both the number of responses and that of the predictors may exceed the sample size. Sometimes viewed as complementary, predictor…

We propose a new estimator for the high-dimensional linear regression model with observation error in the design where the number of coefficients is potentially larger than the sample size. The main novelty of our procedure is that the…

We consider the equivalent problems of estimating the residual variance, the proportion of explained variance $\eta$ and the signal strength in a high-dimensional linear regression model with Gaussian random design. Our aim is to understand…

In this paper, based on the combination of tensor neural network and a posteriori error estimator, a novel type of machine learning method is proposed to solve high-dimensional boundary value problems with homogeneous and non-homogeneous…

We devise a one-shot approach to distributed sparse regression in the high-dimensional setting. The key idea is to average "debiased" or "desparsified" lasso estimators. We show the approach converges at the same rate as the lasso as long…

This paper studies the distributed adaptiveestimation problems for stochastic large regression modelswith an infinite number of parameters. By constructing a re-cursive local cost function, we propose a novel distributedrecursive least…

Estimation and inference with modern longitudinal data from wearable devices, which consist of biological signals at high-frequency time points, is burdened by massive computational costs. We propose a distributed estimation and inference…

Computing with discrete representations of high-dimensional probability distributions is fundamental to uncertainty quantification, Bayesian inference, and stochastic modeling. However, storing and manipulating such distributions suffers…

Fitting regression models with many multivariate responses and covariates can be challenging, but such responses and covariates sometimes have tensor-variate structure. We extend the classical multivariate regression model to exploit such…

We propose a one-step procedure to estimate the latent positions in random dot product graphs efficiently. Unlike the classical spectral-based methods such as the adjacency and Laplacian spectral embedding, the proposed one-step procedure…

We introduce Poisson-response tensor-on-tensor regression (PToTR), a novel regression framework designed to handle tensor responses composed element-wise of random Poisson-distributed counts. Tensors, or multi-dimensional arrays, composed…

Hierarchical statistical models are widely employed in information science and data engineering. The models consist of two types of variables: observable variables that represent the given data and latent variables for the unobservable…

The analysis of samples of random objects that do not lie in a vector space is gaining increasing attention in statistics. An important class of such object data is univariate probability measures defined on the real line. Adopting the…

Modern sensing and metrology systems now stream terabytes of heterogeneous, high-dimensional (HD) data profiles, images, and dense point clouds, whose natural representation is multi-way tensors. Understanding such data requires regression…

We study high-dimensional distribution learning in an agnostic setting where an adversary is allowed to arbitrarily corrupt an $\varepsilon$-fraction of the samples. Such questions have a rich history spanning statistics, machine learning…

In this work we address the problem of approximating high-dimensional data with a low-dimensional representation. We make the following contributions. We propose an inverse regression method which exchanges the roles of input and response,…