This paper proposes an efficient algorithm (HOLRR) to handle regression tasks where the outputs have a tensor structure. We formulate the regression problem as the minimization of a least square criterion under a multilinear rank constraint, a difficult non convex problem. HOLRR computes efficiently an approximate solution of this problem, with solid theoretical guarantees. A kernel extension i...

Stability data are often collected to determine the shelf life of certain characteristics of a pharmaceutical product, for example, a drug's potency over time. Statistical approaches such as the linear regression models are considered as appropriate to analyze the stability data. However, most of these regression models in both theory and practice rely heavily on their underlying parametric ass...

Hawkins and Yin (Comput. Statist. Data Anal. 40 (2002) 253) describe an algorithm for ridge regression of reduced rank data, i.e. data where p, the number of variables, is larger than n, the number of observations. Whereas a direct implementation of ridge regression in this setting requires calculations of order O(np2 + p3), their algorithm uses only calculations of order O(np2). In this paper,...

In wireless communication systems with antenna arrays the spatiotemporal channel can often be described by a low-rank model. By exploiting this information, corresponding low rank equalizers with reduced complexity can be designed. By applying such low rank equalizers to a set of uplink measurements, we demonstrate that the performance loss associated with the lower complexity is small.

We introduce the Reduced-Rank Hidden Markov Model (RR-HMM), a generalization of HMMs that can model smooth state evolution as in Linear Dynamical Systems (LDSs) as well as non-log-concave predictive distributions as in continuous-observation HMMs. RR-HMMs assume anm-dimensional latent state and n discrete observations, with a transition matrix of rank k ≤ m. This implies the dynamics evolve in ...

We propose identi…cation robust inference methods for multivariate reduced rank (MRR) regressions. Such models involve nonlinear restrictions on the coe¢ cients of a multivariate linear regression (MLR), whose identi…cation may raise serious non-regularities leading to the failure of standard asymptotics. To circumvent such problems, we propose con…dence set estimates for parameters of interest...

Diet plays a crucial role in cognitive function. Few studies have examined the relationship between dietary patterns and cognitive functions of older adults in the Korean population. This study aimed to identify the effect of dietary patterns on the risk of mild cognitive impairment. A total of 239 participants, including 88 men and 151 women, aged 65 years and older were selected from health c...

We propose a generalized reduced rank latent factor regression model (GRRLF) for the analysis of tensor field responses and high dimensional covariates. The model is motivated by the need from imaging-genetic studies to identify genetic variants that are associated with brain imaging phenotypes, often in the form of high dimensional tensor fields. GRRLF identifies from the structure in the data...