Related papers: Hierarchical multilinear models for multiway data

We propose a general framework for reduced-rank modeling of matrix-valued data. By applying a generalized nuclear norm penalty we can directly model low-dimensional latent variables associated with rows and columns. Our framework flexibly…

With the increasing availability of various sensor technologies, we now have access to large amounts of multi-block (also called multi-set, multi-relational, or multi-view) data that need to be jointly analyzed to explore their latent…

Transcribing structured data into natural language descriptions has emerged as a challenging task, referred to as "data-to-text". These structures generally regroup multiple elements, as well as their attributes. Most attempts rely on…

Collected data, which is used for analysis or prediction tasks, often have a hierarchical structure, for example, data from various people performing the same task. Modeling the data's structure can improve the reliability of the derived…

Complex systems are high-dimensional nonlinear dynamical systems with intricate interactions among their constituents. To make interpretable predictions about their large-scale behavior, it is typically assumed, without a clear statement,…

A primary interest in dynamic inverse problems is to identify the underlying temporal behaviour of the system from outside measurements. In this work we consider the case, where the target can be represented by a decomposition of spatial…

We show how to achieve a statistical description of the hierarchical structure of a multivariate data set. Specifically we show that the similarity matrix resulting from a hierarchical clustering procedure is the correlation matrix of a…

We propose and analyse a reduced-rank method for solving least-squares regression problems with infinite dimensional output. We derive learning bounds for our method, and study under which setting statistical performance is improved in…

Interaction within small groups can often be represented as a sequence of events, where each event involves a sender and a recipient. Recent methods for modeling network data in continuous time model the rate at which individuals interact…

We propose a novel linear discriminant analysis approach for the classification of high-dimensional matrix-valued data that commonly arises from imaging studies. Motivated by the equivalence of the conventional linear discriminant analysis…

Differentiable systems in this paper means systems of equations that are described by differentiable real functions in real matrix variables. This paper proposes algorithms for finding minimal rank solutions to such systems over (arbitrary…

Disentangled representations, where the higher level data generative factors are reflected in disjoint latent dimensions, offer several benefits such as ease of deriving invariant representations, transferability to other tasks,…

Contingency table analysis routinely relies on log linear models, with latent structure analysis providing a common alternative. Latent structure models lead to a low rank tensor factorization of the probability mass function for…

In this paper, we describe a low-rank matrix completion method based on matrix decomposition. An incomplete matrix is decomposed into submatrices which are filled with a proposed trimming step and then are recombined to form a low-rank…

The singular value decomposition is widely used to approximate data matrices with lower rank matrices. Feng and He [Ann. Appl. Stat. 3 (2009) 1634-1654] developed tests on dimensionality of the mean structure of a data matrix based on the…

Past research into robotic planning with temporal logic specifications, notably Linear Temporal Logic (LTL), was largely based on a single formula for individual or groups of robots. But with increasing task complexity, LTL formulas…

In this paper, we propose a distributed framework for reducing the dimensionality of high-dimensional, large-scale, heterogeneous matrix-variate time series data using a factor model. The data are first partitioned column-wise (or row-wise)…

For statistical analysis of multiway contingency tables we propose modeling interaction terms in each maximal compact component of a hierarchical model. By this approach we can search for parsimonious models with smaller degrees of freedom…

This article focuses on covariance estimation for multi-study data. Popular approaches employ factor-analytic terms with shared and study-specific loadings that decompose the variance into (i) a shared low-rank component, (ii)…

We propose a vector auto-regressive (VAR) model with a low-rank constraint on the transition matrix. This new model is well suited to predict high-dimensional series that are highly correlated, or that are driven by a small number of hidden…