Related papers: A higher-order LQ decomposition for separable cova…
The tensor decomposition addressed in this paper may be seen as a generalisation of Singular Value Decomposition of matrices. We consider general multilinear and multihomogeneous tensors. We show how to reduce the problem to a truncated…
The widespread use of multisensor technology and the emergence of big datasets have created the need to develop tools to reduce, approximate, and classify large and multimodal data such as higher-order tensors. While early approaches…
Dykema, Sukochev and Zanin used a Peano curve covering the support of the Brown measure of an operator T in a diffuse, finite von Neumann algebra to give an ordering to the support of the Brown measure, and create a decomposition T = N + Q,…
We study the decomposition matrices for the unipotent $\ell$-blocks of finite special unitary groups SU$_n(q)$ for unitary primes $\ell$ larger than $n$. Up to very few unknown entries, we give a complete solution for $n=2,\ldots,10$. We…
Using a noise covariance model based on a single Kronecker product of spatial and temporal covariance in the spatiotemporal analysis of MEG data was demonstrated to provide improvement in the results over that of the commonly used diagonal…
Modeling the complex relationships between multiple categorical response variables as a function of predictors is a fundamental task in the analysis of categorical data. However, existing methods can be difficult to interpret and may lack…
Multivariate polynomials arise in many different disciplines. Representing such a polynomial as a vector of univariate polynomials can offer useful insight, as well as more intuitive understanding. For this, techniques based on tensor…
We investigate a general matrix factorization for deviance-based data losses, extending the ubiquitous singular value decomposition beyond squared error loss. While similar approaches have been explored before, our method leverages…
The notion of random self-decomposability is generalized here. Its relation to self-decomposability, Harris infinite divisibility and its connection with a stationary first order generalized autoregressive model are presented. The notion is…
We give a decomposition of the posterior predictive variance using the law of total variance and conditioning on a finite dimensional discrete random variable. This random variable summarizes various features of modeling that are used to…
Efforts to interpret reinforcement learning (RL) models often rely on high-level techniques such as attribution or probing, which provide only correlational insights and coarse causal control. This work proposes replacing nonlinearities in…
Separable, or Kronecker product, dictionaries provide natural decompositions for 2D signals, such as images. In this paper, we describe a highly parallelizable algorithm that learns such dictionaries which reaches sparse representations…
Boolean tensor decomposition approximates data of multi-way binary relationships as product of interpretable low-rank binary factors, following the rules of Boolean algebra. Here, we present its first probabilistic treatment. We facilitate…
Tensor decomposition methods allow us to learn the parameters of latent variable models through decomposition of low-order moments of data. A significant limitation of these algorithms is that there exists no general method to regularize…
We propose a new model for multi-token prediction in transformers, aiming to enhance sampling efficiency without compromising accuracy. Motivated by recent work that predicts the probabilities of subsequent tokens using multiple heads, we…
We study generalized polar decompositions of densely defined, closed linear operators in Hilbert spaces and provide some applications to relatively (form) bounded and relatively (form) compact perturbations of self-adjoint, normal, and…
We propose generalized additive partial linear models for complex data which allow one to capture nonlinear patterns of some covariates, in the presence of linear components. The proposed method improves estimation efficiency and increases…
We introduce a broad lemma, one consequence of which is the higher order singular value decomposition (HOSVD) of tensors defined by DeLathauwer, DeMoor and Vandewalle (2000). By an analogous application of the lemma, we find a complex…
Building on the theory of causal discovery from observational data, we study interactions between multiple (sets of) random variables in a linear structural equation model with non-Gaussian error terms. We give a correspondence between…
In this paper we study the general group classification of systems of linear second-order ordinary differential equations inspired from earlier works and recent results on the group classification of such systems. Some interesting results…