arXiv research

A parallel algorithm learns efficient Kronecker product dictionaries.

This paper presents a new method for estimating high dimensional covariance matrices. The method, permuted rank-penalized least-squares (PRLS), is based on a Kronecker product series expansion of the true covariance matrix. Assuming an i.i.d. Gaussian random sample, we establish high dimensional rates of convergence to…

This paper derives sufficient conditions for local recovery of coordinate dictionaries comprising a Kronecker-structured dictionary that is used for representing $K$th-order tensor data. Tensor observations are assumed to be generated from a Kronecker-structured dictionary multiplied by sparse coefficient tensors that …

In this paper we present two new approaches to efficiently solve large-scale compressed sensing problems. These two ideas are independent of each other and can therefore be used either separately or together. We consider all possibilities. For the first approach, we note that the zero vector can be taken as the initial…

Paper relaxes independence assumption for non-centered data.

We study the classification performance of Kronecker-structured models in two asymptotic regimes and developed an algorithm for separable, fast and compact K-S dictionary learning for better classification and representation of multidimensional signals by exploiting the structure in the signal. First, we study the clas…

Researchers solve the realization of Jordan-Kronecker invariants in Lie algebras.

Extends multivariate regression for tensor-variate data, identifying brain regions and facial characteristics.

Study on rotational hypersurfaces with constant Gauss-Kronecker curvature.

Machine learning predicts Kronecker coefficients with high accuracy.

Bayesian method estimates Kronecker graphical models from autoregressive processes.

TensorSketch is an oblivious linear sketch introduced in Pagh'13 and later used in Pham, Pagh'13 in the context of SVMs for polynomial kernels. It was shown in Avron, Nguyen, Woodruff'14 that TensorSketch provides a subspace embedding, and therefore can be used for canonical correlation analysis, low rank approximation…

KoPA approximates matrices using Kronecker products for better flexibility.

Dictionary learning and component analysis models are fundamental for learning compact representations that are relevant to a given task (feature extraction, dimensionality reduction, denoising, etc.). The model complexity is encoded by means of specific structure, such as sparsity, low-rankness, or nonnegativity. Unfo…

EiGLasso speeds up sparse Kronecker-sum covariance estimation.

Scalable Gaussian processes with latent Kronecker structure for large datasets.

In this paper we consider the use of the space vs. time Kronecker product decomposition in the estimation of covariance matrices for spatio-temporal data. This decomposition imposes lower dimensional structure on the estimated covariance matrix, thus reducing the number of samples required for estimation. To allow a sm…

We investigate 3-dimensional complete minimal hypersurfaces in the hyperbolic space $\mathbb{H}^{4}$ with Gauss-Kronecker curvature identically zero. More precisely, we give a classification of complete minimal hypersurfaces with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and …

Efficient GP framework for scalable non-stationary processes.

The present paper discusses that a prescribed Gauss-Kronecker curvature problem on the product of unit spheres.

We investigate the structure of 3-dimensional complete minimal hypersurfaces in the unit sphere with Gauss-Kronecker curvature identically zero.

Efficiently models learning curves using Gaussian processes with latent Kronecker structure.

Paper proposes a new method for approximating high-dimensional matrices using Kronecker products.

How can we model networks with a mathematically tractable model that allows for rigorous analysis of network properties? Networks exhibit a long list of surprising properties: heavy tails for the degree distribution; small diameters; and densification and shrinking diameters over time. Most present network models eithe…

The study predicts Kronecker coefficients using interpretable machine learning models.

We investigate complete minimal hypersurfaces in the Euclidean space $$, with Gauss-Kronecker curvature identically zero. We prove that, if $f:M^{3}\to {R}^{4}$ is a complete minimal hypersurface with Gauss-Kronecker curvature identically zero, nowhere vanishing second fundamental form and scalar curvature b…

New method for faster graph parameter inference from large random Kronecker graphs.

We consider the problem of detecting whether a tensor signal having many missing entities lies within a given low dimensional Kronecker-Structured (KS) subspace. This is a matched subspace detection problem. Tensor matched subspace detection problem is more challenging because of the intertwined signal dimensions. We s…

This paper studies iteration convergence of Kronecker graphical lasso (KGLasso) algorithms for estimating the covariance of an i.i.d. Gaussian random sample under a sparse Kronecker-product covariance model and MSE convergence rates. The KGlasso model, originally called the transposable regularized covariance model by …

Kronecker product kernel provides the standard approach in the kernel methods literature for learning from graph data, where edges are labeled and both start and end vertices have their own feature representations. The methods allow generalization to such new edges, whose start and end vertices do not appear in the tra…

In this paper we present a local description for complete minimal hypersurfaces in $\mathbb{S}^5$ with zero Gauss-Kronecker curvature, zero $3$-mean curvature and nowhere zero second fundamental form.

In recent years, a class of dictionaries have been proposed for multidimensional (tensor) data representation that exploit the structure of tensor data by imposing a Kronecker structure on the dictionary underlying the data. In this work, a novel algorithm called "STARK" is provided to learn Kronecker structured dictio…

Shampoo optimizes preconditioners for faster convergence in machine learning.

New methods estimate covariance for matrix data without assuming fixed size or specific distributions.

Totally geodesic minimal hypersurfaces in $\mathbb H^5$ with specific curvature properties.

Study mapping class group action on character varieties, proving Kronecker's Theorem.

A new method for optimizing deep neural networks using TKFAC.

We give a partial local description of minimal hypersurfaces $M^3$ with identically zero Gauß-Kronecker curvature function in the unit 4-sphere $\Bbb{S}^4(1)$, without assumption on the compactness of $M^3$.

MCCA extracts shared structure from multiple tensor datasets.

Stochastic Kronecker graphs supply a parsimonious model for large sparse real world graphs. They can specify the distribution of a large random graph using only three or four parameters. Those parameters have however proved difficult to choose in specific applications. This article looks at method of moments estimators…

The aim of this paper is to complete the local classification of minimal hypersurfaces with vanishing Gauss-Kronecker curvature in a 4-dimensional space form. Moreover, we give a classification of complete minimal hypersurfaces with vanishing Gauss-Kronecker curvature and scalar curvature bounded from below.

In this paper, we exhibit the tradeoffs between the (training) sample, computation and storage complexity for the problem of supervised classification using signal subspace estimation. Our main tool is the use of tensor subspaces, i.e. subspaces with a Kronecker structure, for embedding the data into lower dimensions. …

This paper improves compression of large NLP models using doped Kronecker Products.

Kronecker trend filtering improves lattice data smoothing.

Dictionary learning and component analysis are part of one of the most well-studied and active research fields, at the intersection of signal and image processing, computer vision, and statistical machine learning. In dictionary learning, the current methods of choice are arguably K-SVD and its variants, which learn a …

A new optimization method reduces memory and compute requirements for deep learning.

New methods use Kronecker-factored approximations for faster deep learning optimization.

Recent advances in variational inference enable the modelling of highly structured joint distributions, but are limited in their capacity to scale to the high-dimensional setting of stochastic neural networks. This limitation motivates a need for scalable parameterizations of the noise generation process, in a manner t…