Related papers: QUARKS: Identification of large-scale Kronecker Ve…

Kronecker regression is a highly-structured least squares problem $\min_{\mathbf{x}} \lVert \mathbf{K}\mathbf{x} - \mathbf{b} \rVert_{2}^2$, where the design matrix $\mathbf{K} = \mathbf{A}^{(1)} \otimes \cdots \otimes \mathbf{A}^{(N)}$ is…

Kronecker compressed sensing refers to using Kronecker product matrices as sparsifying bases and measurement matrices in compressed sensing. This work focuses on the Kronecker compressed sensing problem, encompassing three sparsity…

A key task in AutoML is to model learning curves of machine learning models jointly as a function of model hyper-parameters and training progression. While Gaussian processes (GPs) are suitable for this task, na\"ive GPs require…

In this paper, we propose and study a technique to reduce the number of parameters and computation time in convolutional neural networks. We use Kronecker product to exploit the local structures within convolution and fully-connected…

Traditionally, batch least squares (BLS) and recursive least squares (RLS) are used for identification of a vector of parameters that form a linear model. In some situations, however, it is of interest to identify parameters in a matrix…

In this work we consider the estimation of spatio-temporal covariance matrices in the low sample non-Gaussian regime. We impose covariance structure in the form of a sum of Kronecker products decomposition (Tsiligkaridis et al. 2013,…

We study the matrix-variate regression problem $Y_i = \sum_{k} \beta_{1k} X_i \beta_{2k}^{\top} + E_i$ for $i=1,2\dots,n$ in the high dimensional regime wherein the response $Y_i$ are matrices whose dimensions $p_{1}\times p_{2}$ outgrow…

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…

Subspace clustering is a useful technique for many computer vision applications in which the intrinsic dimension of high-dimensional data is often smaller than the ambient dimension. Spectral clustering, as one of the main approaches to…

Feed-forward neural networks can be understood as a combination of an intermediate representation and a linear hypothesis. While most previous works aim to diversify the representations, we explore the complementary direction by performing…

We address the problem to estimate a Kronecker graphical model corresponding to an autoregressive Gaussian stochastic process. The latter is completely described by the power spectral density function whose inverse has support which admits…

In this rather brief note we present and discuss techniques for solving Kronecker matrix product least squares problems. Our main contribution is an iterative approach that uses the efficient Kronecker matrix-vector multiplication strategy…

Spatiotemporal forecasting on transportation networks is a complex task that requires understanding how traffic nodes interact within a dynamic, evolving system dictated by traffic flow dynamics and social behavioral patterns. The…

In autoregressive modeling for tensor-valued time series, Tucker decomposition, when applied to the coefficient tensor, provides a clear interpretation of supervised factor modeling but loses its efficiency rapidly with increasing tensor…

The classical vector autoregressive model is a fundamental tool for multivariate time series analysis. However, it involves too many parameters when the number of time series and lag order are even moderately large. This paper proposes to…

We develop a new methodology for forecasting matrix-valued time series with historical matrix data and auxiliary vector time series data. We focus on a time series of matrices defined on a static 2-D spatial grid and an auxiliary time…

In this paper, we study the subgaussian matrix variate model, where we observe the matrix variate data $X$ which consists of a signal matrix $X_0$ and a noise matrix $W$. More specifically, we study a subgaussian model using the Kronecker…

With the rapid development of web services, large amounts of time series data are generated and accumulated across various domains such as finance, healthcare, and online platforms. As such data often co-evolves with multiple variables…

Several problems in neuroimaging and beyond require inference on the parameters of multi-task sparse hierarchical regression models. Examples include M/EEG inverse problems, neural encoding models for task-based fMRI analyses, and climate…

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.…