Related papers: QUARKS: Identification of large-scale Kronecker Ve…
Recurrent Neural Networks (RNN) can be difficult to deploy on resource constrained devices due to their size. As a result, there is a need for compression techniques that can significantly compress RNNs without negatively impacting task…
Predictive linear and nonlinear models based on kernel machines or deep neural networks have been used to discover dependencies among time series. This paper proposes an efficient nonlinear modeling approach for multiple time series, with a…
Matrix normal models have an associated 4-tensor for their covariance representation. The covariance array associated with a matrix normal model is naturally represented as a Kronecker-product structured covariance associated with the…
In finance, economics and many other fields, observations in a matrix form are often generated over time. For example, a set of key economic indicators are regularly reported in different countries every quarter. The observations at each…
Real-world signals typically span across multiple dimensions, that is, they naturally reside on multi-way data structures referred to as tensors. In contrast to standard ``flat-view'' multivariate matrix models which are agnostic to data…
Tensor factorization is a powerful tool to analyse multi-way data. Compared with traditional multi-linear methods, nonlinear tensor factorization models are capable of capturing more complex relationships in the data. However, they are…
Neural encoding studies explore the relationships between measurements of neural activity and measurements of a behavior that is viewed as a response to that activity. The coupling between neural and behavioral measurements is typically…
Traditional econometric analyzes represent observations as vectors despite the inherent complexity of empirical data structures. When data are organized along dual classification dimensions, a matrix representation provides a more natural…
Graph learning aims to infer a network structure directly from observed data, enabling the analysis of complex dependencies in irregular domains. Traditional methods focus on scalar signals at each node, ignoring dependencies along…
One approach to understanding complex data is to study its shape through the lens of algebraic topology. While the early development of topological data analysis focused primarily on static data, in recent years, theoretical and applied…
We study the problem of estimating the trace of a matrix $\mathbf{A}$ that can only be accessed through Kronecker-matrix-vector products. That is, for any Kronecker-structured vector $\mathrm{x} = \otimes_{i=1}^k \mathrm{x}_i$, we can…
We introduce a simple, stochastic, a-posteriori, turbulence closure model based on a reduced subgrid scale term. This subgrid scale term is tailor-made to capture the statistics of a small set of spatially-integrate quantities of interest…
Existing methods of pruning deep neural networks focus on removing unnecessary parameters of the trained network and fine tuning the model afterwards to find a good solution that recovers the initial performance of the trained model. Unlike…
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…
We present a low-order modeling technique for actuated flows based on the regularization of an inverse problem. The inverse problem aims at minimizing the error between the model predictions and some reference simulations. The parameters to…
In this paper we propose and study a technique to reduce the number of parameters and computation time in fully-connected layers of neural networks using Kronecker product, at a mild cost of the prediction quality. The technique proceeds by…
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…
Identifying the topology underlying a set of time series is useful for tasks such as prediction, denoising, and data completion. Vector autoregressive (VAR) model-based topologies capture dependencies among time series and are often…
We propose Deep Kronecker Network (DKN), a novel framework designed for analyzing medical imaging data, such as MRI, fMRI, CT, etc. Medical imaging data is different from general images in at least two aspects: i) sample size is usually…
A novel compressed matrix format is proposed that combines an adaptive hierarchical partitioning of the matrix with low-rank approximation. One typical application is the approximation of discretized functions on rectangular domains; the…