相关论文: Tensor-based Model Reduction and Identification fo…

Modern approaches to generative modeling of continuous data using tensor networks incorporate compression layers to capture the most meaningful features of high-dimensional inputs. These methods, however, rely on traditional Matrix Product…

Tensor completion refers to the task of estimating the missing data from an incomplete measurement or observation, which is a core problem frequently arising from the areas of big data analysis, computer vision, and network engineering. Due…

Tensor data represents a multidimensional array. Regression methods based on low-rank tensor decomposition leverage structural information to reduce the parameter count. Multilinear logistic regression serves as a powerful tool for the…

In this paper we introduce and study the Maximum-Average Subtensor ($p$-MAS) problem, in which one wants to find a subtensor of size $k$ of a given random tensor of size $N$, both of order $p$, with maximum sum of entries. We are motivated…

Tensor networks are efficient for extremely high-dimensional representation, but their model selection, known as tensor network structure search (TN-SS), is a challenging problem. Although several works have targeted TN-SS, most existing…

Random projection (RP) have recently emerged as popular techniques in the machine learning community for their ability in reducing the dimension of very high-dimensional tensors. Following the work in [30], we consider a tensorized random…

We present new alternative complete asymptotic expansions for the time harmonic low--frequency magnetic field perturbation caused by the presence of a conducting permeable object as its size tends to zero for the eddy current approximation…

In this paper we review basic and emerging models and associated algorithms for large-scale tensor networks, especially Tensor Train (TT) decompositions using novel mathematical and graphical representations. We discus the concept of…

The widespread use of multisensor technology and the emergence of big data sets have brought the necessity to develop more versatile tools to represent higher-order data with multiple aspects and high dimensionality. Data in the form of…

Compressed sensing extends from the recovery of sparse vectors from undersampled measurements via efficient algorithms to the recovery of matrices of low rank from incomplete information. Here we consider a further extension to the…

The Gaussian process state-space model (GPSSM) has attracted extensive attention for modeling complex nonlinear dynamical systems. However, the existing GPSSM employs separate Gaussian processes (GPs) for each latent state dimension,…

Tensor classification has become increasingly crucial in statistics and machine learning, with applications spanning neuroimaging, computer vision, and recommendation systems. However, the high dimensionality of tensors presents significant…

Probabilistic topic models are popular unsupervised learning methods, including probabilistic latent semantic indexing (pLSI) and latent Dirichlet allocation (LDA). By now, their training is implemented on general purpose computers (GPCs),…

The deep neural network (DNN) based speech enhancement approaches have achieved promising performance. However, the number of parameters involved in these methods is usually enormous for the real applications of speech enhancement on the…

Neural networks can be significantly compressed by pruning, yielding sparse models with reduced storage and computational demands while preserving predictive performance. Model soups (Wortsman et al., 2022) enhance generalization and…

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…

Learning of low-rank matrices is fundamental to many machine learning applications. A state-of-the-art algorithm is the rank-one matrix pursuit (R1MP). However, it can only be used in matrix completion problems with the square loss. In this…

Generative modeling, which learns joint probability distribution from data and generates samples according to it, is an important task in machine learning and artificial intelligence. Inspired by probabilistic interpretation of quantum…

Producing large complex simulation datasets can often be a time and resource consuming task. Especially when these experiments are very expensive, it is becoming more reasonable to generate synthetic data for downstream tasks. Recently,…

Posynomials are nonnegative combinations of monomials with possibly fractional and both positive and negative exponents. Posynomial models are widely used in various engineering design endeavors, such as circuits, aerospace and structural…