Related papers: Low-rank Characteristic Tensor Density Estimation …
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…
We present a nonlinear regression framework based on tensor algebra tailored to high dimensional contexts where data is scarce. We exploit algebraic properties of a partial tensor product, namely the m-tensor product, to leverage structured…
Tensor regression is an important tool for tensor data analysis, but existing works have not considered the impact of outliers, making them potentially sensitive to such data points. This paper proposes a low tubal rank robust regression…
Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The…
Higher-order tensors arise frequently in applications such as neuroimaging, recommendation system, social network analysis, and psychological studies. We consider the problem of low-rank tensor estimation from possibly incomplete,…
In this paper, we propose a novel tensor learning and coding model for third-order data completion. Our model is to learn a data-adaptive dictionary from the given observations, and determine the coding coefficients of third-order tensor…
Statistical learning additions to physically derived mathematical models are gaining traction in the literature. A recent approach has been to augment the underlying physics of the governing equations with data driven Bayesian statistical…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
Unlike the matrix case, computing low-rank approximations of tensors is NP-hard and numerically ill-posed in general. Even the best rank-1 approximation of a tensor is NP-hard. In this paper, we use convex optimization to develop…
Reliable density estimation is fundamental for numerous applications in statistics and machine learning. In many practical scenarios, data are best modeled as mixtures of component densities that capture complex and multimodal patterns.…
Low-rank regularization is an effective technique for addressing ill-posed inverse problems when the unknown variable exhibits low-rank characteristics. However, global low-rank assumptions do not always hold for seismic wavefields; in many…
Most state of the art deep neural networks are overparameterized and exhibit a high computational cost. A straightforward approach to this problem is to replace convolutional kernels with its low-rank tensor approximations, whereas the…
Most currently used tensor regression models for high-dimensional data are based on Tucker decomposition, which has good properties but loses its efficiency in compressing tensors very quickly as the order of tensors increases, say greater…
Tensor completion can estimate missing values of a high-order data from its partially observed entries. Recent works show that low rank tensor ring approximation is one of the most powerful tools to solve tensor completion problem. However,…
Modern empirical analysis often relies on high-dimensional panel datasets with non-negligible cross-sectional and time-series correlations. Factor models are natural for capturing such dependencies. A tensor factor model describes the…
Density based representations of atomic environments that are invariant under Euclidean symmetries have become a widely used tool in the machine learning of interatomic potentials, broader data-driven atomistic modelling and the…
In this paper, we introduce and analyze a new low-rank multilevel strategy for the solution of random diffusion problems. Using a standard stochastic collocation scheme, we first approximate the infinite dimensional random problem by a…
Tensor neural networks (TNNs) have demonstrated their superiority in solving high-dimensional problems. However, similar to conventional neural networks, TNNs are also influenced by the Frequency Principle, which limits their ability to…
With the advancements in computing technology and web-based applications, data is increasingly generated in multi-dimensional form. This data is usually sparse due to the presence of a large number of users and fewer user interactions. To…
It is now practically the norm for data to be very high dimensional in areas such as genetics, machine vision, image analysis and many others. When analyzing such data, parametric models are often too inflexible while nonparametric…