相关论文: Tucker tensor factor models: matricization and mod…

Higher-order tensor datasets arise commonly in recommendation systems, neuroimaging, and social networks. Here we develop probable methods for estimating a possibly high rank signal tensor from noisy observations. We consider a generative…

Recently, introducing Tensor Decomposition (TD) techniques into unsupervised feature selection (UFS) has been an emerging research topic. A tensor structure is beneficial for mining the relations between different modes and helps relieve…

Valid causal inference in observational studies often requires controlling for confounders. However, in practice measurements of confounders may be noisy, and can lead to biased estimates of causal effects. We show that we can reduce the…

This paper studies a tensor-structured linear regression model with a scalar response variable and tensor-structured predictors, such that the regression parameters form a tensor of order $d$ (i.e., a $d$-fold multiway array) in…

Tucker decomposition is a powerful tensor model to handle multi-aspect data. It demonstrates the low-rank property by decomposing the grid-structured data as interactions between a core tensor and a set of object representations (factors).…

Tensor train is a hierarchical tensor network structure that helps alleviate the curse of dimensionality by parameterizing large-scale multidimensional data via a set of network of low-rank tensors. Associated with such a construction is a…

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…

The factor analysis model is a statistical model where a certain number of hidden random variables, called factors, affect linearly the behaviour of another set of observed random variables, with additional random noise. The main assumption…

In this paper, we consider the statistical inference for several low-rank tensor models. Specifically, in the Tucker low-rank tensor PCA or regression model, provided with any estimates achieving some attainable error rate, we develop the…

The CP decomposition for high dimensional non-orthogonal spiked tensors is an important problem with broad applications across many disciplines. However, previous works with theoretical guarantee typically assume restrictive incoherence…

This paper introduces a Projected Principal Component Analysis (Projected-PCA), which employs principal component analysis to the projected (smoothed) data matrix onto a given linear space spanned by covariates. When it applies to…

Existing models for high-dimensional time series are overwhelmingly developed within the finite-order vector autoregressive (VAR) framework. However, the more flexible vector autoregressive moving averages (VARMA) have been much less…

In this paper, we propose a novel high-dimensional time-varying coefficient estimator for noisy high-frequency observations with a factor structure. In high-frequency finance, we often observe that noises dominate the signal of underlying…

Many problems in computational neuroscience, neuroinformatics, pattern/image recognition, signal processing and machine learning generate massive amounts of multidimensional data with multiple aspects and high dimensionality. Tensors (i.e.,…

We propose a novel framework in high-dimensional factor models to simultaneously analyse multiple tensor time series, each with potentially different tensor orders and dimensionality. The connection between different tensor time series is…

Principal component analysis (PCA) is arguably the most widely used approach for large-dimensional factor analysis. While it is effective when the factors are sufficiently strong, it can be inconsistent when the factors are weak and/or the…

Tensor sparse modeling as a promising approach, in the whole of science and engineering has been a huge success. As is known to all, various data in practical application are often generated by multiple factors, so the use of tensors to…

By representing documents as mixtures of topics, topic modeling has allowed the successful analysis of datasets across a wide spectrum of applications ranging from ecology to genetics. An important body of recent work has demonstrated the…

Tensor decomposition is an effective tool for learning multi-way structures and heterogeneous features from high-dimensional data, such as the multi-view images and multichannel electroencephalography (EEG) signals, are often represented by…

In this paper, we propose three approaches for the estimation of the Tucker decomposition of multi-way arrays (tensors) from partial observations. All approaches are formulated as convex minimization problems. Therefore, the minimum is…