## About this Research Topic

In many application areas, it is common to collect data that are structured as a multiway array or tensor, for example, brain images, facial images, infrared images, gene expression data, social relation data, and climatology data. Tensors are often used to represent complex data sets. Traditional data analysis methods rely on representation and computation in the form of vectors and matrices, where multi-dimensional data are unfolded into a matrix for processing. However, the multilinear structure would be lost in such vectorization or matricization, which leads to sub-optimal performance in processing. It is necessary to explore novel statistical methods to analyze tensor data.

We intend to collect relevant articles and promote the development of tensor analysis, especially tensor completion, tensor decomposition algorithms, and tensor regression. Since the datasets in practice are often incomplete, much of the early research was conducted on tensor decomposition with missing values, which could be regarded as the pioneer problem of tensor completion. In recent years there has been a large amount of literature relating to tensor completion. Moreover, tensor regression frameworks are being developed to better explore the multiway dependencies along the high-dimensional input and output. Efficient statistical inference methods for tensor regression are increasingly important. The goal of this Research Topic is to further the research on tensor completion approaches, parametric estimation methods in various tensor regression methods, and novel applications for tensor analysis approaches.

Particular topics of interest, include, but are not limited to:

• Tensor completion/tensor estimation

• Tensor regression

• Tensor Network analysis

• Bayesian inference for tensor completion/tensor regression

• Variational inference for tensor data

• Image data analysis based on tensor data

• Tensor decomposition/tensor factorization

**Keywords**:
statistical inference, tensor, tensor completion, tensor regression, Bayesian inference, tensor decomposition, tensor factorization

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.

We intend to collect relevant articles and promote the development of tensor analysis, especially tensor completion, tensor decomposition algorithms, and tensor regression. Since the datasets in practice are often incomplete, much of the early research was conducted on tensor decomposition with missing values, which could be regarded as the pioneer problem of tensor completion. In recent years there has been a large amount of literature relating to tensor completion. Moreover, tensor regression frameworks are being developed to better explore the multiway dependencies along the high-dimensional input and output. Efficient statistical inference methods for tensor regression are increasingly important. The goal of this Research Topic is to further the research on tensor completion approaches, parametric estimation methods in various tensor regression methods, and novel applications for tensor analysis approaches.

Particular topics of interest, include, but are not limited to:

• Tensor completion/tensor estimation

• Tensor regression

• Tensor Network analysis

• Bayesian inference for tensor completion/tensor regression

• Variational inference for tensor data

• Image data analysis based on tensor data

• Tensor decomposition/tensor factorization

**Keywords**:
statistical inference, tensor, tensor completion, tensor regression, Bayesian inference, tensor decomposition, tensor factorization

**Important Note**:
All contributions to this Research Topic must be within the scope of the section and journal to which they are submitted, as defined in their mission statements. Frontiers reserves the right to guide an out-of-scope manuscript to a more suitable section or journal at any stage of peer review.