Related papers: Predicting Multidimensional Data via Tensor Learni…

Nonparametric extension of tensor regression is proposed. Nonlinearity in a high-dimensional tensor space is broken into simple local functions by incorporating low-rank tensor decomposition. Compared to naive nonparametric approaches, our…

The problem of prediction in functional linear regression is conventionally addressed by reducing dimension via the standard principal component basis. In this paper we show that an alternative basis chosen through weighted least-squares,…

Dimension reduction is often the first step in statistical modeling or prediction of multivariate spatial data. However, most existing dimension reduction techniques do not account for the spatial correlation between observations and do not…

Tensor time series, which is a time series consisting of tensorial observations, has become ubiquitous. It typically exhibits high dimensionality. One approach for dimension reduction is to use a factor model structure, in a form similar to…

In this work, we present tensor-based linear and nonlinear models for hyperspectral data classification and analysis. By exploiting principles of tensor algebra, we introduce new classification architectures, the weight parameters of which…

Many machine learning applications use latent variable models to explain structure in data, whereby visible variables (= coordinates of the given datapoint) are explained as a probabilistic function of some hidden variables. Finding…

Tensor decomposition of high-dimensional data often struggles to capture semantically or physically meaningful structures, particularly when relying on reconstruction objectives and fixed-rank constraints. We introduce a no-rank tensor…

In modern data science, dynamic tensor data is prevailing in numerous applications. An important task is to characterize the relationship between such dynamic tensor and external covariates. However, the tensor data is often only partially…

Large amount of multidimensional data represented by multiway arrays or tensors are prevalent in modern applications across various fields such as chemometrics, genomics, physics, psychology, and signal processing. The structural complexity…

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…

Latent variable models are an elegant framework for capturing rich probabilistic dependencies in many applications. However, current approaches typically parametrize these models using conditional probability tables, and learning relies…

Marginal Structural Models (MSM) are the most popular models for causal inference from time-series observational data. However, they have two main drawbacks: (a) they do not capture subject heterogeneity, and (b) they only consider fixed…

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,…

We introduce a tensor-based model of shared representation for meta-learning from a diverse set of tasks. Prior works on learning linear representations for meta-learning assume that there is a common shared representation across different…

Tensors naturally model many real world processes which generate multi-aspect data. Such processes appear in many different research disciplines, e.g, chemometrics, computer vision, psychometrics and neuroimaging analysis. Tensor…

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…

This paper considers improved forecasting in possibly nonlinear dynamic settings, with high-dimension predictors ("big data" environments). To overcome the curse of dimensionality and manage data and model complexity, we examine shrinkage…

Many approximations were suggested to circumvent the cubic complexity of kernel-based algorithms, allowing their application to large-scale datasets. One strategy is to consider the primal formulation of the learning problem by mapping the…

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…

We present a windowed technique to learn parsimonious time-varying autoregressive models from multivariate timeseries. This unsupervised method uncovers interpretable spatiotemporal structure in data via non-smooth and non-convex…