Related papers: CP Factor Model for Dynamic Tensors
This paper proposes a novel method for learning highly nonlinear, multivariate functions from examples. Our method takes advantage of the property that continuous functions can be approximated by polynomials, which in turn are representable…
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…
In the framework of multidimensional Compressed Sensing (CS), we introduce an analytical reconstruction formula that allows one to recover an $N$th-order $(I_1\times I_2\times \cdots \times I_N)$ data tensor $\underline{\mathbf{X}}$ from a…
CANDECOMP/PARAFAC (CP) tensor factorization of incomplete data is a powerful technique for tensor completion through explicitly capturing the multilinear latent factors. The existing CP algorithms require the tensor rank to be manually…
Factor analysis for high-dimensional data is a canonical problem in statistics and has a wide range of applications. However, there is currently no factor model tailored to effectively analyze high-dimensional count responses with…
We present methods for constructing Taylor series surrogate models for covariance preconditioned high dimensional mappings that depend implicitly on the solution of a system of nonlinear equations, e.g., the solution of a partial…
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…
We introduce a class of Bayesian matrix dynamic factor models that accommodates time-varying volatility, outliers, and cross-sectional correlation in the idiosyncratic components. For model comparison, we employ an importance-sampling…
This article provides next step towards solving speed bottleneck of any system that intensively uses convolutions operations (e.g. CNN). Method described in the article is applied on deformable part models (DPM) algorithm. Method described…
We consider the problem of decomposing higher-order moment tensors, i.e., the sum of symmetric outer products of data vectors. Such a decomposition can be used to estimate the means in a Gaussian mixture model and for other applications in…
We propose a flexible dual functional factor model for modelling high-dimensional functional time series. In this model, a high-dimensional fully functional factor parametrisation is imposed on the observed functional processes, whereas a…
This paper tackles the problem of recovering a low-rank signal tensor with possibly correlated components from a random noisy tensor, or so-called spiked tensor model. When the underlying components are orthogonal, they can be recovered…
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…
Temporal causal representation learning is a powerful tool for uncovering complex patterns in observational studies, which are often represented as low-dimensional time series. However, in many real-world applications, data are…
In this paper we consider the problem of recovering a low-rank Tucker approximation to a massive tensor based solely on structured random compressive measurements. Crucially, the proposed random measurement ensembles are both designed to be…
The prominence of deep learning, large amount of annotated data and increasingly powerful hardware made it possible to reach remarkable performance for supervised classification tasks, in many cases saturating the training sets. However the…
We propose a flexible nonparametric Bayesian modelling framework for multivariate time series of count data based on tensor factorisations. Our models can be viewed as infinite state space Markov chains of known maximal order with…
I develop a feasible weighted projected principal component (FPPC) analysis for factor models in which observable characteristics partially explain the latent factors. This novel method provides more efficient and accurate estimators than…
Tensor decompositions are a fundamental tool in scientific computing and data analysis. In many applications -- such as simulation data on irregular grids, surrogate modeling for parameterized PDEs, or spectroscopic measurements -- the data…
The structure tensor method is often used for 2D and 3D analysis of imaged structures, but its results are in many cases very dependent on the user's choice of method parameters. We simplify this parameter choice in first order structure…