Given a sparse time-evolving tensor, how can we effectively factorize it to accurately discover latent patterns? Tensor decomposition has been extensively utilized for analyzing various multi-dimensional real-world data. However, existing tensor models have disregarded the temporal property while most data are closely related time. Moreover, they do not address accuracy degradation due sparsity...

In the real-time bidding (RTB) display advertising ecosystem, when receiving a bid request, the demandside platform (DSP) needs to predict the click-through rate (CTR) for ads and calculate the bid price according to the CTR estimated. In addition to challenges similar to those encountered in sponsored search advertising, such as data sparsity and cold start problems, more complicated feature i...

Large CNNs have delivered impressive performance in various computer vision applications. But the storage and computation requirements make it problematic for deploying these models on mobile devices. Recently, tensor decompositions have been used for speeding up CNNs. In this paper, we further develop the tensor decomposition technique. We propose a new algorithm for computing the low-rank ten...

This work considers a computationally and statistically efficient parameter estimation method for a wide class of latent variable models—including Gaussian mixture models, hidden Markov models, and latent Dirichlet allocation—which exploits a certain tensor structure in their low-order observable moments (typically, of secondand third-order). Specifically, parameter estimation is reduced to the...

Generating function (GF) has been used in blind identification for real-valued signals. In this paper, the definition of GF is first generalized for complex-valued random variables in order to exploit the statistical information carried on complex signals in a more effective way. Then an algebraic structure is proposed to identify the mixing matrix from underdetermined mixtures using the genera...

Tensor methods are gaining increasing traction in machine learning. However, there are scant to no resources available to perform tensor learning and decomposition in Python. To answer this need we developed TensorLy. TensorLy is a state of the art general purpose library for tensor learning. Written in Python, it aims at following the same standard adopted by the main projects of the Python sc...

The wave equation for vectors and symmetric tensors in spherical coordinates is studied under the divergence-free constraint. We describe a numerical method, based on the spectral decomposition of vector/tensor components onto spherical harmonics, that allows for the evolution of only those scalar fields which correspond to the divergence-free degrees of freedom of the vector/tensor. The full v...

A novel algorithm is proposed for CANDECOMP/PARAFAC tensor decomposition to exploit best rank-1 tensor approximation. Different from the existing algorithms, our algorithm updates rank-1 tensors simultaneously in-parallel. In order to achieve this, we develop new all-at-once algorithms for best rank-1 tensor approximation based on the Levenberg-Marquardt method and the rotational update. We sho...

Abstract. Suppose A = (aijk) ∈ Rn×n×n is a three-way array or third-order tensor. Many of the powerful tools of linear algebra such as the singular value decomposition (SVD) do not, unfortunately, extend in a straightforward way to tensors of order three or higher. In the twodimensional case, the SVD is particularly illuminating, since it reduces a matrix to diagonal form. Although it is not po...

Cyclops (cyclic-operations) Tensor Framework (CTF) 1 is a distributed library for tensor contractions. CTF aims to scale high-dimensional tensor contractions done in Coupled Cluster calculations on massively-parallel supercomputers. The framework preserves tensor symmetry by subdividing tensors cyclically, producing a highly regular parallel decomposition. The parallel decomposition effectively...