arXiv research

Tensorized random projections reduce high-dimensional tensor size efficiently.

Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.

New algorithms solve tensor problems with random components using SDP.

New concentration inequalities for tensors with heavy-tailed coefficients.

Stochastic trace estimation with tensor train random vectors

Paper studies tensor models using random matrix theory.

Paper optimizes tensor deflation for non-orthogonal signals.

Develops path integral for spiked tensor model dynamics.

The paper studies phase transitions in random matrices and tensor unfolding for detecting signals.

Tensor rank and low-rank tensor decompositions have many applications in learning and complexity theory. Most known algorithms use unfoldings of tensors and can only handle rank up to $n^{\lfloor p/2 \rfloor}$ for a $p$-th order tensor in $\mathbb{R}^{n^p}$. Previously no efficient algorithm can decompose 3rd order ten…

Study on tensor signal estimation from incomplete data.

New approach uses random matrix theory to understand tensor estimation performance.

Study analyzes Hotelling-type tensor deflation for spiked tensors, providing insights into signal and noise.

Estimates metric tensor on neuromanifolds using Fisher information and random methods.

New estimator for tensor weights with improved bias.

Tensors play a central role in many modern machine learning and signal processing applications. In such applications, the target tensor is usually of low rank, i.e., can be expressed as a sum of a small number of rank one tensors. This motivates us to consider the problem of low rank tensor recovery from a class of lin…

A new algorithm speeds up CP decomposition for large tensors.

A new tensor completion method handles missing data with missing not at random entries.

New method approximates high-dimensional probability densities efficiently.

Surveying random sections on Kähler manifolds, leading to metrics.

Estimates the probability of a random symmetric tensor being close to rank-one.

Study analyzes accuracy of tensor deflation in noisy conditions.

Paper generalizes tensor-train approximation for complex random variables.

Estimates joint probability distribution from 1-way marginals using low-rank tensors and random projections.

Paper refutes conjecture on tensor power iteration convergence in overcomplete models.

TEC combines multiple RPSTMs to classify big tensors efficiently.

A new method reduces the complexity of tensor products from cubic to quadratic, improving both speed and accuracy.

Tensor factorization arises in many machine learning applications, such knowledge base modeling and parameter estimation in latent variable models. However, numerical methods for tensor factorization have not reached the level of maturity of matrix factorization methods. In this paper, we propose a new method for CP te…

TTRP method preserves distances in high-dimensional data with reduced storage and speed.

Sketching is a randomized dimensionality-reduction method that aims to preserve relevant information in large-scale datasets. Count sketch is a simple popular sketch which uses a randomized hash function to achieve compression. In this paper, we propose a novel extension known as Higher-order Count Sketch (HCS). While …

Tensor CANDECOMP/PARAFAC (CP) decomposition has wide applications in statistical learning of latent variable models and in data mining. In this paper, we propose fast and randomized tensor CP decomposition algorithms based on sketching. We build on the idea of count sketches, but introduce many novel ideas which are un…

Recent years have demonstrated that using random feature maps can significantly decrease the training and testing times of kernel-based algorithms without significantly lowering their accuracy. Regrettably, because random features are target-agnostic, typically thousands of such features are necessary to achieve accept…

Study uses random matrix theory to improve tensor approximation accuracy.

New method tackles tensor regression with robust Kaczmarz approach.

We show that the spectral norm of a random $n_1\times n_2\times \cdots \times n_K$ tensor (or higher-order array) scales as $O\left(\sqrt{(\sum_{k=1}^{K}n_k)\log(K)}\right)$ under some sub-Gaussian assumption on the entries. The proof is based on a covering number argument. Since the spectral norm is dual to the tensor…

One of the current issues in Brain-Computer Interface is how to deal with noisy Electroencephalography measurements organized as multidimensional datasets. On the other hand, recently, significant advances have been made in multidimensional signal completion algorithms that exploit tensor decomposition models to captur…

This work improves tensor decomposition methods, especially for large datasets.

We formulate and solve a tensor model using a latent-variable approach.

OpEvo automates tensor operator optimization for better efficiency.

Optimizes tensor rank selection for neural network compression.

A new tree method for tensor data improves regression accuracy.

Proposes a nonparametric tensor factorization for sparse data.

Study on estimating rank-one tensors in noisy data with heavy tails.

New local-search methods close the gap in sparse tensor PCA.

We describe the first known mean-field study of landing probabilities for random walks on hypergraphs. In particular, we examine clique-expansion and tensor methods and evaluate their mean-field characteristics over a class of random hypergraph models for the purpose of seed-set community expansion. We describe paramet…

New findings on tensor decomposition complexity, showing polynomial functions can estimate the largest component under certain conditions.

We consider two problems that arise in machine learning applications: the problem of recovering a planted sparse vector in a random linear subspace and the problem of decomposing a random low-rank overcomplete 3-tensor. For both problems, the best known guarantees are based on the sum-of-squares method. We develop new …

Method learns topological states from randomized measurements.