arXiv research

Paper proposes a new model for noisy tensor completion.

The paper tackles tensor factorization and completion from noisy data.

New algorithm completes noisy tensors quickly and accurately.

Paper develops RGN method for estimating low-rank tensors from noisy measurements.

Paper proposes a tensor model for clustering noisy multi-view data.

New method clusters multiway data from noisy tensors.

In this article, we develop methods for estimating a low rank tensor from noisy observations on a subset of its entries to achieve both statistical and computational efficiencies. There have been a lot of recent interests in this problem of noisy tensor completion. Much of the attention has been focused on the fundamen…

Revisits CP tensor decomposition for noisy, non-orthogonal data.

In this paper we study the problem of noisy tensor completion for tensors that admit a canonical polyadic or CANDECOMP/PARAFAC (CP) decomposition with one of the factors being sparse. We present general theoretical error bounds for an estimate obtained by using a complexity-regularized maximum likelihood principle and …

Study recovers spike order in noisy tensor estimation without SNR assumptions.

New method estimates tensors from noisy data with missing entries.

New tensor recovery method uses Riemannian optimization on Segre manifold.

Develops methods to estimate high rank tensors from noisy data.

Study analyzes accuracy of tensor deflation in noisy conditions.

Proposes a method for tensor completion with sparse factors and missing data.

Small initialization improves tensor recovery from noisy data.

This paper tackles tensor recovery from noisy and multi-level quantized measurements.

In the noisy tensor completion problem we observe $m$ entries (whose location is chosen uniformly at random) from an unknown $n_1 \times n_2 \times n_3$ tensor $T$. We assume that $T$ is entry-wise close to being rank $r$. Our goal is to fill in its missing entries using as few observations as possible. Let $n = \max(n…

Tensor CANDECOMP/PARAFAC (CP) decomposition is an important tool that solves a wide class of machine learning problems. Existing popular approaches recover components one by one, not necessarily in the order of larger components first. Recently developed simultaneous power method obtains only a high probability recover…

The popular Alternating Least Squares (ALS) algorithm for tensor decomposition is efficient and easy to implement, but often converges to poor local optima---particularly when the weights of the factors are non-uniform. We propose a modification of the ALS approach that is as efficient as standard ALS, but provably rec…

Study on tensor signal estimation from incomplete data.

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…

In this paper, we provide local and global convergence guarantees for recovering CP (Candecomp/Parafac) tensor decomposition. The main step of the proposed algorithm is a simple alternating rank-$1$ update which is the alternating version of the tensor power iteration adapted for asymmetric tensors. Local convergence g…

Bayesian tensor train method recovers streaming data with high accuracy.

Low-rank signal modeling has been widely leveraged to capture non-local correlation in image processing applications. We propose a new method that employs low-rank tensor factor analysis for tensors generated by grouped image patches. The low-rank tensors are fed into the alternative direction multiplier method (ADMM) …

In this paper, we propose a general framework for sparse and low-rank tensor estimation from cubic sketchings. A two-stage non-convex implementation is developed based on sparse tensor decomposition and thresholded gradient descent, which ensures exact recovery in the noiseless case and stable recovery in the noisy cas…

Paper optimizes tensor deflation for non-orthogonal signals.

Study uncovers statistical optimality of nonconvex tensor completion methods.

Efficient method for tensor linear form inference with noisy incomplete data.

Tensor-EM method learns MoLDS from complex, noisy data.

New method estimates and completes tensors from ordinal data, improving accuracy and efficiency.

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 parameters with the maximum likelihood is NP-hard even in very simple settings. In rece…

SGD recovers multiple signal vectors in noisy tensor PCA.

We analyze low rank tensor completion (TC) using noisy measurements of a subset of the tensor. Assuming a rank-$r$, order-$d$, $N \times N \times \cdots \times N$ tensor where $r=O(1)$, the best sampling complexity that was achieved is $O(N^{\frac{d}{2}})$, which is obtained by solving a tensor nuclear-norm minimizatio…

Study of Langevin dynamics for tensor PCA recovery in high dimensions.

Tensor completion requires fewer samples with weak side information.

Paper tackles subspace estimation from noisy, partial data matrices.

NA$_0$CT$^2$ improves tensor regression predictions with $\ell_0$ regularization.

Study reveals efficient recovery of multi-modal signals via Bayesian methods and sequential learning.

Paper identifies latent factors from noisy measurements using tensor decomposition.

Quantum neural network and tensor network models outperform classical models in Japanese stock market predictions.

Efficiently recovers low-tubal-rank tensors from few measurements.

Tensor factorization uncovers hidden patterns in student behavior data.

New method clusters tensors with heteroskedastic noise.

The completion of tensors, or high-order arrays, attracts significant attention in recent research. Current literature on tensor completion primarily focuses on recovery from a set of uniformly randomly measured entries, and the required number of measurements to achieve recovery is not guaranteed to be optimal. In add…

We study low rank matrix and tensor completion and propose novel algorithms that employ adaptive sampling schemes to obtain strong performance guarantees. Our algorithms exploit adaptivity to identify entries that are highly informative for learning the column space of the matrix (tensor) and consequently, our results …

CNNs achieve remarkable performance by leveraging deep, over-parametrized architectures, trained on large datasets. However, they have limited generalization ability to data outside the training domain, and a lack of robustness to noise and adversarial attacks. By building better inductive biases, we can improve robust…

Algorithm estimates tensors from sparse observations with robust error bounds.