Search Results for author: Tamara G. Kolda

Found 11 papers, 4 papers with code

Convergence of Alternating Gradient Descent for Matrix Factorization

no code implementations NeurIPS 2023 Rachel Ward, Tamara G. Kolda

We show that, for a rank-$r$ matrix $\mathbf{A} \in \mathbb{R}^{m \times n}$, $T = C (\frac{\sigma_1(\mathbf{A})}{\sigma_r(\mathbf{A})})^2 \log(1/\epsilon)$ iterations of alternating gradient descent suffice to reach an $\epsilon$-optimal factorization $\| \mathbf{A} - \mathbf{X} \mathbf{Y}^{T} \|^2 \leq \epsilon \| \mathbf{A}\|^2$ with high probability starting from an atypical random initialization.

Tensor Moments of Gaussian Mixture Models: Theory and Applications

1 code implementation14 Feb 2022 João M. Pereira, Joe Kileel, Tamara G. Kolda

In this work, we develop theory and numerical methods for \emph{implicit computations} with moment tensors of GMMs, reducing the computational and storage costs to $\mathcal{O}(n^2)$ and $\mathcal{O}(n^3)$, respectively, for general covariance matrices, and to $\mathcal{O}(n)$ and $\mathcal{O}(n)$, respectively, for diagonal ones.

Tensor Decomposition

Streaming Generalized Canonical Polyadic Tensor Decompositions

1 code implementation27 Oct 2021 Eric Phipps, Nick Johnson, Tamara G. Kolda

In this paper, we develop a method which we call OnlineGCP for computing the Generalized Canonical Polyadic (GCP) tensor decomposition of streaming data.

Tensor Decomposition

Stochastic Gradients for Large-Scale Tensor Decomposition

no code implementations4 Jun 2019 Tamara G. Kolda, David Hong

The stochastic gradient is formed from randomly sampled elements of the tensor and is efficient because it can be computed using the sparse matricized-tensor-times-Khatri-Rao product (MTTKRP) tensor kernel.

Tensor Decomposition

XPCA: Extending PCA for a Combination of Discrete and Continuous Variables

no code implementations22 Aug 2018 Clifford Anderson-Bergman, Tamara G. Kolda, Kina Kincher-Winoto

If some marginals are continuous but not normal, the semiparametric copula-based principal component analysis (COCA) method is an alternative to PCA that combines a Gaussian copula with nonparametric marginals.

Dimensionality Reduction

Generalized Canonical Polyadic Tensor Decomposition

no code implementations22 Aug 2018 David Hong, Tamara G. Kolda, Jed A. Duersch

Tensor decomposition is a fundamental unsupervised machine learning method in data science, with applications including network analysis and sensor data processing.

Tensor Decomposition

Community structure and scale-free collections of Erdös-Rényi graphs

1 code implementation15 Dec 2011 C. Seshadhri, Tamara G. Kolda, Ali Pinar

Community structure plays a significant role in the analysis of social networks and similar graphs, yet this structure is little understood and not well captured by most models.

Social and Information Networks Physics and Society

On Tensors, Sparsity, and Nonnegative Factorizations

no code implementations11 Dec 2011 Eric C. Chi, Tamara G. Kolda

We present a new algorithm for Poisson tensor factorization called CANDECOMP-PARAFAC Alternating Poisson Regression (CP-APR) that is based on a majorization-minimization approach.

Numerical Analysis

Temporal Link Prediction using Matrix and Tensor Factorizations

1 code implementation21 May 2010 Daniel M. Dunlavy, Tamara G. Kolda, Evrim Acar

We show how the well-known Katz method for link prediction can be extended to bipartite graphs and, moreover, approximated in a scalable way using a truncated singular value decomposition.

Link Prediction Tensor Decomposition

Scalable Tensor Factorizations for Incomplete Data

no code implementations12 May 2010 Evrim Acar, Tamara G. Kolda, Daniel M. Dunlavy, Morten Morup

In the presence of missing data, CP can be formulated as a weighted least squares problem that models only the known entries.

Numerical Analysis Numerical Analysis Data Analysis, Statistics and Probability G.1.3; G.1.6

Cannot find the paper you are looking for? You can Submit a new open access paper.