Publications

A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold

Published in To appear in SIAM Journal on Matrix Analysis and Applications, 2025

We study the maximization of sums of heterogeneous quadratic functions over the Stiefel manifold, a nonconvex problem that arises in several modern signal processing and machine learning applications such as heteroscedastic probabilistic principal component analysis (HPPCA).

Recommended citation: Kyle Gilman, Sam Burer, and Laura Balzano (2022). "A Semidefinite Relaxation for Sums of Heterogeneous Quadratic Forms on the Stiefel Manifold." arXiv preprint arXiv:2205.13653. https://arxiv.org/abs/2205.13653

Streaming Probabilistic PCA for Missing Data with Heteroscedastic Noise

Published in arxiv preprint, 2023

This paper proposes a stochastic alternating expectation maximization approach that jointly learns the low-rank latent factors and the unknown noise variances from streaming data that may have missing entries and heteroscedastic noise.

Recommended citation: Kyle Gilman, David Hong, Jeffrey Fessler and Laura Balzano (2023). "Streaming Probabilistic PCA for Missing Data with Heteroscedastic Noise." arXiv preprint arXiv:2310.06277. https://arxiv.org/abs/2310.06277

Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD

Published in IEEE Transactions on Signal Processing, Vol. 70, 2022

We propose a new fast streaming algorithm for the tensor completion problem of imputing missing entries of a low-tubal-rank tensor using the tensor singular value decomposition (t-SVD) algebraic framework.

Recommended citation: Kyle Gilman, Davoud Ataee Tarzanagh, and Laura Balzano (2022). "Grassmannian Optimization for Online Tensor Completion and Tracking with the t-SVD." IEEE Transactions on Signal Processing, Vol. 70, 2022. https://ieeexplore.ieee.org/abstract/document/9756209)

HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise

Published in IEEE Transactions on Signal Processing, Vol. 69, 2021

This paper develops a probabilistic PCA variant that estimates and accounts for this heterogeneity by incorporating it in the statistical model.

Recommended citation: David Hong, Kyle Gilman, Laura Balzano, and Jeffrey A. Fessler. "HePPCAT: Probabilistic PCA for Data with Heteroscedastic Noise " IEEE Transactions on Signal Processing, Vol. 69, 2021 https://ieeexplore.ieee.org/document/9514397

Online Tensor Completion and Free Submodule Tracking with the t-SVD

Published in 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP), 2020

We propose a new online algorithm, called TOUCAN, for the tensor completion problem of imputing missing entries of a low tubal-rank tensor using the tensor-tensor product (t- product) and tensor singular value decomposition (t-SVD) algebraic framework.

Recommended citation: Kyle Gilman and Laura Balzano. (2020). "Online Tensor Completion and Free Submodule Tracking with the t-SVD." 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). https://ieeexplore.ieee.org/document/9053199

Panoramic Video Separation with Online Grassmannian Robust Subspace Estimation

Published in 2019 Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) - Workshop, 2019

In this work, we propose a new total variation (TV)-regularized robust principal component analysis (RPCA) algorithm for panoramic video data with incremental gradient descent on the Grassmannian.

Recommended citation: Kyle Gilman and Laura Balzano. (2019). "Panoramic Video Separation with Online Grassmannian Robust Subspace Estimation." Proceedings of the IEEE/CVF International Conference on Computer Vision (ICCV) . https://ieeexplore.ieee.org/document/9022344