More Like this

1. DP-PCA: Statistically Optimal and Differentially Private PCA

   Xiyang Liu, Weihao Kong (January 2022, arXivorg)
2. Streaming PCA for Markovian Data

   Syamantak Kumar, Purnamrita Sarkar (June 2023, arXivorg)
3. Streaming PCA for Markovian Data

   Kumar, Syamantak; Sarkar, Purnamrita (January 2024, NeurIPS)
4. Robust PCA by Manifold Optimization

   Zhang, Teng; Yang, Yi (November 2018, Journal of machine learning research)

   Robust PCA is a widely used statistical procedure to recover an underlying low-rank matrix with grossly corrupted observations. This work considers the problem of robust PCA as a nonconvex optimization problem on the manifold of low-rank matrices and proposes two algorithms based on manifold optimization. It is shown that, with a properly designed initialization, the proposed algorithms are guaranteed to converge to the underlying lowrank matrix linearly. Compared with a previous work based on the factorization of low-rank matrices Yi et al. (2016), the proposed algorithms reduce the dependence on the condition number of the underlying low-rank matrix theoretically. Simulations and real data examples con rm the competitive performance of our method. 

   more » « less
5. PROBABILISTIC PCA FOR HETEROSCEDASTIC DATA

   Hong, David; Balzano, Laura; Fessler, Jeffrey (January 2019, IEEE International Workshop on Computational Advances in Multi-Sensor Adaptive Processing (CAMSAP) 2019)

   Principal Component Analysis (PCA) is a standard dimensionality reduction technique, but it treats all samples uniformly, making it suboptimal for heterogeneous data that are increasingly common in modern settings. This paper proposes a PCA variant for samples with heterogeneous noise levels, i.e., heteroscedastic noise, that naturally arise when some of the data come from higher quality sources than others. The technique handles heteroscedasticity by incorporating it in the statistical model of a probabilistic PCA. The resulting optimization problem is an interesting nonconvex problem related to but not seemingly solved by singular value decomposition, and this paper derives an expectation maximization (EM) algorithm. Numerical experiments illustrate the benefits of using the proposed method to combine samples with heteroscedastic noise in a single analysis, as well as benefits of careful initialization for the EM algorithm. 

   more » « less