# Meta Sparse Principal Component Analysis

arXiv: https://arxiv.org/abs/2208.08938 · HTML: https://mlsanity.com/paper/2208.08938/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 7 of its 30 references that are in the map.
- First posted on arXiv 18 Aug 2022.

## Builds on (most cited first, 7 of 7)

- [Convex optimization](https://mlsanity.com/paper/2106.01946/) (2021)
- [An Introduction to Matrix Concentration Inequalities](https://mlsanity.com/paper/1501.01571/) (2015)
- [An improper estimator with optimal excess risk in misspecified density estimation and logistic regression](https://mlsanity.com/paper/1912.10784/) (2019)
- [Sparsistency and agnostic inference in sparse PCA](https://mlsanity.com/paper/1401.6978/) (2014)
- [Meta Learning for Support Recovery in High-dimensional Precision Matrix Estimation](https://mlsanity.com/paper/2006.12598/) (2020)
- [Image Classification base on PCA of Multi-view Deep Representation](https://mlsanity.com/paper/1903.04814/) (2019)
- [The Sample Complexity of Meta Sparse Regression](https://mlsanity.com/paper/2002.09587/) (2020)

## Abstract (arXiv)

We study the meta-learning for support (i.e. the set of non-zero entries) recovery in high-dimensional Principal Component Analysis. We reduce the sufficient sample complexity in a novel task with the information that is learned from auxiliary tasks. We assume each task to be a different random Principal Component (PC) matrix with a possibly different support and that the support union of the PC matrices is small. We then pool the data from all the tasks to execute an improper estimation of a single PC matrix by maximising the l1-regularised predictive covariance to establish that with high probability the true support union can be recovered provided a sufficient number of tasks m and a sufficient number of samples  Oleft(fraclog(p)mright) for each task, for p-dimensional vectors. Then, for a novel task, we prove that the maximisation of the l1-regularised predictive covariance with the additional constraint that the support is a subset of the estimated support union could reduce the sufficient sample complexity of successful support recovery to O(log |J|), where J is the support union recovered from the auxiliary tasks. Typically, |J| would be much less than p for sparse matrices. Finally, we demonstrate the validity of our experiments through numerical simulations.