# Sparsistency and agnostic inference in sparse PCA

arXiv: https://arxiv.org/abs/1401.6978 · HTML: https://mlsanity.com/paper/1401.6978/

## Key facts

- Cited by 8 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 27 Jan 2014.

## Built on by (most cited first, 8 of 8)

- [Oja's Algorithm for Streaming Sparse PCA](https://mlsanity.com/paper/2402.07240/) (2024)
- [Support Recovery in Sparse PCA with Incomplete Data](https://mlsanity.com/paper/2205.15215/) (2022)
- [k-Graph: A Graph Embedding for Interpretable Time Series Clustering](https://mlsanity.com/paper/2502.13049/) (2025)
- [Entrywise Recovery Guarantees for Sparse PCA via Sparsistent Algorithms](https://mlsanity.com/paper/2202.04061/) (2022)
- [Meta Sparse Principal Component Analysis](https://mlsanity.com/paper/2208.08938/) (2022)
- [Theoretical Guarantees for Sparse Principal Component Analysis based on the Elastic Net](https://mlsanity.com/paper/2212.14194/) (2022)
- [Support Recovery in Sparse PCA with Non-Random Missing Data](https://mlsanity.com/paper/2302.01535/) (2023)
- [Sparse PCA with Oracle Property](https://mlsanity.com/paper/2312.16793/) (2023)

## Abstract (arXiv)

The presence of a sparse "truth" has been a constant assumption in the theoretical analysis of sparse PCA and is often implicit in its methodological development. This naturally raises questions about the properties of sparse PCA methods and how they depend on the assumption of sparsity. Under what conditions can the relevant variables be selected consistently if the truth is assumed to be sparse? What can be said about the results of sparse PCA without assuming a sparse and unique truth? We answer these questions by investigating the properties of the recently proposed Fantope projection and selection (FPS) method in the high-dimensional setting. Our results provide general sufficient conditions for sparsistency of the FPS estimator. These conditions are weak and can hold in situations where other estimators are known to fail. On the other hand, without assuming sparsity or identifiability, we show that FPS provides a sparse, linear dimension-reducing transformation that is close to the best possible in terms of maximizing the predictive covariance.