Sparse principal component analysis via axis-aligned random projections
| Autor: | Milana Gataric, Tengyao Wang, Richard J. Samworth |
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| Přispěvatelé: | Gataric, Milana [0000-0003-3915-2266], Samworth, Richard [0000-0003-2426-4679], Apollo - University of Cambridge Repository |
| Rok vydání: | 2021 |
| Předmět: |
Statistics and Probability
FOS: Computer and information sciences Sketching Initialization Mathematics - Statistics Theory Sample (statistics) Machine Learning (stat.ML) 02 engineering and technology Statistics Theory (math.ST) 01 natural sciences Methodology (stat.ME) 010104 statistics & probability Statistics - Machine Learning Ensemble learning 0202 electrical engineering electronic engineering information engineering FOS: Mathematics 62H25 0101 mathematics Statistics - Methodology Eigenvalues and eigenvectors Statistical and computational trade-offs Mathematics Dimensionality reduction Estimator 020206 networking & telecommunications Minimax Rate of convergence Eigenspace estimation Principal component analysis Statistics Probability and Uncertainty Algorithm |
| DOI: | 10.17863/cam.20831 |
| Popis: | We introduce a new method for sparse principal component analysis, based on the aggregation of eigenvector information from carefully-selected axis-aligned random projections of the sample covariance matrix. Unlike most alternative approaches, our algorithm is non-iterative, so is not vulnerable to a bad choice of initialisation. We provide theoretical guarantees under which our principal subspace estimator can attain the minimax optimal rate of convergence in polynomial time. In addition, our theory provides a more refined understanding of the statistical and computational trade-off in the problem of sparse principal component estimation, revealing a subtle interplay between the effective sample size and the number of random projections that are required to achieve the minimax optimal rate. Numerical studies provide further insight into the procedure and confirm its highly competitive finite-sample performance. Comment: 32 pages |
| Databáze: | OpenAIRE |
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