Research map / Learning theory and algorithms / Sample complexity
Fixed-Parameter and Approximation Algorithms for PCA with Outliers
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Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| Restrict the solution subspace dimension r to a constant and use a randomized (1+ε)-approximation via sampling rows by ridge leverage scores | PCA with Outliers · general PCA with Outliers (theoretical) | running time n^{O(r log r / ε^2)} · d^{O(1)} | Helped |
| Sketch the input with a random Gaussian subspace embedding before running the subspace-sampling algorithm (dimensionality reduction from d to t) | alpha-gap PCA with Outliers · alpha-gap instances (theoretical) | running time exponent in d | Helped |
| Sketch the input with a random Gaussian subspace embedding before running the subspace-sampling algorithm | alpha-heavy PCA with Outliers · alpha-heavy instances (theoretical) | running time exponent in d | Helped |
| Bucket points into O(k) buckets via perfect hashing and use only poly(k log n) polynomials instead of C(n,2) pairwise polynomials | subspace-sampling algorithm for alpha-gap/alpha-heavy PCA with Outliers · alpha-gap and alpha-heavy instances (theoretical) | number of sign-condition polynomials and running time exponent | Helped |
| Use the Simonov et al. approach as a baseline (n^{O(rd)} time) versus the new alpha-assumption algorithms | PCA with Outliers · general PCA with Outliers (theoretical) | running time | No clear effect |
Closest papers by meaning
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- A Geometric Analysis of PCA (NeurIPS 2025 · similarity 0.85)
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