Research map / Learning theory and algorithms / Sample complexity
Nonparametric Evaluation of Noisy ICA Solutions
Read the paperCheck your idea against 108,967 papers
AI-extracted summary. Written by AI from the paper's full text. Numbers and claims can be wrong or missing context, so check the paper before you cite or build on it.
Proposes a nonparametric characteristic-function independence score to select among ICA algorithms (Meta algorithm) for noisy ICA with arbitrary Gaussian noise, plus new CHF- and CGF-based contrast functions with convergence guarantees.
Problem
Choosing which ICA / noisy ICA algorithm to trust for a given dataset, since existing methods fail in different regimes (heavy tails, zero kurtosis, unknown Gaussian noise covariance).
Approach
A corrected characteristic-function independence score, using the sample covariance to cancel Gaussian-noise terms, evaluates the quality of any candidate demixing matrix without knowing the noise distribution; a Meta algorithm picks the candidate with the lowest score. New CHF- and CGF-based contrast functions use only a finite second moment and are optimized with a pseudo-Euclidean power iterati
Key results
- On Bernoulli(p) sources with varying kurtosis, the Meta algorithm matched or beat the best candidate in Table 1 (e.g., Amari error about 0.007-0.011 across p where PFICA and CHF fail at small p).
Measured effects reported in the paper
| What was changed | Where | Measured | Effect |
|---|---|---|---|
| use the corrected independence score to select among candidate algorithms | Meta · Bernoulli(p), scaled κ4 = 0 | Amari error: 0.029 -> 0.023 | Helped |
| remove the Gaussian-noise correction from the independence score (ablation) | Meta · Bernoulli(p), scaled κ4 = 0 | Amari error: 0.023 -> 0.0419 | Hurt |
Surprising findings
- The uncorrected independence score (CHFICA) shadows PFICA and performs worse than the corrected Meta algorithm for noisy data.
Limitations
- Theorem 3's third-derivative sign condition is strong and not satisfied by all distributions.
- Subgaussianity assumption used in the uniform convergence result; relaxation needs operator-norm concentration.
- Score is not directly optimizable, so it is used only to select among candidate algorithms rather than as an objective.
Experimental setup
Datasets: synthetic Bernoulli, uniform, exponential sources with Wishart noise image demixing dataset [16] MNIST images
Benchmarks: synthetic noisy ICA simulations image demixing
Metrics: Amari error independence score
Baselines: FastICA JADE PFICA PEGI-κ4 CGF contrast Uncorrected Meta
Builds on: PFICA (CHFICA) PEGI FastICA JADE
Closest papers by meaning
- On the Identifiability of Sparse ICA without Assuming Non-Gaussianity (NeurIPS 2023 · similarity 0.86)
- On the Identifiability of Nonlinear ICA: Sparsity and Beyond (NeurIPS 2022 · similarity 0.86)
- Heavy-Tailed Analogues of the Covariance Matrix for ICA (AAAI 2017 · similarity 0.85)
- Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions (ICML 2025 · similarity 0.82)
- An Iterative Algorithm for Differentially Private $k$-PCA with Adaptive Noise (NeurIPS 2025 · similarity 0.80)
- Diverse Influence Component Analysis: A Geometric Approach to Nonlinear Mixture Identifiability (NeurIPS 2025 · similarity 0.80)
Writing a paper in this area? scime draft is a free LaTeX editor with AI included, real-time co-authors and a check of your references and venue rules before you submit. It also imports OpenAI Prism projects.