# Large Dimensional Independent Component Analysis: Statistical Optimality and Computational Tractability

arXiv: https://arxiv.org/abs/2303.18156 · HTML: https://mlsanity.com/paper/2303.18156/

## Key facts

- Cited by 12 papers in the map (data through 14 Oct 2026).
- Builds on 2 of its 69 references that are in the map.
- First posted on arXiv 31 Mar 2023.

## Builds on (most cited first, 2 of 2)

- [Optimal Spectral Recovery of a Planted Vector in a Subspace](https://mlsanity.com/paper/2105.15081/) (2021)
- [Sample Complexity Analysis for Learning Overcomplete Latent Variable Models through Tensor Methods](https://mlsanity.com/paper/1408.0553/) (2014)

## Built on by (most cited first, 12 of 12)

- [Feature learning from non-Gaussian inputs: the case of Independent Component Analysis in high dimensions](https://mlsanity.com/paper/2503.23896/) (2025)
- [Computational Lower Bounds for Graphon Estimation via Low-degree Polynomials](https://mlsanity.com/paper/2308.15728/) (2023)
- [Causal Discovery of Linear Non-Gaussian Causal Models with Unobserved Confounding](https://mlsanity.com/paper/2408.04907/) (2024)
- [Identifying General Mechanism Shifts in Linear Causal Representations](https://mlsanity.com/paper/2410.24059/) (2024)
- [Tensor Methods in High Dimensional Data Analysis: Opportunities and Challenges](https://mlsanity.com/paper/2405.18412/) (2024)
- [Beyond identifiability: Learning causal representations with few environments and finite samples](https://mlsanity.com/paper/2603.25796/) (2026)
- [Federated Independent Component Analysis via Spectral Alignment and Robust Aggregation](https://mlsanity.com/paper/2505.20532/) (2025)
- [Estimating Treatment Effects with Independent Component Analysis](https://mlsanity.com/paper/2507.16467/) (2025)
- [Learning Rate Should Scale Inversely with High-Order Data Moments in High-Dimensional Online Independent Component Analysis](https://mlsanity.com/paper/2509.15127/) (2025)
- [On Spectral Learning for Odeco Tensors: Perturbation, Initialization, and Algorithms](https://mlsanity.com/paper/2509.25126/) (2025)
- [A 1/R Law for Kurtosis Contrast in Balanced Mixtures](https://mlsanity.com/paper/2602.22334/) (2026)
- [How Many Samples Are Needed to Determine Causal Direction? Sharp Minimax Bounds for Bivariate LiNGAM](https://mlsanity.com/paper/2608.15840/) (2026)

## Abstract (arXiv)

In this paper, we investigate the optimal statistical performance and the impact of computational constraints for independent component analysis (ICA). Our goal is twofold. On the one hand, we characterize the precise role of dimensionality on sample complexity and statistical accuracy, and how computational consideration may affect them. In particular, we show that the optimal sample complexity is linear in dimensionality, and interestingly, the commonly used sample kurtosis-based approaches are necessarily suboptimal. However, the optimal sample complexity becomes quadratic, up to a logarithmic factor, in the dimension if we restrict ourselves to estimates that can be computed with low-degree polynomial algorithms. On the other hand, we develop computationally tractable estimates that attain both the optimal sample complexity and minimax optimal rates of convergence. We study the asymptotic properties of the proposed estimates and establish their asymptotic normality that can be readily used for statistical inferences. Our method is fairly easy to implement and numerical experiments are presented to further demonstrate its practical merits.