Finite-Sample Analysis of Nonlinear Independent Component Analysis:Sample Complexity and Identifiability Bounds

• URL: http://arxiv.org/abs/2604.08850v1
• Date: Fri, 10 Apr 2026 01:15:27 GMT
• Title: Finite-Sample Analysis of Nonlinear Independent Component Analysis:Sample Complexity and Identifiability Bounds
• Abstract summary: Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering structure in data by separating mixed signals into their independent sources.<n>The finite-sample statistical properties of learning algorithms remain poorly understood.<n>This paper presents a comprehensive finite-sample analysis of nonlinear ICA with neural network encoders.
• Score: 1.624454100511275
• License: http://arxiv.org/licenses/nonexclusive-distrib/1.0/
• Abstract: Independent Component Analysis (ICA) is a fundamental unsupervised learning technique foruncovering latent structure in data by separating mixed signals into their independent sources. While substantial progress has been made in establishing asymptotic identifiability guarantees for nonlinear ICA, the finite-sample statistical properties of learning algorithms remain poorly understood. This gap poses significant challenges for practitioners who must determine appropriate sample sizes for reliable source recovery. This paper presents a comprehensive finite-sample analysis of nonlinear ICA with neural network encoders, providing the first complete characterization with matching upper and lower bounds. Our theoretical development introduces three key technical contributions. First, we establish a direct relationship between excess risk and identification error that bypasses parameter-space arguments, thereby avoiding the rate degradation that would otherwise yield suboptimal scaling. Second, we prove matching information-theoretic lower bounds that confirm the optimality of our sample complexity results. Third, we extend our analysis to practical SGD optimization, showing that the same sample efficiency can be achieved with finite-iteration gradient descent under standard landscape assumptions. We validate our theoretical predictions through carefully designed simulation experiments. This gap points toward valuable future research on finite-sample behavior of neural network training and highlights the importance of our validated scaling laws for dimension and diversity.

Related papers

• A Measure-Theoretic Finite-Sample Theory for Adaptive-Data Fitted Q-Iteration [14.808143352500531]
  We develop a framework for fitted Q-iteration (FQI) on general measurable Borel spaces.<n>We prove that sequential Rademacher complexity controls Bellman-regression generalization under policy-dependent data collection.<n>These results lay the necessary foundations for the formal analysis of many modern deep RL algorithms.
  arXiv  Detail & Related papers  (2026-05-07T07:26:58Z)
• Nonconvex Penalized LAD Estimation in Partial Linear Models with DNNs: Asymptotic Analysis and Proximal Algorithms [3.8450418136547224]
  This paper investigates the linear partial model by Least Absolute Deviation (LAD)<n>We formulate the non subgradient parameter using Deep Neural Networks (NNs) and a penalized LAD model.
  arXiv  Detail & Related papers  (2025-11-26T07:01:35Z)
• Improved Sample Complexity For Diffusion Model Training Without Empirical Risk Minimizer Access [47.96419637803502]
  We present a principled theoretical framework analyzing diffusion models, providing a state-of-the-art sample complexity bound to $widetildemathcalO(epsilon-4)$.<n>Our structured decomposition of the score estimation error into statistical and optimization components offers critical insights into how diffusion models can be trained efficiently.
  arXiv  Detail & Related papers  (2025-05-23T20:02:15Z)
• Beyond Discreteness: Finite-Sample Analysis of Straight-Through Estimator for Quantization [2.8948274245812327]
  This work presents the first finite-sample analysis of the straight-through estimator (STE) in the context of neural network quantization.<n>Specifically, by analyzing the quantization-aware training of a two-layer neural network with binary weights and activations, we derive the sample complexity bound in terms of the data dimensionality.<n>In the presence of label noises, we uncover an intriguing recurrence property of STE-gradient method, where the iterate repeatedly escape from and return to the optimal binary weights.
  arXiv  Detail & Related papers  (2025-05-23T17:11:22Z)
• Provably Neural Active Learning Succeeds via Prioritizing Perplexing Samples [53.95282502030541]
  Neural Network-based active learning (NAL) is a cost-effective data selection technique that utilizes neural networks to select and train on a small subset of samples. We try to move one step forward by offering a unified explanation for the success of both query criteria-based NAL from a feature learning view.
  arXiv  Detail & Related papers  (2024-06-06T10:38:01Z)
• Neural Network Approximation for Pessimistic Offline Reinforcement Learning [17.756108291816908]
  We present a non-asymptotic estimation error of pessimistic offline RL using general neural network approximation. Our result shows that the estimation error consists of two parts: the first converges to zero at a desired rate on the sample size with partially controllable concentrability, and the second becomes negligible if the residual constraint is tight.
  arXiv  Detail & Related papers  (2023-12-19T05:17:27Z)
• Understanding Augmentation-based Self-Supervised Representation Learning via RKHS Approximation and Regression [53.15502562048627]
  Recent work has built the connection between self-supervised learning and the approximation of the top eigenspace of a graph Laplacian operator. This work delves into a statistical analysis of augmentation-based pretraining.
  arXiv  Detail & Related papers  (2023-06-01T15:18:55Z)
• Joint Edge-Model Sparse Learning is Provably Efficient for Graph Neural Networks [89.28881869440433]
  This paper provides the first theoretical characterization of joint edge-model sparse learning for graph neural networks (GNNs) It proves analytically that both sampling important nodes and pruning neurons with the lowest-magnitude can reduce the sample complexity and improve convergence without compromising the test accuracy.
  arXiv  Detail & Related papers  (2023-02-06T16:54:20Z)
• Stability and Generalization Analysis of Gradient Methods for Shallow Neural Networks [59.142826407441106]
  We study the generalization behavior of shallow neural networks (SNNs) by leveraging the concept of algorithmic stability. We consider gradient descent (GD) and gradient descent (SGD) to train SNNs, for both of which we develop consistent excess bounds.
  arXiv  Detail & Related papers  (2022-09-19T18:48:00Z)
• Pessimistic Q-Learning for Offline Reinforcement Learning: Towards Optimal Sample Complexity [51.476337785345436]
  We study a pessimistic variant of Q-learning in the context of finite-horizon Markov decision processes. A variance-reduced pessimistic Q-learning algorithm is proposed to achieve near-optimal sample complexity.
  arXiv  Detail & Related papers  (2022-02-28T15:39:36Z)
• The Interplay Between Implicit Bias and Benign Overfitting in Two-Layer Linear Networks [51.1848572349154]
  neural network models that perfectly fit noisy data can generalize well to unseen test data. We consider interpolating two-layer linear neural networks trained with gradient flow on the squared loss and derive bounds on the excess risk.
  arXiv  Detail & Related papers  (2021-08-25T22:01:01Z)
• Identifiability-Guaranteed Simplex-Structured Post-Nonlinear Mixture Learning via Autoencoder [9.769870656657522]
  This work focuses on the problem of unraveling nonlinearly mixed latent components in an unsupervised manner. The latent components are assumed to reside in the probability simplex, and are transformed by an unknown post-nonlinear mixing system. This problem finds various applications in signal and data analytics, e.g., nonlinear hyperspectral unmixing, image embedding, and nonlinear clustering.
  arXiv  Detail & Related papers  (2021-06-16T18:20:58Z)
• Stochastic Approximation for Online Tensorial Independent Component Analysis [98.34292831923335]
  Independent component analysis (ICA) has been a popular dimension reduction tool in statistical machine learning and signal processing. In this paper, we present a by-product online tensorial algorithm that estimates for each independent component.
  arXiv  Detail & Related papers  (2020-12-28T18:52:37Z)

This list is automatically generated from the titles and abstracts of the papers in this site.

This site does not guarantee the quality of this site (including all information) and is not responsible for any consequences.