CW-ICA improves on ANICA for non-linear source separation.
problem Non-linear source separation challenges with many applications.
method CW-ICA extends ANICA by using a simpler, closed-form optimization target.
result CW-ICA achieves comparable results to ANICA without adversarial training.
New model separates images into independent factors quickly and easily.
problem Separating high-dimensional data like images into independent latent factors.
method Combines bijective feature maps with linear ICA model on the Stiefel manifold.
result Models converge quickly and achieve better unsupervised latent factor discovery.
Nonlinear independent component analysis (ICA) provides an appealing framework for unsupervised feature learning, but the models proposed so far are not identifiable. Here, we first propose a new intuitive principle of unsupervised deep learning from time series which uses the nonstationary structure of the data. Our l…
Independent Component Analysis (ICA) is a popular model for blind signal separation. The ICA model assumes that a number of independent source signals are linearly mixed to form the observed signals. We propose a new algorithm, PEGI (for pseudo-Euclidean Gradient Iteration), for provable model recovery for ICA with Gau…
New model combines ICA and HMM for unsupervised learning of nonstationary time series.
problem Manual segmentation of non-stationary data is computationally expensive and inaccurate.
method Combines Hidden Markov Model with nonlinear ICA for unsupervised learning.
result Proves identifiability of the model for general mixing nonlinearity.
New ICA algorithm improves source PDF estimation for better performance.
problem Inaccurate estimation of source PDFs leads to poor ICA performance.
method Entropy maximization with kernels, using global and local constraints.
result ICA-EMK outperforms competing algorithms in simulations and real-world data.
Paper proposes compressive ICA algorithms for ICA model.
problem Efficiently solving ICA model with reduced memory and computational complexity.
method Compressive learning approach to ICA model, proving existence of compressive ICA scheme, proposing two algorithms (IPG and ASD).
result Proposed algorithms achieve substantial memory gains over well-known ICA algorithms.
Robust methods for nonlinear ICA improve performance in outlier presence.
problem Outliers degrade performance of nonlinear ICA methods.
method Developed robust nonlinear ICA methods based on γ-divergence.
result Robust methods outperform existing methods in outlier presence.
Faster ICA for real data using Hessian approximations.
problem Efficiently solving ICA on large real datasets.
method Preconditioned ICA with sparse Hessian approximations.
result Superior performance on real data compared to other algorithms.
New ICA method exploits sparsity for better brain imaging analysis.
problem ICA's independence assumption is too strict for real-world data.
method Entropy bound minimization with sparsity exploitation.
result Improved ICA performance through direct incorporation of sparsity.
A new framework for nonlinear ICA using auxiliary variables and contrastive learning.
problem Recovering underlying latent variables from data.
method Augmenting data with auxiliary variables and using contrastive learning for identification.
result General theoretical framework and practical algorithm for nonlinear ICA.
AVICA estimates noise levels for better group ICA source recovery.
problem Estimating shared independent sources from multiple noisy views.
method AVICA models each view as a linear mixture of shared sources with additive noise, optimizing noise levels alongside sources.
result AVICA yields better source estimates than other methods, especially in real-world applications like MEG and fMRI.
WICA improves ICA results with a new method.
problem Finding independent components in nonlinear data.
method New nonlinear ICA model (WICA) with efficient correlation coefficient verification.
result WICA yields better and more stable results than other algorithms.
FPGA speeds up ICA by orders of magnitude.
problem Slow convergence of adaptive ICA algorithms.
method Equivariant adaptive separation via independence algorithm.
result FPGA implementation improves clock frequency and throughput.
Causal Mosaic distinguishes cause from effect using nonlinear ICA and ensemble methods.
problem Distinguishing cause from effect in bivariate settings.
method Nonlinear ICA and ensemble framework (Causal Mosaic).
result Causal Mosaic shows state-of-the-art performance on artificial and real-world datasets.
Develops flexible ICA and IVA algorithms for medical image analysis.
problem Improper estimation of PDF leads to deviation from theoretical optimality.
method Flexible ICA and IVA algorithms using effective PDF estimation and sparsity.
result Unified mathematical framework for statistical independence and sparsity.
Generalizes PCA and ICA for continuous-time signals using neural networks.
problem Low-rank decomposition of continuous-time vector-valued signals.
method Implicit neural network framework to learn numerical approximations of PCA and ICA.
result Unified approach to PCA and ICA in continuous domain, enforcing decorrelation and independence.
Picard-O improves ICA for faster, robust separation of signals.
problem Efficiently separating signals in multi-channel data.
method Preconditioned L-BFGS over orthogonal matrices.
result Picard-O outperforms FastICA in speed and robustness.
This paper reviews nonlinear ICA for disentangled representations in unsupervised learning.
problem Finding useful disentangled representations in unsupervised deep learning.
method Review of nonlinear ICA theory and algorithms for disentanglement.
result Nonlinear ICA can be shown to estimate useful disentangled representations.
Empirical comparison of PCA and ICA on noisy time series.
problem Comparing PCA and ICA performance on noisy data.
method Applied PCA and ICA to two simulated noisy time series with varying distribution parameters and noise levels.
result ICA outperforms PCA due to considering higher moments of data distribution.
New framework for identifying spatial data components using TP latent components.
problem Identifying complex dependencies in spatial data.
method Introduces a new nonlinear ICA framework with t t t -process latent components and develops a learning and inference algorithm. result Identifiability of TP independent components under general conditions and Gaussian Process limit.
A new ICA method adds L1-regularization for better interpretability of fMRI data.
problem Improving interpretability of ICA features in high-dimensional fMRI data.
method L1-regularization added to ICA cost function, solved by DCA.
result Validated on synthetic and real fMRI data, improving feature interpretability.
New ICA method for sources with mixed spectra.
problem Inaccurate separation of sources with temporal autocorrelations and mixed spectra.
method Estimates spectral density functions and line spectra using cubic splines and indicator functions, then maximizes the Whittle likelihood function.
result Outperforms existing ICA methods in simulations and EEG data applications.
OT-ICA uses optimal transport to find independent components, outperforming traditional methods.
problem Finding independent components from linear mixtures of signals.
method OT-ICA uses the squared Wasserstein distance to maximize non-Gaussianity, optimizing projections via gradient descent.
result OT-ICA outperforms traditional proxy-based methods in various applications.
New ICA method uses third-order moment for better performance.
problem ICA methods often assume kurtosis, which may not always fit data.
method ICA based on Split Generalized Gaussian distribution (SGGD).
result Method works better for heavy-tailed and non-symmetric data.
New model improves transfer learning and semi-supervised learning.
problem Improving transfer learning and semi-supervised learning performance.
method Developed a new conditional energy-based model (ICE-BeeM) based on nonlinear ICA.
result Identifiable representations learned by ICE-BeeM improve performance in transfer learning and semi-supervised learning tasks.
Improves ICA via novel mutual dependence measures.
problem Improving Independent Component Analysis (ICA) for better component independence.
method Combines distance-based and kernel-based mutual dependence measures, introduces Latin hypercube sampling and Bayesian optimization for initialization.
result MDMICA outperforms other methods in terms of mutual independence of estimated components, especially when the ICA model is misspecified.
New method identifies latent sources from nonlinear mixtures without auxiliary variables.
problem Identifying latent sources from nonlinear mixtures without additional information.
method Structural Sparsity assumptions on the mixing process.
result Latent sources can be identified up to permutation and transformation.
ICA accurately estimates treatment effects even with confounders.
problem Estimating treatment effects in the presence of confounding variables.
method Uses Independent Component Analysis (ICA) to identify latent sources and estimate mixing coefficients.
result Linear ICA can consistently estimate multiple treatment effects, even with Gaussian confounders, and is more sample-efficient than Orthogonal Machine Learning (OML).
New ICA method improves on existing techniques.
problem Finding independent components in data.
method Multiple-weighted Independent Component Analysis (MWeICA) based on approximate diagonalization of weighted covariance matrices.
result MWeICA achieves better results than state-of-the-art ICA methods with similar computational time.
A new ICA algorithm robustifies independent component analysis by accounting for group-wise stationary noise.
problem Tackles the challenge of independent component analysis in the presence of group-wise stationary confounding noise.
method Introduces coroICA, a novel ICA algorithm that extends the ordinary ICA model to incorporate group-wise confounding.
result Demonstrates improved performance and robustness of ICA in settings where other methods fail.
Independent component analysis (ICA) has become a standard data analysis technique applied to an array of problems in signal processing and machine learning. This tutorial provides an introduction to ICA based on linear algebra formulating an intuition for ICA from first principles. The goal of this tutorial is to prov…
LNGCA extends ICA to non-Gaussian signals and noise, improving estimation and testing.
problem Modeling multivariate data with non-Gaussian components and Gaussian noise.
method Linear latent factor model, simultaneous estimation of non-Gaussian and Gaussian components, discrepancy maximization, resampling-based test.
result Improved estimation and testing of non-Gaussian components over competing methods.
New models learn stable latent clusters without side info.
problem Stability of non-linear ICA representations without side information.
method Deep generative models with latent clusterings, compared to standard VAEs and auxiliary labeled models.
result Deep generative models with latent clusterings are as stable as models with side information.
SKR-VAE improves VAEs for ICA with reduced computational cost.
problem Efficiently performing ICA in VAEs with large datasets.
method Structured kernel functions to avoid costly GP kernel matrix inversion.
result SKR-VAE achieves greater computational efficiency and reduced resource consumption.
Half-AVAE enhances VAE for underdetermined ICA with adversarial training.
problem Challenges in ICA under underdetermined conditions.
method Encoder-free VAE with adversarial networks and EE terms.
result Half-AVAE outperforms baseline models in underdetermined ICA.
A new ICA model identifies shared brain activity patterns across subjects.
problem Challenges in modeling shared responses in neuroimaging studies with large cohorts.
method MultiView Independent Component Analysis (ICA) model with closed-form likelihood and alternate quasi-Newton method.
result Improved sensitivity in identifying common brain activity patterns.
New algorithms improve ICA performance without manual tuning.
problem Improving Independent Component Analysis (ICA) performance.
method Developed majorization-minimization framework for non-convex loss function.
result Stochastic algorithms guarantee loss function decrease at each iteration.
A new method improves ICA performance by approximating MDI.
problem Improving F astICA's performance with nonlinear functions.
method Second-order approximation of MDI for joint maximization.
result Efficiency validated through experiments compared to other ICA algorithms.
New algorithm HTICA solves heavy-tailed ICA problems efficiently.
problem Heavy-tailed data in ICA problems.
method Uses centroid body and explicit analytic representations to bypass ellipsoid method and random walks.
result Outperforms other algorithms in heavy-tailed regimes on real and synthetic data.
New methods generalize nonlinear ICA beyond structural sparsity.
problem Identify true latent sources from nonlinear mixtures without structural sparsity assumptions.
method Propose identifiability results for undercomplete, partial sparsity, and flexible grouping structures.
result Prove identifiability in general settings of undercompleteness, partial sparsity, and flexible grouping structures.
Adversarial nets learn independent features from joint distributions.
problem Learning independent features from complex joint distributions.
method Adversarial objectives to optimize mutual information implicitly.
result Adversarial nets can solve both linear and non-linear ICA problems.
Paper analyzes online tensorial ICA convergence with stochastic approximation.
problem Online tensorial ICA convergence analysis.
method Stochastic approximation for nonconvex optimization.
result Sharp finite-sample error bound of O ~ ( d / T ) \tilde{O}(\sqrt{d/T}) O ~ ( d / T ) . New framework extends ICA for non-independent variables, identifying pairwise mean independence.
problem Non-independent variables complicating ICA recovery.
method Algebraic recovery algorithm based on least-squares optimization over the orthogonal group.
result Pairwise mean independence is identifiable, robust to independence constraints.
Paper investigates optimization methods for ICA on real signals, overcoming convergence issues.
problem Optimizing likelihood for ICA on real signals, especially with constrained white signals.
method Rewrites algorithms as quasi-Newton methods, focusing on Hessian approximation.
result Preconditioned ICA for Real Data (Picard) algorithm improves convergence on real signals.
Study uses Wasserstein distance to identify causal orders and unmix sources.
problem Identifying causal relationships and separating sources in non-Gaussian data.
method Wasserstein distance for non-Gaussianity, linear ICA, causal inference.
result Exact identification of ICA unmixing matrix and causal orders.
New theory allows ICA without assuming non-Gaussian sources.
problem Traditional ICA struggles with Gaussian sources.
method Developed identifiability theory based on second-order statistics and sparsity.
result Identifiability theory and estimation methods validated experimentally.
This paper is an attempt to separate cardiac and respiratory signals from an electrical bio-impedance (EBI) dataset. For this two well-known algorithms, namely Principal Component Analysis (PCA) and Independent Component Analysis (ICA), were used to accomplish the task. The ability of the PCA and the ICA methods first …