DDICA separates nonlinear mixed signals robustly.
problem Blind source separation of nonlinear mixed signals.
method Deep deterministic neural network with matrix-based entropy function.
result DDICA effectively separates independent components with high accuracy.
New method for separating mixed signals with nonlinear functions.
problem Recovering source signals from nonlinear mixtures.
method Optimisation-based function approximation to minimize mutual statistical dependence.
result The method can recover source signals from nonlinear mixtures under certain conditions.
New approach tackles nonidentifiability in nonlinear blind source separation.
problem Nonidentifiability in nonlinear blind source separation.
method Independent mechanism analysis, incorporating causal assumptions.
result Empirical and theoretical evidence shows improved identifiability.
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.
IMA addresses non-identifiability in nonlinear ICA by assuming orthogonal Jacobian columns.
problem Non-identifiability in nonlinear ICA.
method IMA assumes orthogonal Jacobian columns and extends to manifold settings.
result IMA circumvents non-identifiability issues and can be beneficial for higher-dimensional observations.
This work closes the gap between theory and practice for nICA identifiability.
problem Identifying latent components in nonlinearly mixed data.
method Finite-sample analysis of GCL-based nICA, combining GCL properties, statistical generalization, and numerical differentiation.
result Establishes a trade-off between function learner complexity and expressiveness.
Independent Component Analysis (ICA) aims to find a coordinate system in which the components of the data are independent. In this paper we construct a new nonlinear ICA model, called WICA, which obtains better and more stable results than other algorithms. A crucial tool is given by a new efficient method of verifying…
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.
Study adapts β-TCVAE for fMRI to recover nonlinear brain components.
problem Capturing nonlinear brain dynamics in fMRI data.
method Adapted β-TCVAE framework for fMRI data. result Recovery of meaningful nonlinear spatial components in fMRI data.
New method identifies latent components in PNL mixtures without strong assumptions.
problem Identifying latent components in PNL mixtures under unknown nonlinear functions.
method Carefully designed UML criterion to identify a null space associated with the mixing system.
result Identification/removal of unknown nonlinearity under minimal conditions.
New framework IIA identifies innovations in general nonlinear vector autoregressive processes.
problem Limited generality of NVAR models due to additive innovation assumption.
method Independent Innovation Analysis (IIA) framework, assuming mutual independence and modulation by an auxiliary variable.
result Guarantees identifiability of innovations with arbitrary nonlinearities, up to permutation and component-wise invertible nonlinearities.
We consider the problem of recovering a common latent source with independent components from multiple views. This applies to settings in which a variable is measured with multiple experimental modalities, and where the goal is to synthesize the disparate measurements into a single unified representation. We consider t…
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 framework for disentangling features from noisy data.
problem Disentangling identifiable features from noisy data.
method Structured Nonlinear Independent Component Analysis (SNICA).
result Identifiability holds even in the presence of noise of unknown distribution.
New findings on identifying latent variables in nonlinear ICA models.
problem Identifying latent variables in nonlinear ICA models is challenging due to spurious solutions.
method Proved that conformal maps are identifiable and provided theoretical results on preventing spurious solutions.
result Conformal maps are identifiable in nonlinear ICA models, preventing spurious solutions.
Paper extends ICA to ISA with auxiliary variables for better speech representation learning.
problem Learning unsupervised speech representations with independent subspaces.
method Theoretical framework of nonlinear ISA with auxiliary variables.
result Proposes an algorithm to learn speech representations with independent subspaces.
We address the problem of distinguishing cause from effect in bivariate setting. Based on recent developments in nonlinear independent component analysis (ICA), we train nonparametrically general nonlinear causal models that allow non-additive noise. Further, we build an ensemble framework, namely Causal Mosaic, which …
This paper extends robust principal component analysis (RPCA) to nonlinear manifolds. Suppose that the observed data matrix is the sum of a sparse component and a component drawn from some low dimensional manifold. Is it possible to separate them by using similar ideas as RPCA? Is there any benefit in treating the mani…
Proposes σ-PCA to learn identifiable linear transformations without whitening.
problem Cannot identify axes with equal variances in PCA.
method Unified model for linear and nonlinear PCA, introducing a missing piece to eliminate rotational indeterminacy.
result Eliminates subspace rotational indeterminacy in PCA.
For many years, a combination of principal component analysis (PCA) and independent component analysis (ICA) has been used for blind source separation (BSS). However, it remains unclear why these linear methods work well with real-world data that involve nonlinear source mixtures. This work theoretically validates that…
Causal Component Analysis aims to recover latent variables with causal relationships.
problem Recover latent variables with causal relationships from observed mixtures.
method Introduces a likelihood-based approach using normalizing flows to estimate unmixing function and causal mechanisms.
result Demonstrates effectiveness through synthetic experiments in CauCA and ICA settings.
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.
Linear principal component analysis (PCA) can be extended to a nonlinear PCA by using artificial neural networks. But the benefit of curved components requires a careful control of the model complexity. Moreover, standard techniques for model selection, including cross-validation and more generally the use of an indepe…
Study on robustness of unsupervised representation learning in slightly misspecified settings.
problem Identify nonlinear representation learning in slightly misspecified settings.
method Formalize and investigate Independent Component Analysis (ICA) with observations generated by a mixing function close to a local isometry.
result Approximate identifiability of nonlinear ICA with almost isometric mixing functions.
The paper reviews identifiability in linear and nonlinear models, from Gaussian to non-Gaussian.
problem Identifiability issues in latent-variable and structural-equation models, especially in nonlinear cases.
method Review of identifiability theory for linear and nonlinear models, including factor analysis and structural equation models.
result Even nonparametric nonlinear models can be estimated with additional assumptions.
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).
Reservoir subspace injection improves online ICA by preserving injected features.
problem Discarding injected features in top-n whitening can degrade performance. method Formalized reservoir subspace injection (RSI) and developed diagnostics (IER, SSO, ρ_x) to identify and mitigate the failure mode.
result RSI controller preserves passthrough retention, improving performance by up to 2.2 dB.
We consider the identifiability theory of probabilistic models and establish sufficient conditions under which the representations learned by a very broad family of conditional energy-based models are unique in function space, up to a simple transformation. In our model family, the energy function is the dot-product be…
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.
This paper tackles sequential distribution shifts in representation learning.
problem Learning meaningful representations in a sequence of distribution shifts.
method Nonlinear Independent Component Analysis (ICA) framework for continual causal representation learning.
result The method achieves performance comparable to joint training on multiple offline distributions and shows no benefit from the incoming new distribution on all latent variables.
In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian d…
The paper discovers a hidden component in data using an autoencoder with a discriminator.
problem Discovering a single independent latent variable in data.
method An autoencoder with a discriminator is used to recover the hidden component.
result The approach can recover the hidden component up to entropy-preserving transformations.
Recently, an extension of independent component analysis (ICA) from one to multiple datasets, termed independent vector analysis (IVA), has been the subject of significant research interest. IVA has also been shown to be a generalization of Hotelling's canonical correlation analysis. In this paper, we provide the ident…
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) - one of the basic tools in data analysis - aims to find a coordinate system in which the components of the data are independent. In this paper we present Multiple-weighted Independent Component Analysis (MWeICA) algorithm, a new ICA method which is based on approximate diagonalizat…
Nonlinear independent component analysis (ICA) is a general framework for unsupervised representation learning, and aimed at recovering the latent variables in data. Recent practical methods perform nonlinear ICA by solving a series of classification problems based on logistic regression. However, it is well-known that…
Boosting improves ICA for better component recovery.
problem Improving ICA's reliance on prior knowledge of sources.
method Maximizing likelihood via boosting and fixed-point unmixing.
result Boosting-based ICA outperforms existing methods.
In this dissertation, the main goal is visualisation of financial time series. We expect that visualisation of financial time series will be a useful auxiliary for technical analysis. Firstly, we review the technical analysis methods and test our trading rules, which are built by the essential concepts of technical ana…
We analyze the dynamics of an online algorithm for independent component analysis in the high-dimensional scaling limit. As the ambient dimension tends to infinity, and with proper time scaling, we show that the time-varying joint empirical measure of the target feature vector and the estimates provided by the algorith…
Study nonparametric factor analysis with arbitrary noise.
problem Identify latent variables in noisy, non-invertible settings.
method Developed a general framework and estimation methods.
result Identify latent variables up to certain indeterminacies.
IMA improves representation learning even when assumptions are violated.
problem Recovering true latent codes from mixed data.
method IMA, which assumes independent causal mechanisms.
result IMA's benefits extend to violations of its assumptions.
Paper connects contrastive learning to MI maximization and establishes robust methods for nonlinear ICA and subspace estimation.
problem Understanding and improving unsupervised representation learning and density ratio estimation.
method The paper connects contrastive learning to MI maximization, establishes new recovery conditions for nonlinear ICA, and proposes a practical outlier-robust method for nonlinear subspace estimation.
result The proposed methods can be seen as maximizing MI, performing nonlinear ICA, or estimating nonlinear subspaces, and are robust to outliers.
Linear mixture models have proven very useful in a plethora of applications, e.g., topic modeling, clustering, and source separation. As a critical aspect of the linear mixture models, identifiability of the model parameters is well-studied, under frameworks such as independent component analysis and constrained matrix…
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-process latent components and develops a learning and inference algorithm. result Identifiability of TP independent components under general conditions and Gaussian Process limit.
Multiview analysis aims at extracting shared latent components from data samples that are acquired in different domains, e.g., image, text, and audio. Classic multiview analysis, e.g., canonical correlation analysis (CCA), tackles this problem via matching the linearly transformed views in a certain latent domain. More…
New method tests independence with single nonstationary time series.
problem Testing independence in nonstationary nonlinear time series.
method Time-varying nonlinear regression, local long-run covariance estimation, strong Gaussian approximation.
result First framework for conditional independence testing with a single realization of a nonstationary nonlinear process.
Principal component analysis (PCA) is largely adopted for chemical process monitoring and numerous PCA-based systems have been developed to solve various fault detection and diagnosis problems. Since PCA-based methods assume that the monitored process is linear, nonlinear PCA models, such as autoencoder models and kern…
New tools in nonlinear random matrices improve understanding of the Sum of Squares hierarchy.
problem Improving the Sum of Squares (SoS) hierarchy's performance on average-case problems.
method Developed new tools in nonlinear random matrices and applied them to analyze the SoS hierarchy.
result Subexponential-time SoS lower bounds for various problems, offering evidence for the low-degree likelihood ratio hypothesis.