We apply belief propagation to a Bayesian bipartite graph composed of discrete independent hidden variables and discrete visible variables. The network is the Discrete counterpart of Independent Component Analysis (DICA) and it is manipulated in a factor graph form for inference and learning. A full set of simulations …
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48 results for “Bayesian independent component analysis”
We apply both distance-based (Jin and Matteson, 2017) and kernel-based (Pfister et al., 2016) mutual dependence measures to independent component analysis (ICA), and generalize dCovICA (Matteson and Tsay, 2017) to MDMICA, minimizing empirical dependence measures as an objective function in both deflation and parallel m…
Many data-driven approaches exist to extract neural representations of functional magnetic resonance imaging (fMRI) data, but most of them lack a proper probabilistic formulation. We propose a group level scalable probabilistic sparse factor analysis (psFA) allowing spatially sparse maps, component pruning using automa…
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…
Independent Component Analysis (ICA) is a dimensionality reduction technique that can boost efficiency of machine learning models that deal with probability density functions, e.g. Bayesian neural networks. Algorithms that implement adaptive ICA converge slower than their nonadaptive counterparts, however, they are cap…
A new VAE approach solves inverse problems without explicit inverse mapping.
problem Solving inverse problems without explicit inverse mapping.
method Discarding the encoder in VAE architecture, directly optimizing latent variables.
result The latent variables can exhibit mutually independent properties without an encoding process.
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.
NSGLD improves SGLD for non-convex optimization problems.
problem Optimizing non-convex objectives efficiently.
method Introducing non-reversible SGLD by adding an anti-symmetric matrix to the drift term of the Langevin diffusion.
result NSGLD converges faster to the same stationary distribution with non-asymptotic guarantees.
New algorithms learn simple staged trees from data, improving model fit.
problem Complex conditional independences in categorical data vectors.
method Structural learning algorithms for simple staged trees, coalescing the underlying tree.
result Data-learned simple staged trees often outperform Bayesian networks in model fit.
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.
Correlated component analysis as proposed by Dmochowski et al. (2012) is a tool for investigating brain process similarity in the responses to multiple views of a given stimulus. Correlated components are identified under the assumption that the involved spatial networks are identical. Here we propose a hierarchical pr…
Improves model predictability by mixing forecasts and orthogonalizing models.
problem Redundant models contaminate model space and degrade predictive performance.
method Principal Component Analysis for model orthogonalization in Bayesian forecast mixing.
result Better prediction accuracy and excellent uncertainty quantification.
Independent component analysis (ICA) decomposes multivariate data into mutually independent components (ICs). The ICA model is subject to a constraint that at most one of these components is Gaussian, which is required for model identifiability. Linear non-Gaussian component analysis (LNGCA) generalizes the ICA model t…
Generative model identifies temporal count data components with regime-dependent contributions.
problem Modeling temporal count data with regime-dependent dynamics.
method Generative framework combining regime-adaptive dynamics with Poisson log-normal emissions.
result Established identifiability of the model and revealed co-variation patterns and regime shifts.
Contrastive ICA identifies features in experimental groups relative to controls.
problem Jointly analyzing experimental and control datasets to identify salient features.
method Developed contrastive ICA (cICA) using tensor decomposition.
result cICA identifies patterns and visualizes data effectively, outperforming existing methods.
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.
Bayesian QFSTS model tackles feature selection in quantile time series analysis.
problem Quantile feature selection in correlated multivariate time series data.
method Bayesian dimension reduction methodology using QFSTS model with multivariate asymmetric Laplace distribution, spike-and-slab prior, Metropolis-Hastings algorithm, and Bayesian model averaging.
result QFSTS model outperforms in feature selection, parameter estimation, and forecasting.
We present a generalization of independent component analysis (ICA), where instead of looking for a linear transform that makes the data components independent, we look for a transform that makes the data components well fit by a tree-structured graphical model. Treating the problem as a semiparametric statistical prob…
New algorithm improves source separation with multi-trial supervision.
problem Non-convex optimization and interpretability of independent components.
method Proximal gradient-type algorithm in invertible matrices with backpropagation for joint learning.
result Increased success rate of non-convex optimization and improved interpretability.
Second-order Approximation of Minimum Discrimination Information in Independent Component Analysisstat.ML
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.
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.
Causal Component Analysisstat.ML
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.
CrossCat: A Fully Bayesian Nonparametric Method for Analyzing Heterogeneous, High Dimensional Datacs.AI
There is a widespread need for statistical methods that can analyze high-dimensional datasets with- out imposing restrictive or opaque modeling assumptions. This paper describes a domain-general data analysis method called CrossCat. CrossCat infers multiple non-overlapping views of the data, each consisting of a subset…
Study improves Bayesian optimisation with ensemble transfer learning.
problem Improving sample efficiency in Bayesian optimisation of expensive functions.
method Empirical analysis of ensemble-based transfer learning methods and pipeline components.
result Two components (warm start initialisation and positive weight constraint) improve transfer learning Bayesian optimisation performance.
This study examines whether PCA can effectively identify nitrogen pollution sources in rivers.
problem Identifying pollution sources in rivers for effective environmental management.
method Principal Component Analysis and its modifications, along with Independent Component Analysis and Factor Analysis, are applied to nitrogen pollution source identification.
result PCA and related techniques can be powerful tools for uncovering nitrogen pollution sources in rivers.
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.
Bayesian analysis of financial time series using R-INLA.
problem Analyzing interdependencies between stock volatility measures.
method Flexible level correlated model (LCM) with INLA approximation.
result Fast approximate Bayesian modeling of positive-valued time series.
Bayesian SPCA method tackles orthogonality constraint with spike and slab prior.
problem Bayesian SPCA method for high-dimensional data with orthogonality constraint.
method Parameter-expanded coordinate ascent variational inference (PX-CAVI) with spike and slab prior.
result PX-CAVI algorithm outperforms existing SPCA approaches in performance.
CAVI converges exponentially fast for Bayesian PCA models.
problem Characterizing the convergence speed of CAVI for BPCA.
method Proved exponential convergence using power iteration analogy and novel lower bounds.
result Exponential convergence of CAVI for BPCA models with any number of principal components.
Study predicts gender from brain FC at multiple scales using deep learning and Bayesian methods.
problem Predicting gender from brain functional connectivity.
method Deep learning and Bayesian deep learning applied to brain FC data from 1003 healthy adults.
result Bayesian deep learning provides accurate predictions and uncertainty information.
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.
Principal component analysis (PCA) is very popular to perform dimension reduction. The selection of the number of significant components is essential but often based on some practical heuristics depending on the application. Only few works have proposed a probabilistic approach able to infer the number of significant c…
A new method improves uncertainty quantification in Bayesian inference.
problem Poor uncertainty quantification in traditional Gibbs posteriors.
method Sequential Gibbs posteriors with a Bernstein-von Mises theorem.
result Sequential Gibbs posteriors provide better frequentist coverage.
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.
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…
Independent component analysis (ICA) has been widely used for blind source separation in many fields such as brain imaging analysis, signal processing and telecommunication. Many statistical techniques based on M-estimates have been proposed for estimating the mixing matrix. Recently, several nonparametric methods have…
We present a new method for the separation of superimposed, independent, auto-correlated components from noisy multi-channel measurement. The presented method simultaneously reconstructs and separates the components, taking all channels into account and thereby increases the effective signal-to-noise ratio considerably…
We develop a coherent framework for integrative simultaneous analysis of the exploration-exploitation and model order selection trade-offs. We improve over our preceding results on the same subject (Seldin et al., 2011) by combining PAC-Bayesian analysis with Bernstein-type inequality for martingales. Such a combinatio…
Subjective classification of galaxies can mislead us in the quest of the origin regarding formation and evolution of galaxies since this is necessarily limited to a few features. The human mind is not able to apprehend the complex correlations in a manyfold parameter space, and multivariate analyses are the best tools …
The paper tackles mean-variance analysis in Bayesian optimization under uncertainty.
problem Optimizing decisions in uncertain environments considering trade-offs between average and variance of risk.
method Developed bounds for mean and variance risk measures in Gaussian Process models and proposed AL algorithms for multi-task, multi-objective, and constrained optimization scenarios.
result Proposed AL algorithms effectively address the mean-variance trade-off in uncertain optimization scenarios.
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.
Novel prior for orthogonal functions improves functional component estimation.
problem Improving orthogonality in functional principal component analysis.
method Sequential adaptive priors for orthogonal functions using hierarchical conditionally normal distributions.
result Proposed prior leads to nearly orthogonal posterior estimates.
Bayesian nonparametric (BNP) models provide elegant methods for discovering underlying latent features within a data set, but inference in such models can be slow. We exploit the fact that completely random measures, which commonly used models like the Dirichlet process and the beta-Bernoulli process can be expressed a…
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 .
New method learns disentangled signals without prior or model constraints.
problem Learning disentangled signals from data without prior or model constraints.
method Minimizes conditional KL divergence using a sequential algorithm to learn de-mixing flow models.
result Method learns self-sufficient signals that can reconstruct missing values.
Sparse Gaussian ICAstat.ML
Independent component analysis (ICA) is a cornerstone of modern data analysis. Its goal is to recover a latent random vector S with independent components from samples of X=AS where A is an unknown mixing matrix. Critically, all existing methods for ICA rely on and exploit strongly the assumption that S is not Gaussian…
Independent component analysis (ICA) is a statistical method for transforming an observable multi-dimensional random vector into components that are as statistically independent as possible from each other. Usually the ICA framework assumes a model according to which the observations are generated (such as a linear tra…
In the present work, eigenvalue distributions defined by a random rectangular matrix whose components are neither independently nor identically distributed are analyzed using replica analysis and belief propagation. In particular, we consider the case in which the components are independently but not identically distri…