The Kalman filter is extensively used for state estimation for linear systems under Gaussian noise. When non-Gaussian Lévy noise is present, the conventional Kalman filter may fail to be effective due to the fact that the non-Gaussian Lévy noise may have infinite variance. A modified Kalman filter for linear systems wi…
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48 results for “linear non-Gaussian”
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…
New algorithm for learning causal structures with disjoint cycles in linear non-Gaussian models.
problem Learning causal structures with cycles in linear non-Gaussian models.
method Characterizing when graphs determine the same model, using quadratic and cubic polynomial relations, and a strategy of decorrelating cycles and multivariate regression.
result Consistent and computationally efficient algorithm for learning causal structures with disjoint cycles.
New algorithm for estimating MLR parameters with non-Gaussian noise.
problem Estimating MLR parameters with non-Gaussian noise.
method Combining ADMM with EM algorithm idea.
result Our method outperforms EM algorithm in non-Gaussian noise case.
Improved Kalman filter for non-linear, non-Gaussian data.
problem Estimating hidden variables with non-linear, non-Gaussian observations.
method Reproduces and extends Burkhart et al.'s discriminative Kalman filter.
result Enhanced filter performance for complex observation models.
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.
Non-Gaussian component analysis (NGCA) is aimed at identifying a linear subspace such that the projected data follows a non-Gaussian distribution. In this paper, we propose a novel NGCA algorithm based on log-density gradient estimation. Unlike existing methods, the proposed NGCA algorithm identifies the linear subspac…
New algorithms learn polytree structures from data.
problem Learning causal graphs from non-Gaussian data.
method Combines Chow-Liu algorithm with edge orientation schemes.
result Established high-dimensional consistency results.
Efficiently learns linear non-Gaussian DAGs with noisy nodes.
problem Learning DAGs with non-Gaussian noise and diverging number of nodes.
method Proposes a novel method using topological layers for bottom-up reconstruction and consistent parent-child relations.
result Topological layers can be exactly reconstructed and parent-child relations established without faithfulness assumption.
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.
Sparse non-Gaussian component analysis (SNGCA) is an unsupervised method of extracting a linear structure from a high dimensional data based on estimating a low-dimensional non-Gaussian data component. In this paper we discuss a new approach to direct estimation of the projector on the target space based on semidefinit…
New methods discover causal relationships from multiple related data views.
problem Causal discovery from non-Gaussian data.
method Multi-view linear Structural Equation Model (SEM) with weak assumptions.
result Identifiability of acyclic SEMs and successful causal graph estimation.
Study non-Gaussian measures' concentration properties in metric spaces.
problem Concentration properties for non-linear Gaussian functionals with non-Gaussian tails.
method Prove generalised Transportation-Cost Inequalities (TCIs) for specific functionals.
result Extended TCIs for rough volatility and Parabolic Anderson Model.
In recent years, several methods have been proposed for the discovery of causal structure from non-experimental data (Spirtes et al. 2000; Pearl 2000). Such methods make various assumptions on the data generating process to facilitate its identification from purely observational data. Continuing this line of research, …
We revisit the Bayesian online inference problems for the linear dynamic systems (LDS) under non- Gaussian environment. The noises can naturally be non-Gaussian (skewed and/or heavy tailed) or to accommodate spurious observations, noises can be modeled as heavy tailed. However, at the cost of such noise robustness, the…
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the datagenerating process of variables. Recently, it was shown that use of non-Gaussianity identifies a causal ordering …
Improves signal detection in non-Gaussian noise using transformed data.
problem Signal detection in rank-one signal-plus-noise data matrices.
method Pre-transforming matrix entries and using linear spectral statistics for hypothesis testing.
result Sharp phase transition of largest eigenvalues in spiked rectangular matrices.
New method detects causal relationships from noisy measurements.
problem Discover causal relationships from noisy, imperfect measurements.
method Transformed Independent Noise (TIN) condition and ordered group decomposition.
result Identifies causal graph structure without over-complete ICA.
Study identifies parameters in causal models with latent confounding.
problem Parameter identification in linear non-Gaussian causal models with latent confounding.
method Graphical criterion for necessary and sufficient identifiability of direct causal effects, with polynomial-time algorithm.
result Developed a graphical criterion for identifying direct causal effects in latent variable models with arbitrary non-linear confounding.
Paper optimizes WGAN parameters for non-Gaussian data.
problem Optimizing parameters for non-Gaussian data in WGAN.
method Characterization of optimal solutions for population WGAN beyond LQG setting, using sliced Wasserstein framework.
result Closed-form optimal parameters for non-linear activation functions and non-Gaussian data derived.
Random neural networks with ReLU activations are non-Gaussian processes.
problem Understanding the behavior of neural networks with random initialization and rectified linear units.
method Proving these networks are non-Gaussian processes and deriving their properties.
result These networks can converge to non-Gaussian processes under certain conditions.
Structural equation models and Bayesian networks have been widely used to analyze causal relations between continuous variables. In such frameworks, linear acyclic models are typically used to model the data-generating process of variables. Recently, it was shown that use of non-Gaussianity identifies the full structur…
This work preserves linear invariants in ensemble filters for non-Gaussian data assimilation.
problem Maintaining critical invariants like mass, stoichiometric balance, and charge in non-Gaussian data assimilation.
method Introducing a novel class of nonlinear ensemble filters using measure transport theory.
result Recovery of a constrained Kalman filter for Gaussian settings and combination with regularization techniques.
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 method learns graph structure with hidden causes from observational data.
problem Learning the structure of linear non-Gaussian models with hidden causes.
method Augments hidden variable structure by learning multidirected edges and uses higher order cumulants.
result Correct structure recovery for bow-free acyclic mixed graphs with multi-directed edges.
Non-Gaussian component analysis (NGCA) is an unsupervised linear dimension reduction method that extracts low-dimensional non-Gaussian "signals" from high-dimensional data contaminated with Gaussian noise. NGCA can be regarded as a generalization of projection pursuit (PP) and independent component analysis (ICA) to mu…
We consider to learn a causal ordering of variables in a linear non-Gaussian acyclic model called LiNGAM. Several existing methods have been shown to consistently estimate a causal ordering assuming that all the model assumptions are correct. But, the estimation results could be distorted if some assumptions actually a…
The statistical dependencies which independent component analysis (ICA) cannot remove often provide rich information beyond the linear independent components. It would thus be very useful to estimate the dependency structure from data. While such models have been proposed, they usually concentrated on higher-order corr…
A Bayesian estimation approach to analyze non-Gaussian data-generating processes with latent classesstat.ML
A large amount of observational data has been accumulated in various fields in recent times, and there is a growing need to estimate the generating processes of these data. A linear non-Gaussian acyclic model (LiNGAM) based on the non-Gaussianity of external influences has been proposed to estimate the data-generating …
Time series models generalize ARMA and ARFIMA with non-Gaussian dependence.
problem Modeling non-Gaussian serial dependence in time series data.
method Infinite-order partial copula dependence in s-vine processes.
result Rich class of models that generalize linear processes.
Robust method estimates state, input, and parameters of linear systems online.
problem Joint estimation of state, input, and parameters in noisy or outlier-prone measurements.
method Combines recursive, alternating, and iteratively-reweighted least squares into a single algorithm.
result Good performance in presence of outliers and compared to state-of-the-art methods.
A linear non-Gaussian structural equation model called LiNGAM is an identifiable model for exploratory causal analysis. Previous methods estimate a causal ordering of variables and their connection strengths based on a single dataset. However, in many application domains, data are obtained under different conditions, t…
We consider learning the possible causal direction of two observed variables in the presence of latent confounding variables. Several existing methods have been shown to consistently estimate causal direction assuming linear or some type of nonlinear relationship and no latent confounders. However, the estimation resul…
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 robust discriminant analysis for non-Gaussian data.
problem Classical discriminant analysis struggles with non-Gaussian distributions and contaminated datasets.
method Each data point follows its own ES distribution with arbitrary scale, leading to robust classification.
result Maximum-likelihood estimation and classification are simple, fast, and robust.
Identifiability Without Gaussianity: Symbolic World Models and Near-Infinite Temporal Consistencystat.ML
Symbolic grounding in causal dynamics achieves near-infinite temporal consistency.
problem Achieving linear identifiability in non-Gaussian physical systems.
method Physics-Grounded Symbolic Architecture (PGSA)
result PGSA achieves exact linear identifiability for all physical regimes.
New algorithm identifies causal effects in latent confounding models.
problem Identifying causal effects in linear non-Gaussian models with latent confounding.
method Recursive algorithm using rank conditions on higher-order cumulants.
result Algorithm achieves comparable performance to overcomplete ICA without knowing the number of latent variables.
A new robust and flexible classification method for non-Gaussian data.
problem Robustness to scale changes and non-Gaussian distributions in classical discriminant analysis.
method FEMDA uses arbitrary Elliptically Symmetrical distributions and scale parameters for each data point.
result FEMDA is robust to scale changes and outperforms other methods.
Least-Squares Independence Regression for Non-Linear Causal Inference under Non-Gaussian Noisestat.ML
The discovery of non-linear causal relationship under additive non-Gaussian noise models has attracted considerable attention recently because of their high flexibility. In this paper, we propose a novel causal inference algorithm called least-squares independence regression (LSIR). LSIR learns the additive noise model…
Adaptive algorithm improves nonlinear data assimilation for non-Gaussian systems.
problem Challenges of non-Gaussian statistics in data assimilation.
method Triangular measure transport with P-spline basis functions and an information criterion.
result Automatic selection of parsimonious parametrization for efficient adaptation.
Fat Tailed Factorsq-fin.PM
A new factor analysis method using ICA reduces portfolio concentration and diversifies excess kurtosis.
problem Standard factor analysis suffers from issues with pairwise correlations of asset returns.
method Identifies factors based on non-Gaussianity instead of variance, using ICA.
result Fat-tailed portfolios significantly reduce portfolio concentration and winner-takes-all problem.
New algorithm estimates causal effects for non-Gaussian data.
problem Estimating causal effects in non-Gaussian distributions.
method Generalized k-Triangle Faithfulness Assumption and Edge Estimation Algorithm.
result Uniformly consistent estimates of causal effects.
Estimating causal models from observational data is a crucial task in data analysis. For continuous-valued data, Shimizu et al. have proposed a linear acyclic non-Gaussian model to understand the data generating process, and have shown that their model is identifiable when the number of data is sufficiently large. Howe…
We consider the problem of learning causal models from observational data generated by linear non-Gaussian acyclic causal models with latent variables. Without considering the effect of latent variables, one usually infers wrong causal relationships among the observed variables. Under faithfulness assumption, we propos…
We consider the problem of discriminative factor analysis for data that are in general non-Gaussian. A Bayesian model based on the ranks of the data is proposed. We first introduce a new {\em max-margin} version of the rank-likelihood. A discriminative factor model is then developed, integrating the max-margin rank-lik…
Optimizes experiment design for causal structure learning in linear models with cycles.
problem Causal structure learning from combined observational and interventional data in linear non-Gaussian cyclic models.
method Combinatorial characterization of equivalence classes, adaptive stochastic optimization, greedy policy with near-optimal performance guarantee, sampling-based estimator for reward function.
result Optimal experiment design reduces the equivalence class of causal graphs to a single true graph with a small number of interventions.
Study of deep linear neural networks with proportional width and depth.
problem Lack of descriptive power in Gaussian limit of deep linear neural networks.
method Proportional infinite-width infinite-depth limit for deep linear neural networks.
result Characterization of limiting distribution as a nontrivial mixture of Gaussians.
Study on linear regression with dependent covariates, proving universality and error characterization.
problem Linear regression with dependent covariates in high-dimensional settings.
method Analysis of ridge regression performance, Gaussian universality theorem, spectral properties of covariance matrices.
result Asymptotic performance of ridge regression is invariant under non-Gaussian covariates with preserved mean and covariance.