Paper solves NGCA for discrete distributions using LLL method.
problem Learning hidden non-Gaussian components in discrete distributions.
method Utilizes LLL lattice basis reduction method.
result Sample and computationally efficient algorithm for NGCA in discrete distributions.
The problem of Non-Gaussian Component Analysis (NGCA) is about finding a maximal low-dimensional subspace E in Rn so that data points projected onto E follow a non-gaussian distribution. Although this is an appropriate model for some real world data analysis problems, there has been little progress on t…
The paper analyzes the non-Gaussian behavior of inflation and unemployment over 70 years using multifractal methods.
problem Capturing unusual fluctuations in inflation and unemployment over long periods.
method Coupled multifractal approach to analyze non-Gaussian distributions of inflation and unemployment over 70 years.
result The non-Gaussianity of unemployment is noticeable only for periods smaller than 1 year, while inflation's non-Gaussianity persists across all time scales.
Algorithm learns non-Gaussian graphical models via Hessian scores and triangular transport.
problem Learning graph structure from non-Gaussian data.
method Score based on integrated Hessian information, coupled with triangular transport map.
result Algorithm successfully recovers graph structure for non-Gaussian data.
Study compares various non-Gaussian models for financial returns.
problem Leptokurtic, heavy-tailed financial returns defy Gaussian assumptions.
method Compared and simulated various non-Gaussian models using Monte Carlo.
result Consistency in modeling scaling properties of large price changes.
Bayesian inference for wide neural networks using Edgeworth expansion.
problem Analyzing the non-Gaussian behavior of wide neural networks in Bayesian inference.
method Proposed a non-Gaussian distribution using multivariate Edgeworth expansion for finite-width neural networks.
result Derived non-Gaussian posterior distribution in Bayesian regression tasks.
The analysis of observed conditional distributions of both lagged and simultaneous intraday price increments of a basket of stocks reveals phenomena of dependence - induced volatility smile and kurtosis reduction. A model based on multivariate t-Student distribution shows that the observed effects are caused by colelct…
Stock prices are known to exhibit non-Gaussian dynamics, and there is much interest in understanding the origin of this behavior. Here, we present a model that explains the shape and scaling of the distribution of intraday stock price fluctuations (called intraday returns) and verify the model using a large database fo…
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.
This paper presents a method for efficient density estimation in nonlinear systems.
problem Accurate representation of non-Gaussian distributions in nonlinear dynamical systems is challenging.
method Uses Seminonparametric (SNP) densities with probabilists' Hermite polynomial basis and Monte Carlo approximation for maximum likelihood estimation.
result Demonstrates that the method can accurately capture non-Gaussian density structure and compute quantiles using fewer samples than raw Monte Carlo.
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.
Bayesian method identifies causal DAG structure from non-Gaussian errors.
problem Learning causal structure from non-Gaussian errors in Bayesian networks.
method Bayesian hierarchical model with DAG prior for non-Gaussian errors.
result Posterior DAG selection consistency achieved under mild assumptions.
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.
This work extends Tweedie's formulae to non-Gaussian processes for better diffusion model generation.
problem Limited exploration of non-Gaussian diffusion models and corresponding Tweedie's formulae.
method Extended Tweedie's formulae to geometric Brownian motion, squared Bessel, and Cox-Ingersoll-Ross processes.
result Demonstrated potential of non-Gaussian models in image and financial time series generation.
New method compresses non-Gaussian distributions exponentially.
problem Efficiently representing and computing non-Gaussian probability distributions.
method Tensor-Network Fourier Methods using QTT representation.
result Exponential compression of non-Gaussian distributions.
GGMPs improve non-Gaussian conditional density estimation.
problem Multimodality, heteroscedasticity, and strong non-Gaussianity in conditional density estimation.
method GGMP combines local Gaussian mixture fitting, cross-input component alignment, and per-component heteroscedastic GP training.
result GGMPs improve distributional approximation on synthetic and real-world datasets.
Improves graph-based active learning for non-Gaussian models.
problem Efficiently selecting data points for labeling in graph-based semi-supervised learning.
method Approximates non-Gaussian distributions, introduces rank-one update and model change acquisition function.
result Enhanced active learning for graph-based SSL under non-Gaussian models.
The paper uses Tukey g-and-h neural networks for non-Gaussian data regression.
problem Regression with non-Gaussian data.
method Training neural networks to predict Tukey g-and-h distribution parameters via negative log-likelihood minimization.
result Efficiency demonstrated in simulated and real-world datasets.
The paper shows how to infer conditional independence from non-Gaussian data.
problem Inferring conditional independence from non-Gaussian distributions.
method Developed a method to recover conditional independence structure from the precision matrix of generalized nonparanormal data.
result The conditional independence structure can be inferred from the precision matrix of generalized nonparanormal data.
Improved spatial distribution learning with Bayesian transport maps and parametric shrinkage.
problem Learning non-Gaussian spatial distributions with limited training data.
method Proposed ShrinkTM approach using Bayesian transport maps with parametric shrinkage.
result ShrinkTM outperforms existing BTM, especially with few training samples.
Gaussian processes are ubiquitous in nature and engineering. A case in point is a class of neural networks in the infinite-width limit, whose priors correspond to Gaussian processes. Here we perturbatively extend this correspondence to finite-width neural networks, yielding non-Gaussian processes as priors. The methodo…
New Stein identity for q-Gaussians reduces gradient variance in machine learning.
problem Improving gradient estimators for non-Gaussian distributions.
method Deriving a new Stein identity for bounded-support q-Gaussians and simplifying previous results.
result Gradient estimators for q-Gaussians have nearly identical forms to Gaussian ones, reducing variance.
Develops a new method for functional regression that works with non-Gaussian data.
problem Limited models for regression in function spaces with Gaussian process priors.
method Introduces Neural Operator Flows (OpFlow) for non-Gaussian function spaces.
result OpFlow enables robust and accurate uncertainty quantification for functional regression.
The generalized correlation approach, which has been successfully used in statistical radio physics to describe non-Gaussian random processes, is proposed to describe stochastic financial processes. The generalized correlation approach has been used to describe a non-Gaussian random walk with independent, identically d…
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…
The paper examines non-Gaussian models for financial data.
problem Modeling financial data with non-Gaussian distributions.
method Analysis of multivariate non-Gaussian models focusing on parsimony, dependence structure, and computational aspects.
result Characterization and calibration of models for financial log-returns.
The paper finds non-Gaussian directions in high-dimensional data using Wasserstein distance.
problem Locating interesting non-Gaussian features in high-dimensional data.
method Projection pursuit using 2-Wasserstein distance to maximize the difference from Gaussian.
result Statistical guarantees for accurately approximating an unknown low-dimensional non-Gaussian subspace.
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.
The ACCRU framework improves probabilistic forecasts by capturing input-dependent uncertainty.
problem Uncertainty in deterministic predictions, especially for skewed and non-Gaussian errors.
method Neural network trained with a loss function balancing accuracy and reliability to learn input-dependent, non-Gaussian uncertainty distributions.
result Improves probabilistic forecasts relative to existing methods, capturing skewed and non-Gaussian errors.
Proposes efficient Gaussian approximations for non-Gaussian likelihoods.
problem Computational challenges in learning and inference with non-Gaussian likelihoods.
method Variational inference and moment matching in transformed bases.
result Good approximation quality for binary and multiclass classification.
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the returns distribution in terms of a Student-t distribution. Non-Gaussian closed-fo…
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.
Diagonal transformations preserve independence structures in non-Gaussian distributions.
problem Preserving independence structures in non-Gaussian distributions.
method Diagonal nonlinear transformations of multivariate normal variables.
result Independence structures are preserved in non-Gaussian distributions under diagonal transformations.
New bounds for kernel regression under non-Gaussian noise.
problem Uncertainty quantification for function estimates from noisy observations.
method Novel non-asymptotic probabilistic uniform error bounds for kernel-based regression.
result Proposed bounds apply to a broad class of non-Gaussian noise distributions.
Improved VB algorithm for NIG mixtures outperforms Gaussian mixtures for non-Gaussian data.
problem Clustering non-Gaussian data, especially heavy-tailed and asymmetric.
method Proposed an improved VB algorithm for NIG mixture models and extended Dirichlet process mixture models.
result Outperforms Gaussian mixtures and existing NIG mixture models, especially for highly non-normative data.
Forecast stock return distributions using neural networks.
problem Accurately modeling non-Gaussian stock return features.
method Two-stage quantile neural network with spline interpolation.
result Improved mean and variance forecasts compared to standard models.
Study on Kyle-Back model with risk aversion and non-Gaussian beliefs.
problem Existence of equilibrium in Kyle's insider trading model.
method Forward-backward system coupled via optimal transport constraint, stochastic representation, well-posedness of solutions.
result Existence and properties of equilibrium for small risk aversion parameter.
Sum-of-Squares lower bound shows NGCA requires more samples than known algorithms.
problem Finding a non-Gaussian direction in a high-dimensional dataset.
method Sum-of-Squares (SoS) framework to prove lower bounds.
result First super-constant degree SoS lower bound for NGCA.
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.
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.
The paper shows how to construct non-Gaussian Martingales using hyperbolic diffusion.
problem The challenge of modeling extreme financial events.
method Constructing Martingale processes with Cauchy distribution in the large volatility limit.
result Financial justification for using non-Gaussian distributions in modeling extreme events.
New EM algorithm for mixtures of elliptical distributions handles missing data and outliers.
problem Missing data imputation for noisy and non-Gaussian data.
method Investigation of a new EM algorithm for mixtures of elliptical distributions.
result The proposed algorithm is robust to outliers and competitive with other methods.
Reliable calculations of financial risk require that the fat-tailed nature of prices changes is included in risk measures. To this end, a non-Gaussian approach to financial risk management is presented, modeling the power-law tails of the returns distribution in terms of a Student-t (or Tsallis) distribution. Non-Gau…
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.
Proposes a new regression method using Lp-norms for non-Gaussian noise.
problem Non-Gaussian noise in residuals affects the performance of local least squares regression.
method Introduces local polynomial Lp-norm regression, replacing weighted least squares with weighted Lp-norm estimation. result Demonstrates superior performance over local least squares in one-dimensional data and higher dimensions.
Paper analyzes holdout cross-validation for large non-Gaussian covariance estimation.
problem Estimating large covariance matrices for non-Gaussian data.
method Use of Weingarten calculus and Ledoit-Péché formula for theoretical error derivation.
result Optimal train-test split ratio is proportional to square root of matrix dimension.
Fast approximate inference for non-Gaussian data.
problem Efficient inference for non-Gaussian data.
method Laplace Matching for fast approximate inference in latent Gaussian models.
result Achieves high approximation quality with low computational cost.
We present an algorithm to identify sparse dependence structure in continuous and non-Gaussian probability distributions, given a corresponding set of data. The conditional independence structure of an arbitrary distribution can be represented as an undirected graph (or Markov random field), but most algorithms for lea…