The abstract proposes a neural network theory using quantum field theory.
problem Understanding the behavior of neural networks in the asymptotic and non-asymptotic limits.
method Mapping neural networks to Wilsonian effective field theory, using Gaussian processes and Feynman diagrams.
result Established a direct connection between overparameterization and simplicity of neural network likelihoods.
Inverse modeling for the estimation of non-Gaussian hydraulic conductivity fields in subsurface flow and solute transport models remains a challenging problem. This is mainly due to the non-Gaussian property, the non-linear physics, and the fact that many repeated evaluations of the forward model are often required. In…
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 …
This research develops an evolutionary approach to discover non-Gaussian stochastic dynamical systems.
problem Discovering explicit governing equations of stochastic dynamical systems with Lévy noise from data.
method ESSR approach using genetic programming, sparse regression, and nonlocal Kramers-Moyal formulas.
result The approach effectively extracts non-Gaussian stochastic dynamical systems from sample path data.
Modeling spatial extremes with non-Gaussian fields using SAR models and CNNs.
problem Challenges in modeling spatial data with heavy-tailed distributions and missing cells.
method Spatial autoregressive models with Generalized Extreme Value innovations, combined with CNN for fast parameter estimation.
result Effective modeling of spatial extremes in non-Gaussian fields, demonstrated on precipitation 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.
A2-SBNN models spatial data with copulas for non-Gaussian dependencies.
problem Capturing complex spatial relationships and extreme dependencies in non-Gaussian data.
method Embedding A2 copula into a Bayesian neural network, trained with Wasserstein loss and moment matching.
result A2-SBNN consistently delivers high accuracy across various dependency strengths.
Non-linear image reconstruction and signal analysis deal with complex inverse problems. To tackle such problems in a systematic way, I present information field theory (IFT) as a means of Bayesian, data based inference on spatially distributed signal fields. IFT is a statistical field theory, which permits the construc…
New framework models neural systems with random architecture on manifolds.
problem Complex, uncertain systems with non-Gaussian outputs.
method Latent random field on compact manifold generates neural architecture and weights.
result Synthetic neural systems can produce stochastic outputs for deterministic inputs.
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…
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…
VMGP extends Gaussian processes for Bayesian meta-learning, improving uncertainty prediction.
problem Bayesian meta-learning for few-shot tasks with non-Gaussian uncertainty.
method VMGP (Variational Meta-Gaussian Processes) extends Gaussian processes to model non-Gaussian predictive posteriors.
result VMGP significantly outperforms existing Bayesian meta-learning methods on complex tasks.
Weak lensing maps contain information beyond two-point statistics on small scales. Much recent work has tried to extract this information through a range of different observables or via nonlinear transformations of the lensing field. Here we train and apply a 2D convolutional neural network to simulated noiseless lensi…
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.
This work extracts stochastic dynamical systems with α-stable Lévy noise.
problem Extracting data-driven governing laws of dynamical systems with non-Gaussian noise.
method End-to-end deep learning approach for learning drift and diffusion coefficients for α-stable Lévy noise. result Effectiveness of the method confirmed by numerical experiments.
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…
Real world systems typically feature a variety of different dependency types and topologies that complicate model selection for probabilistic graphical models. We introduce the ensemble-of-forests model, a generalization of the ensemble-of-trees model. Our model enables structure learning of Markov random fields (MRF) …
A new model for stock price fluctuations is proposed, based upon an analogy with the motion of tracers in Gaussian random fields, as used in turbulent dispersion models and in studies of transport in dynamically disordered media. Analytical and numerical results for this model in a special limiting case of a single-sca…
ICA reveals deep learning's feature learning mechanisms from non-Gaussian data.
problem Understanding feature learning from non-Gaussian inputs in deep neural networks.
method Investigates ICA and SGD on synthetic and real data.
result FastICA requires n≳d4 samples for single non-Gaussian direction recovery, while SGD outperforms and optimised SGD reaches n≳d2. 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 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…
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.
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.
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.
A new flow-based Bayesian filter tackles high-dimensional nonlinear stochastic systems.
problem Bayesian filtering for high-dimensional nonlinear systems is challenging due to non-Gaussian distributions and computational limitations.
method Integrates normalizing flows to construct a latent linear state-space model with efficient density estimation and sampling.
result Demonstrates superior accuracy and efficiency in numerical experiments.
A new vine copula mixture model improves clustering accuracy for non-Gaussian data.
problem Finite mixture models struggle with asymmetric tail dependencies and non-elliptical clusters.
method Proposes a vine copula mixture model for clustering non-Gaussian data, addressing model selection and parameter estimation.
result Significant improvement in clustering accuracy for data with asymmetric tail dependencies or non-Gaussian margins.
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…
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.
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.
Wavelet scattering spectra model non-Gaussian time-series, proving scale invariance for self-similar processes.
problem Modeling non-Gaussian time-series with stationary increments.
method Complex wavelet transform for scale variations, joint correlation matrix for scale dependencies, second wavelet transform for diagonalization, maximum entropy models conditioned by scattering spectra coefficients.
result Scattering spectra of self-similar processes are scale invariant, allowing statistical testing and generation of new time-series.
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.
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.
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…
The inference of correlated signal fields with unknown correlation structures is of high scientific and technological relevance, but poses significant conceptual and numerical challenges. To address these, we develop the correlated signal inference (CSI) algorithm within information field theory (IFT) and discuss its n…
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.
Study large deviations in fractional volatility models with non-Gaussian volatility.
problem Large deviations in fractional volatility models with non-Gaussian volatility.
method Established a small-noise large deviation principle for log-price.
result Logarithmic call price asymptotics for large strikes in a special case.
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…
TURB-Rot provides a large database of turbulent rotating flow snapshots for research.
problem Lack of large-scale, high-resolution datasets for turbulent rotating flows.
method Direct Numerical Simulations of Navier-Stokes equations with rotation.
result Provides a diverse set of 300K complex images and fields for testing.
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.
Researchers develop a new spatial process model for non-Gaussian data.
problem Non-Gaussian spatial data with asymmetry and heavy-tailedness.
method Re-parameterized Unified Skew-Normal (SUN) distribution, GSUN process, neural Bayes inference with GATs.
result GSUN process captures non-Gaussian spatial data properties and outperforms conventional models.
Study of a risk-averse informed trader in a multi-asset market with non-Gaussian prices.
problem Existence of equilibrium in a multi-asset market with non-Gaussian prices and a risk-averse informed trader.
method Constructed equilibrium using Fokker-Planck equation and coupled partial differential equations with an optimal transport constraint.
result Equilibrium exists in a market with multiple assets and non-Gaussian prices.
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.
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.
Method extracts governing laws from non-Gaussian stochastic systems data.
problem Modeling complex dynamics with non-Gaussian Lévy noise.
method Data-driven method to extract stochastic dynamical systems from noisy data.
result Established a theoretical framework and numerical algorithm to compute Lévy jump measure, drift, and diffusion.
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.
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.
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.
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…