Simplified proof of Gaussian concentration inequality using covariance.
problem Gaussian concentration inequality proof
method Covariance representation based on characteristic functions
result Elementary proof of Gaussian concentration inequality
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48 results for “Gaussian representations”
CKA with Gaussian RBF kernels converges linearly as bandwidth increases.
problem Understanding the behavior of CKA with large bandwidth Gaussian kernels.
method Analyzing the convergence of CKA based on Gaussian RBF kernels in the large-bandwidth limit.
result CKA based on Gaussian RBF kernels converges linearly as bandwidth increases.
Ens-CGP synthesizes ensemble-based inference with Gaussian processes.
problem Ensemble-based inference and Gaussian process modeling.
method Formulates Ens-CGP as a conditional Gaussian process for ensemble moments.
result Ens-CGP provides a unified probabilistic foundation for Kalman-type methods.
Generalized Gaussian Bridgesmath.PR
A generalized bridge is the law of a stochastic process that is conditioned on N linear functionals of its path. We consider two types of representations of such bridges: orthogonal and canonical. The orthogonal representation is constructed from the entire path of the underlying process. Thus, future knowledge of the …
Proposes a Bayesian Autoencoder with sparse Gaussian process priors to capture data correlations.
problem Autoencoders' i.i.d. assumption of latent representations fails to capture data correlations.
method Imposes fully Bayesian sparse Gaussian Process priors on the latent space of a Bayesian Autoencoder and uses stochastic gradient Hamiltonian Monte Carlo for posterior estimation.
result Consistently outperforms alternatives relying on Variational Autoencoders on various tasks.
The Information Bottleneck (IB) is a conceptual method for extracting the most compact, yet informative, representation of a set of variables, with respect to the target. It generalizes the notion of minimal sufficient statistics from classical parametric statistics to a broader information-theoretic sense. The IB curv…
A new method for Gaussian filtering using gradient flows and Wasserstein metrics.
problem Approximating Gaussian and mixture-of-Gaussians filtering for complex systems.
method Variational approximation via gradient-flow representation on Wasserstein metric space.
result Competitive performance in posterior representation and parameter estimation for systems with multiplicative noise and multi-modal distributions.
New theory explains deep learning's success in transforming inputs.
problem Standard theoretical approaches eliminate representation learning.
method Developed a new infinite width limit for representation learning.
result Deep Gaussian processes (DGPs) have multivariate Gaussian posteriors.
Develops a smooth operator framework for analyzing neural network representations.
problem Analyzing the geometry of feedforward neural network representations.
method Introduces a smooth operator-theoretic approach based on diffusion Markov operators derived from feature clouds.
result Establishes a stable operator-geometric framework for tracking training, width, and perturbation stability.
A new probabilistic polygonal curve representation using Gaussian Mixture Models.
problem Capturing curves with uncertainty in both tangent and normal directions.
method Probabilistic polygonal approximation with Gaussian Mixture Model (GMM).
result The GMM accurately captures the local geometry and uncertainty of curves.
Topic models are widely used to discover the latent representation of a set of documents. The two canonical models are latent Dirichlet allocation, and Gaussian latent Dirichlet allocation, where the former uses multinomial distributions over words, and the latter uses multivariate Gaussian distributions over pre-train…
Proposes NUV priors for half-space and box constraints.
problem Adding constraints to linear Gaussian models without computational cost.
method Introduces NUV representations for half-space and box constraints.
result Adds constraints to linear Gaussian models without affecting computational tractability.
This work brings together two powerful concepts in Gaussian processes: the variational approach to sparse approximation and the spectral representation of Gaussian processes. This gives rise to an approximation that inherits the benefits of the variational approach but with the representational power and computational …
Gaussian Measures Conditioned on Nonlinear Observations: Consistency, MAP Estimators, and Simulationstat.ML
Study on conditioning Gaussian measures on nonlinear observations, including representer theorem and mode estimation.
problem Conditioning Gaussian measures on nonlinear observations in Bayesian inference and machine learning.
method Representer theorem, novel mode definition, maximum a posteriori estimation, Laplace approximation.
result Identification of infinite-dimensional Gaussian and finite-dimensional non-Gaussian components in conditioned measures.
Inference via Interpolation: Contrastive Representations Provably Enable Planning and Inferencecs.LG
The paper shows how to answer future and past questions from high-dimensional time series data.
problem Challenges in answering probabilistic inference questions from high-dimensional time series data.
method Temporal contrastive learning to learn Gaussian representations that enable compact closed-form solutions.
result Representations learned via contrastive learning follow a Gauss-Markov chain, enabling efficient inference and planning.
Identifiability of Potentially Degenerate Gaussian Mixture Models With Piecewise Affine Mixingstat.ML
Method identifies latent variables from high-dimensional data with piecewise affine mixing.
problem Identifying latent variables from high-dimensional observations with dependencies and piecewise affine transformations.
method Proposes a two-stage method with sparsity and Gaussianity regularization.
result Effectively recovers ground-truth latent variables from synthetic and image data.
Improved Gaussian process models for interpretable predictions.
problem Complex responses require high-dimensional interaction terms in additive Gaussian processes.
method Orthogonal additive kernel (OAK) with orthogonality constraint on additive functions.
result OAK models achieve similar or better predictive performance with fewer terms, retaining interpretability.
Smoothed SGD improves quantile estimation without crossing curves.
problem Estimating quantiles without crossing estimated curves.
method Smoothed SGD algorithm with Bahadur representation and Gaussian approximation.
result Smoothed SGD provides non-asymptotic tail probability bounds and a Gaussian approximation for quantile estimates.
DeepCCG adapts classifiers to representation shifts in one step.
problem Adapting classifiers to shifts in continuous representation.
method Empirical Bayesian approach using class conditional Gaussian classifier and KL divergence for selection.
result DeepCCG reduces performance change due to representation shifts.
Generalization Guarantees for Representation Learning via Data-Dependent Gaussian Mixture Priorsstat.ML
The study improves representation learning bounds using data-dependent Gaussian mixtures.
problem Improving generalization in representation learning.
method Established bounds using relative entropy and MDL of latent variables.
result The approach significantly improves generalization over existing methods.
Minimalistic model captures head direction system properties.
problem Representing head direction system in a high-dimensional space.
method A minimalistic representation model of the rotation group U(1), including fully connected and convolutional versions.
result Emergence of Gaussian-like tuning profiles and 2D circle geometry in both model versions.
New method learns disentangled discrete representations using categorical variational autoencoders.
problem Learning disentangled representations from discrete latent spaces.
method Replaced standard Gaussian VAE with a categorical VAE to mitigate rotational invariance.
result Categorical distributions improve learning of disentangled representations.
Paper estimates Gaussian curvature of minimal graphs in a specific manifold.
problem Estimating Gaussian curvature of minimal graphs in .
method Using Weierstrass representation via harmonic mappings and Schwarz lemma type results.
result Proves Schwarz lemma type and Heinz type results for harmonic mappings.
Proposes diffusion models using mixed Gaussian priors for better data representation.
problem Improving data representation in diffusion models.
method Structured diffusion models with a mixture of Gaussians as prior.
result Improved model performance compared to classical diffusion models.
Gaussian processes for dynamical systems with Koopman equivariance.
problem Forecasting and learning representations of nonlinear dynamical systems.
method Koopman-equivariant Gaussian processes with linear time-invariant responses and trajectory-based equivariance.
result Enhanced forecasting performance compared to kernel-based methods.
We pursue an early stopping technique that helps Gaussian Restricted Boltzmann Machines (GRBMs) to gain good natural image representations in terms of overcompleteness and data fitting. GRBMs are widely considered as an unsuitable model for natural images because they gain non-overcomplete representations which include…
The state space (SS) representation of Gaussian processes (GP) has recently gained a lot of interest. The main reason is that it allows to compute GPs based inferences in O(n), where is the number of observations. This implementation makes GPs suitable for Big Data. For this reason, it is important to provide a SS …
Study cost-driven state representation learning for control from partial observations.
problem Learning state representation for control from partial and high-dimensional observations.
method Cost-driven state representation learning via predicting cumulative costs.
result Established finite-sample guarantees for near-optimal representation and controller.
The paper studies multi-view representation learning with generalization guarantees and a new regularizer.
problem Distributed multi-view representation learning with correct estimation at a decoder.
method Generalization bounds using relative entropy and MDL, data-dependent Gaussian mixture priors.
result Data-dependent Gaussian mixture priors lead to good performance and outperform existing methods.
Efficiently searches through Gaussian process kernels using symbolic representation and Bayesian optimization.
problem Manual selection of kernels in Gaussian processes is complex and computationally expensive.
method Proposes a novel method using symbolic representation and Bayesian optimization to search through a structured kernel space.
result Empirically shows a computationally more efficient way of searching through a discrete kernel space.
The paper proposes a new framework for accurate uncertainty representation and propagation.
problem Inaccurate representation and propagation of uncertainty in measurement systems.
method The paper introduces a comprehensive framework using Gaussian Mixture Models (GMMs) for representing and propagating quantitative attributes in measurement systems.
result GMMs offer improved accuracy in representing and propagating measurement uncertainty compared to traditional Gaussian methods, while maintaining computational tractability.
Bayesian approach approximates probability functions of Gaussian mixtures.
problem Approximating probability functions of non-spherical Gaussian mixtures.
method Bayesian decomposition, spherical radial decomposition, random sampling.
result Established differentiability and integral representation of gradient for probability functions.
A model learns causal representations from high-dimensional data.
problem Challenges in learning causal representations from high-dimensional data.
method Formulated a latent variable decoder model, Decoder BCD, for Bayesian causal discovery.
result Shows that using known intervention targets as labels helps in unsupervised Bayesian inference over structure and parameters.
Learning word representations has garnered greater attention in the recent past due to its diverse text applications. Word embeddings encapsulate the syntactic and semantic regularities of sentences. Modelling word embedding as multi-sense gaussian mixture distributions, will additionally capture uncertainty and polyse…
tvGP-VAE models tensor-valued latent variables with Gaussian processes for better data structure representation.
problem Agnostic latent variables in VAEs ignore data structure correlations.
method Proposes tensor-variate Gaussian process prior for variational autoencoder.
result Explicitly modeling correlation structures improves model performance in reconstruction.
The paper analyzes meta-learning in a Gaussian setting, providing bounds and matching algorithms.
problem Understanding how task distributions influence transfer risk in meta-learning.
method Fixed design linear regression with Gaussian noise, Gaussian task distribution, weighted biased regularized regression method.
result A novel weighted version of biased regularized regression method matches distribution-dependent lower bounds on transfer risk up to a constant factor.
The study investigates deformations of swallowtails in 3D space, preserving curvature signs.
problem Deforming swallowtails in 3D space while maintaining curvature signs.
method Representation formula for swallowtails, investigation of map germs, and analysis of Gaussian curvatures.
result Swallowtails can be deformed into a swallowtail of constant Gaussian curvature while preserving curvature signs.
Meta-learning neural networks for better clustering representations.
problem Improving clustering performance with appropriate representations.
method Meta-learning method that trains neural networks for representations using VB inference with an infinite Gaussian mixture model.
result The method achieves higher clustering performance than existing methods.
LVM-GP solves PDEs with uncertainty using latent variables and Gaussian processes.
problem Uncertainty quantification in PDE solutions with noisy data.
method Combines latent variable model and Gaussian process for uncertainty-aware prediction.
result Efficiently captures functional dependencies and robust uncertainty quantification.
In this we paper we recast the Cox--Ingersoll--Ross model of interest rates into the chaotic representation recently introduced by Hughston and Rafailidis. Beginning with the ``squared Gaussian representation'' of the CIR model, we find a simple expression for the fundamental random variable X. By use of techniques fro…
CVAE learns disentangled and coupled representations without prior knowledge.
problem Learning disentangled and coupled representations in latent space.
method Introduces CVAE, a self-supervised VAE that factorizes posterior and uses Gaussian copula for dependencies.
result Demonstrates strong effect in enhancing disentangled representation learning.
The Dynamical Gaussian Process Latent Variable Models provide an elegant non-parametric framework for learning the low dimensional representations of the high-dimensional time-series. Real world observational studies, however, are often ill-conditioned: the observations can be noisy, not assuming the luxury of relative…
Meta learning with information theory and Gaussian processes.
problem Few-shot learning problems.
method Information bottleneck, mutual information, variational approximations, Gaussian processes.
result Competitive accuracy on few-shot classification problems.
We simplify matrix computations for block matrices, especially useful for covariance and correlation matrices.
problem Complex computations for block matrices, especially for covariance and correlation matrices.
method Obtained a canonical representation for block matrices, facilitating computation of various matrix operations.
result Simplified computation of matrix operations for block matrices, particularly useful for covariance and correlation matrices.
Study learns state representations from observations for control, proving guarantees.
problem Learning state representations from high-dimensional observations for control.
method Cost-driven approach, learning latent state model to predict costs.
result Proves finite-sample guarantees for near-optimal state representation and controller.
A fundamental question in deep learning concerns the role played by individual layers in a deep neural network (DNN) and the transferable properties of the data representations which they learn. To the extent that layers have clear roles, one should be able to optimize them separately using layer-wise loss functions. S…
UT module refines VAE latent space, improving disentanglement and interpretability.
problem Irregular latent distributions cause posterior collapse and misalignment in VAEs.
method UT module uses G-KDE clustering, GM modeling, and PIT to transform latent space into uniform distribution.
result UT module enhances disentanglement and interpretability of latent representations.
Off-the-shelf Gaussian Process (GP) covariance functions encode smoothness assumptions on the structure of the function to be modeled. To model complex and non-differentiable functions, these smoothness assumptions are often too restrictive. One way to alleviate this limitation is to find a different representation of …