A new method improves likelihood-free Bayesian inference by transforming summary statistics and using efficient Variational Bayes.
problem Incorrectly assuming normally distributed summary statistics in likelihood-free Bayesian inference.
method Wasserstein Gaussianization transformation combined with robust BSL and efficient Variational Bayes.
result Highly efficient and reliable approximate Bayesian inference for likelihood-free problems.
SGPA calibrates transformer uncertainty for safety-critical tasks.
problem Uncertainty estimation in transformer models for safety-critical domains.
method Bayesian inference in transformer's output space using sparse Gaussian processes.
result SGPA-based Transformers improve in-distribution calibration and out-of-distribution robustness.
Algorithm learns polynomial transformations of Gaussian distributions.
problem Learning high-dimensional polynomial transformations of Gaussian distributions.
method Polynomial-time algorithms for smoothed settings, tensor ring decomposition.
result First end-to-end guarantees for learning pushforwards under neural networks.
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.
Gaussianization flows transform any random vector into a Gaussian, enabling efficient computation and sample generation.
problem Transforming any random vector into a Gaussian for efficient computation and sample generation.
method Iterative Gaussianization and normalizing flow model.
result Gaussianization flows are universal approximators and achieve better performance on tabular datasets.
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.
In this paper we consider the Gaussian thermostat ray transform on both closed Riemannian surfaces and compact Riemannian surfaces with boundary. We establish certain results on the injectivity of the thermostat ray transform and the surjectivity of its adjoint.
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.
Transformers converge linearly to optimal models for Gaussian mixtures classification.
problem Theoretical understanding of transformers' in-context classification.
method Gradient descent training of a single-layer transformer for Gaussian mixtures classification.
result Transformers converge linearly to globally optimal models for Gaussian mixtures classification.
TM-VI uses flexible transformation models to approximate complex posteriors in Bayesian models.
problem Approximating complex posteriors in Bayesian models with limited flexibility.
method Transformation models for variational inference (TM-VI).
result TM-VI allows accurate approximation of complex posteriors in models with one parameter and works in a mean-field fashion for multi-parameter models.
Diffusion Transformer captures spatial-temporal dependencies in sequential data.
problem Capturing rich spatial and temporal dependencies in sequential data.
method Established theoretical guarantees for diffusion transformers learning Gaussian process data.
result Spatial-temporal dependencies are captured within attention layers of diffusion transformers.
Deep Transformed Gaussian Processes extend TGPs with variational inference for scalable multi-layer modeling.
problem Flexible modeling of complex data distributions.
method DTGPs are a multi-layer model of TGPs using variational inference for scalability.
result DTGPs achieve good scalability and performance in multiple regression datasets.
A new method reparameterizes Gaussian noise for better flexibility and performance.
problem Improving the Gumbel-Softmax for better flexibility and performance.
method Invertible Gaussian Reparameterization (IGR) using modified softmax and transformations.
result IGR outperforms Gumbel-Softmax in various experiments.
Modified Wasserstein metric for Gaussian distributions, invariant to isometries.
problem Distance measurement for latent Gaussian distributions invariant to isometries.
method Modified Benamou-Brenier approach leading to a Procrustes Wasserstein metric.
result For Gaussian distributions, the metric reduces to Euclidean distance between eigenvalues.
Fast Bayesian inference with adaptable priors for real-time applications.
problem Intractable exact posterior computation limits Bayesian inference's adoption.
method Distribution Transformer architecture that learns mappings between priors and posteriors.
result Significant reduction in computation time from minutes to milliseconds.
Transformers can cluster data from Gaussian mixtures without supervision.
problem Clustering data from Gaussian mixtures without labeled data.
method Theoretical analysis of attention-based layers, focusing on a simplified two-head attention layer and an identity matrix attention layer.
result Attention-based layers can align with true mixture centroids and adapt to input-specific distributions.
Transformers solve Gaussian Mixture Models without supervision.
problem Solving Gaussian Mixture Models (GMMs) unsupervised.
method Proposes TGMM, a transformer-based framework for GMM tasks.
result Transformers can effectively solve GMM tasks, improving upon classical methods.
Variational Auto-Encoders enforce their learned intermediate latent-space data distribution to be a simple distribution, such as an isotropic Gaussian. However, this causes the posterior collapse problem and loses manifold structure which can be important for datasets such as facial images. A GAN can transform a simple…
VAEs and GANs use simple distributions and neural networks to implicitly approximate complex data distributions.
problem Approximating high-dimensional complex distributions explicitly is often intractable.
method VAEs and GANs use simple base distributions and neural networks to implicitly approximate complex distributions.
result Implicit approximation of complex distributions is crucial but introduces limitations, especially in VAEs with fixed Gaussian priors.
Neural network models transform physical systems into latent Gaussian distributions.
problem Simplifying and solving classical Hamiltonian systems.
method Symplectic neural networks for canonical transformations.
result Captures nonlinear collective modes in latent space.
A new method models volatile financial time series using v-transforms and copulas.
problem Modeling volatile financial time series with standard methods.
method v-transforms and copulas to describe and estimate time series with arbitrary marginal distributions and copula dynamics.
result The model replicates stylized facts of financial return series and facilitates risk quantification.
Methodology for visualizing labeled datasets with mixed features.
problem Visualization of labeled mixed-featured datasets.
method Developed a Max-Ratio Projection (MRP) method for continuous features and extended it to datasets with discrete and continuous features using Gaussianized distributional transforms and copula models.
result Visualization of labeled mixed-featured datasets using Max-Ratio Projection and Gaussianized distributional transforms.
Tensorized Rademacher projections outperform Gaussian projections in reducing tensor dimensions.
problem Reducing the dimension of high-dimensional tensors for machine learning.
method Tensorized Rademacher random projections using Tensor Train decomposition.
result Tensorized Rademacher projections can replace Gaussian projections in tensor compression.
DGPs collapse to near-deterministic transformations, limiting their compositional structure discovery.
problem Limitations of variational inference in DGPs lead to suboptimal posterior approximations.
method Examine alternative variational inference schemes allowing for dependencies across different layers.
result Alternative variational inference schemes can better capture the compositional structure in DGPs.
This paper proposes a new RV prediction model using neural distributional transformation and co-training.
problem Predicting skewed and fat-tailed realized volatility (RV) is challenging.
method The paper uses a neural distributional transformation and co-training to predict RV. It jointly trains the transformation and prediction model using a maximum-likelihood objective function.
result The proposed method significantly outperforms other methods on a dataset of 100 stocks.
Improves data normality with robust transformations.
problem Skewed data distribution.
method Modified Box-Cox and Yeo-Johnson transformations with robust parameter estimation.
result Transformed data approximates normality in the center with outliers.
In this paper, we propose novel strategies for neutral vector variable decorrelation. Two fundamental invertible transformations, namely serial nonlinear transformation and parallel nonlinear transformation, are proposed to carry out the decorrelation. For a neutral vector variable, which is not multivariate Gaussian d…
The inference of deep hierarchical models is problematic due to strong dependencies between the hierarchies. We investigate a specific transformation of the model parameters based on the multivariate distributional transform. This transformation is a special form of the reparametrization trick, flattens the hierarchy a…
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.
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.
Efficient algorithm learns mixture models of heavy-tailed distributions.
problem Learning mixture models of heavy-tailed distributions.
method Efficient high-dimensional sparse Fourier transforms.
result Algorithm succeeds for heavy-tailed distributions, including Laplace but excluding Gaussians.
Based on the stochastic model proposed by Patriarca-Kaski-Chakraborti that describes the exchange of wealth between n economic agents, we analyze the evolution of the corresponding economies under the assumption of a Gaussian background, modeling the exchange parameter ε. We demonstrate, that within Gaussian noise,…
TTF improves performance of normalizing flows for heavy-tailed distributions.
problem Improving performance of normalizing flows for heavy-tailed distributions.
method Uses a Gaussian base distribution and a final transformation layer to produce heavy tails.
result Experimental results show TTF outperforms current methods, especially in high-dimensional or heavy-tailed scenarios.
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.
Transformers improve with Fourier integral attentions.
problem Inefficiency of dot-product attention in capturing feature dependencies.
method Interpreted attention as kernel regression, proposed FourierFormer with generalized Fourier integral kernels.
result FourierFormer achieves better accuracy and reduces redundancy.
Paper analyzes infinite-width attention layers using Tensor Programs.
problem Capturing the infinite-width limit of attention layers.
method Tensor Programs framework to rigorously identify the limit distribution.
result Derives exact form of infinite-width limit distribution without Gaussian approximations.
Transformers can approximate posterior predictive distributions through in-context learning.
problem Bayesian prediction tasks, especially beyond point predictions.
method Gradient descent algorithm targeting posterior predictive mean and variance, followed by nonlinear mappings.
result Transformers can implement algorithms to approximate posterior predictive distributions.
Transformer improves parameter estimation without needing closed-form solutions.
problem Parameter estimation in statistics, especially for complex distributions.
method Transformer-based approach for parameter estimation without closed-form solutions or derivations.
result Transformer-based approach achieves similar or better accuracy than maximum likelihood estimation.
GTMs model complex multivariate data with varying conditional independencies.
problem Modeling multivariate data with intricate marginals and complex dependency structures.
method Semiparametric approach using penalized splines and lasso regularization.
result GTMs accurately learn complex dependencies and identify conditional independencies.
A Fourier transform approach optimizes clustering algorithms.
problem Optimizing clustering algorithms for accuracy and reliability.
method Fourier transform and Gaussian filtering to smooth density functions, detecting peaks as cluster centroids.
result Remarkable accuracy in finding cluster centroids, overcoming initialization problems.
Bayesian model for discrete data with conditional transformations.
problem Handling discrete ordinal and count data with excess zeros.
method Bayesian framework with conditional transformation functions and modular MCMC algorithm.
result Flexible modeling of linear and nonlinear covariate effects for ordinal and count data.
In this paper, we propose an auto-encoder based generative neural network model whose encoder compresses the inputs into vectors in the tangent space of a special Lie group manifold: upper triangular positive definite affine transform matrices (UTDATs). UTDATs are representations of Gaussian distributions and can strai…
FTIP uses normalizing flows to improve posterior inference in function space.
problem Challenges in posterior inference with implicit-process priors.
method FTIP uses normalizing flows to define a richer variational distribution over combination weights.
result FTIP captures asymmetric and multimodal posterior structure better than Gaussian coefficient approximations.
Transformers interpret as probabilistic mixtures, offering new insights.
problem Understanding Transformers from a probabilistic perspective.
method Modeling Transformers as mixtures of Gaussian models.
result Transformers can be seen as maximum posterior probability estimators.
Transformer with denoising diffusion improves probabilistic density estimation.
problem Estimating non-Gaussian and multimodal probability distributions for regression problems.
method Training a denoising diffusion head on top of a Transformer model.
result The model provides reasonable probability density estimation for high-dimensional inputs.
Two methods improve Gaussian process predictive distributions' calibration.
problem Improving the reliability of Gaussian process predictive intervals.
method Introduces two methods: cps-gp and bcr-gp, both adapting conformal predictive systems to GP interpolation.
result Both methods provide finite-sample marginal calibration and smooth predictive distributions.
The paper provides theoretical guarantees for transformation-based models in variational inference.
problem Theoretical justification for transformation-based models in variational inference.
method Theoretical analysis of non-linear latent variable models and Gaussian process priors.
result Theoretical guarantees for implicit variational inference, achieving optimal risk bounds and approximating the true posterior.
Researchers derive an explicit Laplace transform for integrated Volterra Wishart process.
problem Modeling and pricing financial instruments with complex covariance structures.
method Explicit expression for conditional Laplace transform of integrated Volterra Wishart process, linking to matrix Riccati equations.
result Derivation of Laplace transform for a special case of convolution kernel, leading to efficient pricing methods.