The paper defines MTCov for skewed elliptical distributions.
problem No specific problem stated, but dealing with skewed elliptical distributions.
method Defined MTCov for generalized skew-elliptical distributions and compared with skewed and non-skewed normal distributions.
result Special formula for MTCov of generalized skew-elliptical distributions.
Paper proposes a new method for designing materials using deep learning.
problem Designing high-performance material distributions from given distributions.
method Iterative process of selecting, generating, and merging material distributions using a deep generative model.
result The method improves material performance through iterative refinement.
Study on continuous sequence classification with distribution uncertainty.
problem Classifying continuous sequences with varying distribution uncertainty.
method Proposes distribution-free tests for three test designs: fixed-length, sequential, and two-phase tests.
result Error probabilities decay exponentially fast for all test designs.
The paper calculates moments and conditional risks for skewed elliptical distributions.
problem Estimating moments and tail conditional risks for skewed elliptical distributions.
method Derives explicit expressions for multivariate doubly truncated moments and conditional risks for generalized skew-elliptical distributions.
result Explicit formulas for multivariate doubly truncated moments and conditional risks are derived for various skewed elliptical distributions.
New method ensures generated data statistics match real data distributions.
problem Ensuring generated data statistics match real data distributions in GANs.
method Added a new loss term to the generator loss function using f-divergences and kernel density estimation.
result Improved performance on synthetic and real-world datasets.
New polynomial convergence guarantees for SGM on general data distributions.
problem Efficient guarantees for multimodal and non-smooth distributions in SGM.
method Polynomial convergence guarantees for denoising diffusion models on general data distributions, with no assumptions on functional inequalities or smoothness.
result Wasserstein distance guarantees for distributions of bounded support or decaying tails, and TV guarantees for further smoothness assumptions.
Proves Sard conjecture for specific distributions, controlling divergence of vector fields.
problem Proving the Sard conjecture for certain types of distributions.
method Constructs a singular distribution capturing essential abnormal lifts, proving the conjecture for rank 3 distributions in dimension 4 and generic corank 1 distributions.
result Proves the Sard conjecture for generic co-rank one distributions.
Study on how kernel regression models generalize to out-of-distribution data.
problem Understanding generalization in machine learning models under distributional shifts.
method Replica method from statistical physics to derive analytical formula for generalization error.
result Identified overlap matrix as key determinant of generalization performance under distribution shift.
Generates samples conditioned on labels using optimal transport.
problem Estimating conditional distributions for specific labels.
method Wasserstein geodesic generator based on optimal transport theory.
result Learned conditional distributions and optimal transport maps.
Generative Distribution Embeddings learn multiscale representations of distributions.
problem Learning representations of entire distributions for multiscale reasoning.
method Introducing GDE framework that lifts autoencoders to the space of distributions, using conditional generative models and distributional invariance.
result GDEs learn predictive sufficient statistics embedded in Wasserstein space, recovering distances and trajectories for Gaussian and Gaussian mixture distributions.
BDSG generates samples on distribution boundaries, improving anomaly detection.
problem Difficulty in capturing multimodal supports and approximating distribution tails.
method Invertible Residual Network (IResNet) and Residual Flow (ResFlow) for density estimation; compound loss function for boundary samples.
result Competitive performance on synthetic and multimodal data compared to existing methods.
Improved likelihood estimation for singular distributions using deep models.
problem Estimating singular distributions using deep generative models.
method Data perturbation to avoid singularity issues in likelihood estimation.
result Consistent estimation of target distribution with desirable rates.
Recent work has shown that deep generative models assign higher likelihood to out-of-distribution inputs than to training data. We show that a factor underlying this phenomenon is a mismatch between the nature of the prior distribution and that of the data distribution, a problem found in widely used deep generative mo…
Smooth distributions on subcartesian spaces can be globally finitely generated.
problem Understanding smooth distributions on subcartesian spaces.
method Embedding in Euclidean space, Whitney Embedding Theorem, and distribution theory.
result Smooth generalized distributions and subbundles on connected subcartesian spaces are globally finitely generated.
New theory of distributions on spaces with singular submanifolds.
problem Defining distributions on spaces with singular submanifolds.
method Construction of thick distributions, operations, and special distributions.
result Clarified connection between thick and classical distributions.
GANs learn distributions by matching low-degree moments.
problem Understanding when GANs learn the target distribution efficiently.
method Theoretical analysis and empirical observation of GAN training process.
result GANs can learn notable distributions by matching polynomially many low-degree moments.
Paper introduces CWDAE for better synthetic data generation.
problem Measuring discrepancy between generative and ground-truth distributions.
method Introduces mixture Cramer-Wold distance for joint and marginal distributional learning.
result CWDAE shows remarkable performance in generating synthetic data.
This note shows how independent elliptical distributions minimize the Wasserstein distance.
problem Minimizing the Wasserstein distance between elliptical distributions.
method Analyzing the Wasserstein distance between independent elliptical distributions with the same density generators.
result Independent elliptical distributions minimize their Wasserstein distance from other elliptical distributions with the same density generators.
DCMA uses generative models to analyze treatment effects on entire outcome distributions.
problem Traditional mediation analysis focuses on summary contrasts, missing complex distributional changes.
method DCMA learns conditional generative models for mediators and outcome, reconstructing interventional distributions via Monte Carlo simulation.
result DCMA captures both summary effects and rich distributional contrasts like energy distance and Wasserstein distance.
DCMA uses generative models to analyze complex treatment effects on outcome distributions.
problem Analyzing complex and nonlinear causal mechanisms through outcome-level summary contrasts.
method Generative learning framework for identifying and estimating treatment effects on entire outcome distributions.
result Reconstructs interventional outcome distributions via Monte Carlo forward simulation, capturing both summary and distributional contrasts.
Generative models help make decisions under changing data distributions.
problem Making decisions based on historical data when the actual data distribution changes.
method Flow- and score-based generative models to represent and transform distributions.
result Generative models can learn nominal uncertainty, create stressed distributions, and produce conditional distributions.
GRAM enhances deep RL for reliable real-world deployment.
problem Generalizing deep RL across in-distribution and out-of-distribution scenarios.
method Introduces a robust adaptation module and a joint training pipeline.
result GRAM achieves strong generalization performance in simulations and hardware.
Deep neural networks can generate any 2D distribution with high accuracy.
problem Generating accurate high-dimensional distributions from random noise.
method A deep neural network with a space-filling property of sawtooth functions.
result The network can approximate any 2D Lipschitz-continuous distribution arbitrarily closely.
In this study, a numerical quadrature for the generalized inverse Gaussian distribution is derived from the Gauss-Hermite quadrature by exploiting its relationship with the normal distribution. The proposed quadrature is not Gaussian, but it exactly integrates the polynomials of both positive and negative orders. Using…
New approach to Generalized Beta family using SDEs.
problem Understanding the Generalized Beta family of distributions.
method Using a mean-reverting SDE for a power of the variable, leading to a modified GB distribution.
result Provides alternative forms and cumulative distribution functions for GB distributions.
Constructs canonical frames for specific distributions, proving maximality and describing germs.
problem Local geometry of rank 2 distributions with specific cube dimensions.
method Uniform construction of canonical absolute parallelism, iterative Cartan deprolongation.
result Automatic maximality condition holds at generic points, covering all cases.
The paper uses FRFT to fit GTS distribution to asset returns.
problem Modeling asset returns with GTS distribution.
method Fractional Fourier Transform (FRFT) for fitting.
result GTS distribution fits SPY ETF and Bitcoin BTC returns.
New generalization concept considers distribution of errors, not just average error.
problem Classical generalization fails to capture distributional differences in classifier outputs.
method Formal conjectures about distributional generalization based on model architecture, training procedure, and data distribution.
result Distributional generalization can be expected in specific conditions, as evidenced by empirical results.
New RL algorithm minimizes distributional learning error.
problem Improving distributional reinforcement learning for better error minimization.
method Proposes a new model-based algorithm with theoretical minimax optimality.
result Proves minimax optimality for approximating return distributions.
Analyzes generalization error in distributed linear regression.
problem Understanding generalization performance in distributed learning.
method Analytical characterization of generalization error in linear regression with distributed learning.
result Generalization error increases dramatically when nodes estimate close to the number of observations.
Random variables of the generalized Pareto distribution, can be transformed to that of the Pareto distribution. Explicit expressions exist for the maximum likelihood estimators of the parameters of the Pareto distribution. The performance of the estimation of the shape parameter of generalized Pareto distributed using …
ADB framework improves OOD generalization by increasing ID bias during training.
problem Machine learning models degrade on new data distributions.
method ADB framework introduces controlled statistical diversity during training.
result Higher in-distribution bias leads to better out-of-distribution generalization.
Paper proposes a new generative model for discrete distributions using flows on submanifolds.
problem Discretization issues and complex statistical dependencies in discrete data.
method Continuous normalizing flows on factorizing discrete measures, geodesic flow matching.
result Efficient training and broad applicability demonstrated through experiments.
Developments in deep generative models have allowed for tractable learning of high-dimensional data distributions. While the employed learning procedures typically assume that training data is drawn i.i.d. from the distribution of interest, it may be desirable to model distinct distributions which are observed sequenti…
A new distribution family extends the α-stable distribution with a degree of freedom parameter.
problem Lack of moments in the α-stable distribution. method Wright function framework to combine and extend distribution families.
result Generalized α-stable distribution with valid moments. A quantum walk-based method for generating precise probability distributions efficiently.
problem Generating high-precision probability distributions for various applications.
method Integrates variational quantum circuits with split-step quantum walks to dynamically tune coin parameters and evolve quantum states.
result Achieves high simulation fidelity and reduces computational overhead compared to conventional methods.
Evidential Softmax preserves multimodality in sparse probability distributions for generative models.
problem Sparse probability distributions in deep generative models make exact marginalization computationally intractable.
method Introduce ev-softmax, a sparse normalization function that preserves multimodality and can be trained with probabilistic loss functions.
result ev-softmax outperforms existing techniques in distributional accuracy and dimensionality reduction.
Paper explores how text generation quality and diversity metrics relate to distribution fitting.
problem Unclear relation between text generation quality and diversity metrics and distribution fitting.
method Theoretical approach to prove a linear combination of quality and diversity metrics can be a divergence metric.
result CR/NRR proposed as a better substitute for BLEU/Self-BLEU metrics.
New method generates molecular conformations efficiently.
problem Generating accurate molecular conformations efficiently.
method Variational approximation of rotatable bond torsion angles as a mixture of von Mises distributions.
result VonMisesNet generates conformations orders of magnitude faster than existing methods.
Quantum models learn unitary actions on entangled states from product states.
problem Generalization to out-of-distribution data in quantum machine learning.
method Proved out-of-distribution generalization for learning unitary actions.
result Learned unitary actions on entangled states from product states.
Four new methods for computing generalized chi-square distribution.
problem Computing the generalized chi-square distribution accurately and efficiently.
method Two exact and two approximate methods, with software for cdf, pdf, and inverse cdf.
result Comparison of methods' accuracy and speed, identifying best for different cases.
RML improves generative modeling of complex distributions.
problem Learning complex distributions in applications.
method RML defines a forward process to a known distribution, then learns a reverse Markov process.
result RML efficiently captures complex distributions in simulations and climate data.
In this paper, we discuss spectral properties of Laplacians associated with an arbitrary smooth distribution on a compact manifold. First, we give a survey of results on generalized smooth distributions on manifolds, Riemannian structures and associated Laplacians. Then, under the assumption that the singular foliation…
The paper explores solutions to the distributional Bellman equation in reinforcement learning.
problem Distributional reinforcement learning considers complete return distributions, not just expected returns.
method Study existence and uniqueness of solutions to general distributional Bellman equations, linking them to multivariate affine equations.
result Any solution to a distributional Bellman equation can be derived from a multivariate affine distributional equation.
Method learns conditional distributions using neural entropic optimal transport.
problem Challenges in learning multiple conditional distributions.
method Neural entropic optimal transport method with two networks and regularization.
result Effective learning of conditional distributions with limited samples.
Researchers develop a method to generate diffusion-based samples from a tilted distribution.
problem Generating samples from a distribution that has been tilted by a parameter.
method Developed a plug-in estimator and proved Wasserstein bounds and TV-accuracy under certain conditions.
result The method is minimax-optimal and can be applied in various domains like finance and climate modeling.
Deep networks can approximate high-dimensional distributions from low-dimensional ones.
problem Approximating high-dimensional distributions from low-dimensional ones.
method Proved neural networks can transform low-dimensional distributions to high-dimensional ones with arbitrary closeness measured by Wasserstein distances and maximum mean discrepancy.
result Upper bounds of the approximation error are obtained in terms of the width and depth of neural network.
RIA method improves OoD generalization for covariate shift.
problem Improving out-of-distribution generalization under covariate shift.
method Adversarial label invariant graph data augmentations for OoD generalization.
result RIA method achieves high accuracy compared to OoD baselines.