A new method trains discrete EBMs without sampling.
problem Training EBMs on discrete spaces is hard.
method Energy Discrepancy (ED), a contrastive loss.
result ED offers theoretical guarantees for various perturbation types.
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48 results for “discrepancy energy”
Paper introduces a modified Allen-Cahn equation for better energy equipartition.
problem Improving energy equipartition in mean curvature flow.
method Developed a modified Allen-Cahn equation (MAC) by time-dependent parameter and Z-transform.
result Improved estimate on discrepancy energy for better equipartition.
A new loss function ED simplifies training energy-based models without scores.
problem Training energy-based models is computationally expensive.
method Energy Discrepancy (ED) loss function that does not rely on scores or MCMC.
result ED effectively interpolates between score matching and negative log-likelihood.
New foliations found for critical surfaces of Hawking energy, resolving discrepancies.
problem Finding consistent critical surfaces for the Hawking energy in non-totally geodesic spacelike hypersurfaces.
method Constructing a unique local foliation of area constrained critical surfaces of the Hawking energy in the general case of non-totally geodesic spacelike hypersurfaces.
result Discrepancy found in the small sphere limit of the Hawking energy, explained and resolved.
Energy distance measures feature heterogeneity in federated learning.
problem Heterogeneity across data sources hinders model aggregation in federated learning.
method Introduced Taylor approximations of energy distance for efficient computation.
result Taylor approximations accurately capture feature discrepancies, improving convergence.
A new method using energy distance for ensemble and scenario reduction.
problem Solving complex dynamic and stochastic programs, especially in energy systems.
method Proposes a new method based on energy distance for ensemble and scenario reduction.
result Reduced scenario sets exhibit better statistical properties for energy distance than Wasserstein distance.
A new framework SIMBA improves graph classification performance on size-imbalanced datasets.
problem Size imbalance in graph classification leads to poor model performance.
method Energy-guided structural smoothing between head and tail graphs, re-weighting based on energy propagation.
result SIMBA outperforms existing methods in size-imbalanced graph classification tasks.
On Rank Energy Statistics via Optimal Transport: Continuity, Convergence, and Change Point Detectionstat.ML
Paper uses optimal transport-based statistics for change point detection.
problem Change point detection in multivariate data.
method Soft rank energy and entropically regularized optimal transport.
result Soft rank energy performs better in real datasets with strong continuity and convergence properties.
Approximate Bayesian computation (ABC) has become an essential part of the Bayesian toolbox for addressing problems in which the likelihood is prohibitively expensive or entirely unknown, making it intractable. ABC defines a pseudo-posterior by comparing observed data with simulated data, traditionally based on some su…
We propose a notion of distance between two parametrized planar curves, called their discrepancy, and defined intuitively as the minimal amount of deformation needed to deform the source curve into the target curve. A precise definition of discrepancy is given as follows. A curve of transformations in the special Eucli…
Learning the Stein Discrepancy for Training and Evaluating Energy-Based Models without Samplingstat.ML
We present a new method for evaluating and training unnormalized density models. Our approach only requires access to the gradient of the unnormalized model's log-density. We estimate the Stein discrepancy between the data density and the model density defined by a vector function of the data. We paramete…
Paper presents variational estimates for EBLVMs without structural assumptions.
problem Challenges in learning and evaluating EBLVMs due to intractable true posteriors and partition functions.
method Variational estimates of the score function and its gradient (VaES and VaGES) in a general EBLVM.
result The estimates can be applied to KSD and SM-based methods to learn EBLVMs and estimate Fisher divergence.
We present an analysis of oil prices in US$ and in other major currencies that diagnoses unsustainable faster-than-exponential behavior. This supports the hypothesis that the recent oil price run-up has been amplified by speculative behavior of the type found during a bubble-like expansion. We also attempt to unravel t…
AI methods are energy-intensive, but efficiency alone isn't enough for sustainability.
problem AI methods are energy-intensive and contribute to climate change.
method Critically examines the limitations of efficiency in improving environmental sustainability of AI.
result Efficiency alone is insufficient to address the environmental impacts of AI.
Study on kernel tests for high-dimensional data, focusing on MMD and CLT.
problem Asymptotic behavior of kernel two-sample tests in high dimensions and large samples.
method Maximum mean discrepancy (MMD) with isotropic kernels, deriving asymptotic expansions and CLT.
result Interplay between moment discrepancy and dimension-and-sample orders in kernel tests.
Researchers introduce new energies to study constant scalar curvature metrics.
problem Understanding constant scalar curvature metrics on compact Kähler manifolds.
method Introduced a family of energies using Berman's quantization and intersection theory. Combined with non-Archimedean techniques, provided a uniform Yau-Tian-Donaldson correspondence.
result Uniform Yau-Tian-Donaldson correspondence characterizes the existence of a unique constant scalar curvature Kähler metric.
This research quantifies cross-sectoral inequalities using latent class analysis.
problem Addressing multiple and intersecting forms of inequality in various sectors.
method Innovative latent class analysis approach to quantify discrepancies.
result Significant discrepancies found among minority ethnic groups and between them and non-minority groups.
Quantum models face barren plateaus, but specific losses can be trainable.
problem Barren plateaus and loss concentration in quantum generative models.
method Investigated explicit and implicit losses, and their interplay.
result Explicit losses lead to new barren plateaus, while implicit losses can be trainable.
In this paper we are concerned with the learnability of energies from data obtained by observing time evolutions of their critical points starting at random initial equilibria. As a byproduct of our theoretical framework we introduce the novel concept of mean-field limit of critical point evolutions and of their energy…
New framework improves experimental design using integral probability metrics.
problem Challenges in Bayesian Optimal Experimental Design (BOED) with KL divergence.
method Integrates integral probability metrics (IPMs) for stability and flexibility.
result IPM-based designs yield more robust and accurate credible sets.
New biclustering algorithm in Hilbert spaces for complex data.
problem Discovering new biological functions in gene expression data.
method Model-free biclustering algorithm using energy distance and maximum mean discrepancy.
result The method can learn more general and complex cluster shapes.
Improved generative models using overparametrized shallow neural networks.
problem Improving generative models for data with hidden low-dimensional structure.
method Using energy-based models with overparametrized shallow neural networks as approximators.
result Models trained in the 'active' regime outperform those in the 'lazy' or kernel regime, leading to better adaptivity to hidden structure.
EBR improves NMT by re-ranking samples drawn from MLE-trained models.
problem Discrepancy between MLE and BLEU score in neural machine translation.
method Train an energy-based model to mimic BLEU score, then use it for re-ranking.
result EBR consistently improves NMT performance by +4 BLEU points on IWSLT'14 German-English.
Learning algorithms for implicit generative models can optimize a variety of criteria that measure how the data distribution differs from the implicit model distribution, including the Wasserstein distance, the Energy distance, and the Maximum Mean Discrepancy criterion. A careful look at the geometries induced by thes…
We provide a unifying framework linking two classes of statistics used in two-sample and independence testing: on the one hand, the energy distances and distance covariances from the statistics literature; on the other, maximum mean discrepancies (MMD), that is, distances between embeddings of distributions to reproduc…
Proposes a new method for posterior sampling using MMD with negative distance kernel.
problem Posterior sampling and conditional generative modeling.
method Approximates joint distribution using discrete Wasserstein gradient flows of MMD with negative distance kernel.
result Establishes an error bound for posterior distributions and proves the method is a Wasserstein gradient flow.
A physics-based method improves data interpolators and regression tasks.
problem Improving accuracy and efficiency in function learning.
method Inspired by statistical mechanics, introduces corrections to minimize energy.
result Improves performance in interpolation and regression tasks, especially in high-dimensional spaces.
EBMs trained on discrete data using heat equations on graph structures.
problem Training EBMs on discrete or mixed data.
method Heat equations on graph structures for data perturbation.
result Efficacy demonstrated in various applications.
FAST selects coresets more efficiently by matching distributions in the frequency domain.
problem Efficiently selecting representative subsets of large datasets for deep learning.
method FAST uses spectral graph theory and CFD to match distributions, addressing limitations of existing methods.
result FAST significantly outperforms state-of-the-art coreset selection methods in accuracy and energy efficiency.
Particle physics or High Energy Physics (HEP) studies the elementary constituents of matter and their interactions with each other. Machine Learning (ML) has played an important role in HEP analysis and has proven extremely successful in this area. Usually, the ML algorithms are trained on numerical simulations of the …
The limits of the nuclear landscape are determined by nuclear binding energies. Beyond the proton drip lines, where the separation energy becomes negative, there is not enough binding energy to prevent protons from escaping the nucleus. Predicting properties of unstable nuclear states in the vast territory of proton em…
We study the information content of nuclear masses from the perspective of global models of nuclear binding energies. To this end, we employ a number of statistical methods and diagnostic tools, including Bayesian calibration, Bayesian model averaging, chi-square correlation analysis, principal component analysis, and …
Paper explores Fisher-Rao gradient flows and their kernel approximations.
problem Understanding and analyzing approximations of Fisher-Rao gradient flows.
method Rigorous investigation of Fisher-Rao and Wasserstein type gradient flows, focusing on kernel approximations.
result Proves evolutionary Γ-convergence for kernel-approximated Fisher-Rao flows, providing theoretical guarantees.
Optimizes kernel discrepancies by selecting subsets efficiently.
problem Improving kernel discrepancies for QMC methods.
method Introduces a novel subset selection algorithm for kernel discrepancies.
result Efficiently generates low-discrepancy samples from various distributions.
Paper introduces a new method to improve GANs by leveraging the discriminator's energy.
problem Improving the quality of generated samples in GANs.
method Discriminator Contrastive Divergence (DCD) method.
result Significant improvement in generation quality on synthetic and real-world data.
New discrepancy function compares discrete probability measures considering space geometry.
problem Comparing discrete probability measures in a geometrically meaningful way.
method Proposes the Fourier Discrepancy Function, proving convexity, differentiability, and providing gradient formula.
result Proves the Fourier Discrepancy is convex, twice differentiable, and provides an explicit gradient formula.
This paper introduces localized discrepancy theories for unsupervised domain adaptation.
problem Improving generalization bounds for unsupervised domain adaptation.
method Localized discrepancies defined on the hypothesis space after localization, leading to smaller and asymmetric values.
result Improved generalization bounds and sample complexity reduction.
Maximum mean discrepancy (MMD), also called energy distance or N-distance in statistics and Hilbert-Schmidt independence criterion (HSIC), specifically distance covariance in statistics, are among the most popular and successful approaches to quantify the difference and independence of random variables, respectively. T…
The article introduces practical estimators for kernel discrepancies.
problem Estimating kernel discrepancies accurately and efficiently.
method Presented various estimators for MMD, HSIC, and KSD, including V-statistics, U-statistics, and incomplete U-statistics. Stressed the importance of kernel bandwidth and introduced adaptive estimators.
result Adaptive estimators combining multiple estimators with various kernels address the problem of kernel selection.
MPMC generates low-discrepancy points using graph neural networks.
problem Generating efficient low-discrepancy point sets.
method Leveraging Graph Neural Networks to model geometric properties.
result Achieves state-of-the-art performance in generating low-discrepancy points.
Sliced kernelized Stein discrepancy improves goodness-of-fit tests and model learning in high dimensions.
problem The curse-of-dimensionality in kernelized Stein discrepancy (KSD).
method Sliced Stein discrepancy and its scalable variants using optimal one-dimensional projections.
result Significantly outperforms KSD and baselines in goodness-of-fit tests and improves model learning.
Much of machine learning relies on comparing distributions with discrepancy measures. Stein's method creates discrepancy measures between two distributions that require only the unnormalized density of one and samples from the other. Stein discrepancies can be combined with kernels to define kernelized Stein discrepanc…
Study shows the corrected Akaike criterion is inadmissible for estimating Kullback-Leibler discrepancy.
problem Inadmissibility of the corrected Akaike information criterion for estimating Kullback-Leibler discrepancy.
method Loss estimation framework to demonstrate inadmissibility and provide improved estimators.
result Improved estimators of Kullback-Leibler discrepancy are provided and perform well in reduced-rank situations.
The study finds minimal distortion embeddings of surfaces into small domains.
problem Finding the minimal distortion of embeddings between two-dimensional manifolds.
method Proving a lower bound on distortion in terms of areas' discrepancy, characterizing minimizers, and proving stability.
result Homotheties are the unique minimizers for , and non-homothetic minimizers exist for .
This paper defines the notion of class discrepancy for families of functions. It shows that low discrepancy classes admit small offline and streaming coresets. We provide general techniques for bounding the class discrepancy of machine learning problems. As corollaries of the general technique we bound the discrepancy …
Semi-parametric framework for nonlinear system identification
problem Nonlinear system identification
method Orthogonal Gaussian process regression
result Interpretable models from incomplete physics
TMDA aligns subdomain data distribution discrepancies across domains using manifold representations.
problem Transfer learning challenges due to domain divergence.
method TMDA uses low-dimensional manifolds to represent subdomains and aligns local data distribution discrepancies across domains using M3D.
result TMDA is a promising method for various transfer learning tasks.
The performance of standard learning procedures has been observed to differ widely across groups. Recent studies usually attribute this loss discrepancy to an information deficiency for one group (e.g., one group has less data). In this work, we point to a more subtle source of loss discrepancy---feature noise. Our mai…