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.
New Nuclear Discrepancy bound improves active learning performance.
problem Improving active learning algorithms to minimize generalization bounds.
method Proposed a new Nuclear Discrepancy bound and compared it with existing bounds.
result The Nuclear Discrepancy bound outperforms other bounds in active learning.
Feature noise causes loss discrepancies across groups even with equal data.
problem Loss discrepancies observed in learning procedures across different groups.
method Characterized the effect of feature noise on loss discrepancy in linear regression.
result Feature noise leads to loss discrepancy even when groups have equal data.
Stochastic Stein Discrepancies improve inference efficiency.
problem Intractable computation of Stein discrepancies.
method Subsampled approximations of Stein operators.
result Stochastic Stein Discrepancies inherit convergence properties of standard SDs.
A new ensemble filter uses transport maps and MMD optimization for high-dimensional data assimilation.
problem High-dimensional data assimilation challenges in ensemble filtering.
method Optimized Maximum Mean Discrepancy (MMD) for transport map construction.
result Significant improvement in robustness and posterior approximation.
New method discovers discrepancies between simplified models and experimental data.
problem Model discrepancies in nonlinear systems lead to significant deviations from true behavior.
method Sparse Identification of Nonlinear Dynamics (SINDy) algorithm to discover sparse model terms.
result Improvement in performance with a discrepancy model in simulations.
The paper highlights the importance of model discrepancy in cardiac simulations.
problem Uncertainty in model structure and equations affects predictions.
method The authors use Gaussian processes and autoregressive-moving-average models to account for model discrepancy.
result Different methods to account for model discrepancy have advantages and shortcomings.
Two methods using low-discrepancy points improve data compression for neural networks.
problem Efficiently compress large datasets for neural network training.
method Two methods based on low-discrepancy points: digital nets with averaging and clustering.
result Second method outperforms supercompress in compression error and neural network accuracy.
A new metric MSD detects bias in datasets efficiently.
problem Detecting bias in AI systems and datasets.
method Introduced Maximum Subgroup Discrepancy (MSD) metric and a practical algorithm based on MIO.
result MSD provides a linear sample complexity for practical applications, distinguishing biases effectively.
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.
Generative neural network simulates characteristic functions.
problem Simulating from characteristic functions inaccessible in closed form.
method Generative neural network with Maximum-Mean-Discrepancy loss.
result Universal algorithm independent of dimensionality and function properties.
A new test detects differences between two distributions without flow.
problem Detecting differences between two distributions without flow.
method Zero-flow discrepancy (ZFD) and zero-flow two-sample test (ZF2ST).
result ZF2ST can detect strong differences in structured distributions.
New link topology connects permutation discrepancies to Diaconis-Graham inequalities.
problem Characterize permutations for which Diaconis-Graham inequalities hold with equality.
method Relate permutation discrepancies to the Euler characteristic of their associated links.
result Permutation discrepancies are directly related to the Euler characteristic of their associated links.
We present a new analysis of the problem of learning with drifting distributions in the batch setting using the notion of discrepancy. We prove learning bounds based on the Rademacher complexity of the hypothesis set and the discrepancy of distributions both for a drifting PAC scenario and a tracking scenario. Our boun…
China uses two Renminbi markets to hedge cross-border risks, leading to a price discrepancy.
problem China's two Renminbi markets (onshore and offshore) create a price discrepancy for currency forwards.
method Joint equilibrium model for spot and forward trading with transaction costs and segmented supply.
result The model explains the observed forward price discrepancy in terms of offshore liquidity stress.
Proposes CDDA method to adapt models across domains with minimized discrepancy and increased discriminative power.
problem Transfer learning across domains with different distributions.
method CDDA method that minimizes discrepancy and increases discriminative power through latent feature representation.
result Consistently outperforms state-of-the-art methods in cross-domain image classification tasks.
A new method for training GNNs without a teacher model.
problem Training over-parameterized GNN models is difficult and inefficient.
method GNN Self-Distillation (GNN-SD) with NDR and ADR.
result Improves GNN performance with less training cost and better generalization.
This work tackles domain generalization by minimizing discrepancy between domains.
problem Domain generalization: learning to handle unseen domains with i.i.d. data assumptions violated.
method The approach involves minimizing discrepancy between domains using a lemma and deriving a generalization bound.
result Low risk over unseen domains can be achieved by representing data in a space where training distributions are indistinguishable and relevant information is preserved.
Language models are miscalibrated, leading to overestimated entropy rates and memory usage.
problem Miscalibration of language models leading to overestimated entropy rates and memory usage.
method Calibration-based approach to measure discrepancies and improve models.
result State-of-the-art language models are miscalibrated, causing overestimated entropy rates and memory usage.
Bayesian Neural Networks improve accuracy and robustness.
problem Training and optimizing Bayesian Neural Networks (BNNs).
method Replace Kullback-Leibler divergence with Maximum Mean Discrepancy (MMD) in ELBO term.
result Higher accuracy on multiple benchmarks, including image classification tasks.
Deep neural networks can approximate any target probability distribution given certain conditions.
problem Approximating complex probability distributions with deep neural networks.
method Proving the existence of a deep neural network mapping that approximates a target distribution under various integral probability metrics.
result Upper bounds on the size of the neural network in terms of dimension and approximation error for different metrics.
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.
Generative model for realistic text generation using feature matching.
problem Applying GAN to text generation due to convergence issues and difficulties with discrete data.
method Employing a long short-term memory network as generator and a convolutional network as discriminator. Matching latent feature distributions via a kernelized discrepancy metric.
result Superior performance in generating realistic-looking sentences compared to standard GAN.
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.
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.
New method corrects output-side domain shift without labeled data.
problem Learning mapping from input to output space with domain shift.
method Adapts learned function using unlabeled outputs from target distribution.
result Derives generalization bounds using discrepancy terms.
Study examines the impact of target data in transfer learning.
problem Understanding the value of target data in transfer learning.
method Established minimax-rates for source and target sample sizes, introduced transfer exponents.
result Performance limits in transfer learning are captured by transfer exponents.
Proposes PHD to measure domain discrepancy for complex models.
problem Insufficient domain discrepancy measures for complex models.
method Introduces PHD, a novel discrepancy measure for complex models.
result PHD is computationally efficient and applicable to multi-class classification.
A new metric detects non-Markovian states in partially observable environments.
problem Learning state representations in partially observable environments.
method Introducing the λ-discrepancy metric to detect non-Markovian states. result The λ-discrepancy is zero for Markov processes and non-zero for partially observable environments. Paper defines class discrepancy for machine learning problems and provides coresets.
problem Addressing discrepancies in machine learning models.
method Defines class discrepancy, provides techniques for bounding discrepancy, and develops coresets and streaming sketches.
result Establishes coresets of size O(sqrt{d}/epsilon) for various machine learning problems.
New KCC-SDs improve distribution comparison in high dimensions.
problem Challenges in high-dimensional Stein discrepancies.
method Kernelized complete conditional Stein discrepancies (KCC-SDs).
result KCC-SDs outperform baselines in distinguishing distributions.
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.
A new embedding method extracts dataset-scale metric distribution into vectorial representation for graph data.
problem Classifying graph-structured data based on overall dataset-scale discrepancies.
method MetricDistribution2vec embedding strategy.
result Significant improvement in supervised prediction tasks on real-world graph datasets.
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.
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.
Framework synthesizes geological images minimizing patch distribution discrepancy.
problem Synthesizing realistic geological images from a single exemplar.
method Uses kernel discrepancies and generative neural networks for efficient synthesis.
result Synthesized images match visual patterns and spatial statistics of the exemplar.
Modeling gas fee competition in decentralized exchanges to optimize arbitrage profits.
problem Gas fees and transaction ordering in decentralized exchanges create arbitrage opportunities.
method Developed a first equilibrium model of gas fee competition between two arbitrageurs under three transaction reversion settings.
result Mixed equilibria exist, and their characteristics depend on inventory risk and transaction settings.
We analyze the mapping class group of extendible automorphisms of the exterior boundary W of a compression body of dimension 3 or 4, which extend over the compression body (Q,V), where V is the interior boundary. Those that extend as automorphisms of (Q,V) rel V are called discrepant automorphisms, forming the mapping …
A new discrepancy method improves efficiency and accuracy in unsupervised domain adaptation.
problem Measuring the difference between source and target domains without labeled target data.
method Source-guided discrepancy (S-disc) that uses source domain labels for efficient computation and tighter generalization bounds.
result S-disc provides a tighter generalization error bound than existing discrepancies.
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.
New partition designs reduce star discrepancy in high-dimensional sampling.
problem Improving the expected star discrepancy in high-dimensional sampling.
method Developed non-equal volume partitions to achieve lower expected star discrepancy.
result Explicit upper bounds for expected star discrepancy under non-equal volume partitions.
Proposes DWMD for better matching of hidden representations across domains.
problem Measuring data distribution discrepancy between semantically related domains for feature representation matching.
method DWMD, a moment-based probability distribution metric that explicitly orders and weights higher-order moments.
result DWMD is error-free and can strictly reflect distribution differences without feature distribution assumptions.
This work proves the optimal estimation rates for popular kernel discrepancies.
problem Estimating the disagreement of distributions using kernel discrepancies.
method Proving minimax lower bounds for MMD, HSIC, and KSD.
result The minimax lower bound for estimation of MMD, HSIC, and KSD is \( n^{-1/2} \) on general topological spaces.
The paper explores conditions for interval exchange transformations to yield low-discrepancy sequences.
problem Conditions for interval exchange transformations to produce low-discrepancy sequences.
method Analyzes interval exchange transformations and applies ergodic theory.
result Constructs infinitely many interval exchange transformations with low-discrepancy orbits for n≥4. A new metric DJP-MMD improves domain adaptation by balancing transferability and discriminability.
problem Improving domain adaptation performance by balancing transferability and discriminability.
method Discriminative Joint Probability Maximum Mean Discrepancy (DJP-MMD) replaces the traditional joint MMD.
result DJP-MMD outperforms traditional MMDs in image classification tasks.
A new method for density estimation using mixture discrepancy and moments.
problem Generalizing histogram statistics to higher dimensions.
method Density estimation via mixture discrepancy and moments (DSP-mix and MSP).
result DSP-mix and MSP are computationally tractable and maintain accuracy with increased speed.
We approximate the Sobolev discrepancy for finite dimensional kernels from samples.
problem Estimating the Sobolev discrepancy for complex models from finite data.
method Approximating the Sobolev discrepancy using finite samples and analyzing the approximation error.
result The Sobolev discrepancy can be approximated from finite samples and its error depends on the approximation and statistical errors.