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.
Study finds polynomial convergence rate for Farey sequences linked to Riemann hypothesis.
problem Understanding convergence rates of maximum mean discrepancies for Farey sequences.
method Identifying positive-semidefinite kernels and their polynomial convergence rates.
result Polynomial convergence rate of maximum mean discrepancies of Farey sequences is equivalent to the Riemann hypothesis.
The paper proposes a method to produce well-calibrated predictions in regression tasks using maximum mean discrepancy.
problem The need for accurate uncertainty quantification in machine learning predictions.
method The method uses maximum mean discrepancy to minimize the kernel embedding measure and calibrate predictions.
result The method produces well-calibrated and sharp prediction intervals, outperforming state-of-the-art methods.
Residual flows are shown to approximate MMD well.
problem Lack of theoretical understanding of normalizing flows' expressiveness.
method Proved residual flows are universal approximators in MMD.
result Residual flows can approximate MMD with a bounded number of blocks.
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.
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.
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.
Maximum mean discrepancy (MMD) has been widely adopted in domain adaptation to measure the discrepancy between the source and target domain distributions. Many existing domain adaptation approaches are based on the joint MMD, which is computed as the (weighted) sum of the marginal distribution discrepancy and the condi…
Paper proposes MMD-Sense-Analysis for detecting word sense shifts.
problem Detecting and interpreting shifts in word meanings over time.
method Leverages Maximum Mean Discrepancy (MMD) to identify and explain word sense changes.
result Demonstrates effectiveness of MMD-Sense-Analysis through empirical results.
A new gradient flow for MMD with closed-form implementation.
problem Existing gradient flows either lack tractable numerical implementation or require strong assumptions.
method Introduces a (de)-regularized Maximum Mean Discrepancy (DrMMD) and its gradient flow.
result Guarantees near-global convergence for a broad class of targets in both continuous and discrete time.
MMD test detects adversarial attacks by addressing kernel limitations and non-independence issues.
problem MMD test's failure to detect adversarial attacks.
method Replaced Gaussian kernel with deep kernel, maximized test power, and used wild bootstrap for non-independence.
result MMD test is aware of adversarial attacks.
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 conditions ensure MMDs separate and converge to target distributions.
problem Ensuring MMDs separate and converge to target distributions.
method Deriving new sufficient and necessary conditions for MMDs on separable metric spaces.
result First KSDs that exactly metrize weak convergence to P.
Optimizes MMD learning for generative models with theoretical guarantees.
problem Theoretical guarantees for optimizing non-convex MMD objectives.
method Analyzes MMD optimization landscape for specific distributions.
result Gradient-based methods globally minimize MMD objective for certain distributions.
New algorithms minimize MMD to approximate probability measures efficiently.
problem Approximating probability measures by representative point sets.
method Sequential greedy minimization of maximum mean discrepancy (MMD) over candidate sets, with mini-batch variants.
result Consistency of proposed algorithms and mini-batch variants established.
A new method uses neural tangent kernel to efficiently compute MMD statistic.
problem Efficiently computing Maximum Mean Discrepancy (MMD) statistic with low memory and computational complexity.
method Identifies a connection between neural tangent kernel (NTK) and MMD to develop a computationally and memory-efficient approach.
result The proposed NTK-MMD statistic is validated through numerical experiments on synthetic and real-world datasets.
SDRF estimates complex survey designs for conditional distributions.
problem Estimating conditional distributions under complex survey designs.
method Survey-calibrated distributional random forest (SDRF) with pseudo-population bootstrap and MMD split criterion.
result Established design consistency and model consistency for survey designs.
The paper shows how MMD metrizes weak convergence for certain kernels.
problem Characterizing MMD metrizing weak convergence for a wide class of kernels.
method Proving MMD metrizes weak convergence for specific kernels on a locally compact space.
result Corrected prior results and identified new kernels metrizing weak convergence.
A new method for kernel tests without data splitting increases power.
problem Lack of power in kernel-based tests due to data splitting.
method Selective inference framework to learn hyperparameters and test on full sample.
result Empirically larger test power without data splitting, regardless of split proportion.
Though machine learning algorithms excel at minimizing the average loss over a population, this might lead to large discrepancies between the losses across groups within the population. To capture this inequality, we introduce and study a notion we call maximum weighted loss discrepancy (MWLD), the maximum (weighted) d…
MMD-Flagger detects hallucinations in LLMs by tracking MMD between outputs and temperature-generated counterparts.
problem Detecting hallucinations in large language models.
method Maximum Mean Discrepancy (MMD) to track the difference between model outputs and temperature-generated counterparts.
result MMD-Flagger detects most hallucinations by analyzing the shape of the MMD trajectory.
Improved MMD estimator for likelihood-free inference.
problem Computational challenges in estimating MMD for likelihood-free inference.
method Optimally-weighted MMD estimator with improved sample complexity.
result Significantly improved sample complexity for accurate MMD estimation.
Secure SMMD enables data privacy in federated learning.
problem Data privacy in federated learning.
method Homomorphic encryption-based Secure Maximum Mean Discrepancy (SMMD).
result Secure SMMD avoids data leakage and enables effective knowledge transfer.
New method improves source separation using NMF and adversarial learning.
problem Source separation in single channel data.
method Maximum Discrepancy Generative Regularization applied to NMF.
result Improvement in reconstructed signals, especially in weak supervision scenarios.
Proposes TFDF to learn transferable and discriminative features for unsupervised domain adaptation.
problem Difficult to induce supervised classifier without labeled data in unsupervised domain adaptation.
method TFDF optimizes transferability and discriminability by aligning distributions and minimizing class confusion.
result TFDF achieves better performance on real-world datasets compared to existing methods.
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.
Generative networks trained with sketching reduce computational burden.
problem Computational expense of training generative networks on large datasets.
method Compressive learning using a single sketch vector to approximate Maximum Mean Discrepancy.
result Cost-efficient optimization of generative networks on large datasets.
Do two data samples come from different distributions? Recent studies of this fundamental problem focused on embedding probability distributions into sufficiently rich characteristic Reproducing Kernel Hilbert Spaces (RKHSs), to compare distributions by the distance between their embeddings. We show that Regularized Ma…
PolyGraph Discrepancy improves graph generative model evaluation.
problem Inability of existing metrics to provide an absolute performance measure and comparability across different graph descriptors.
method Approximates Jensen-Shannon distance using binary classifiers trained to distinguish between real and generated graphs.
result PGD provides a more robust and insightful evaluation compared to MMD metrics.
The paper analyzes greedy algorithms for MMD minimization, showing their efficiency and approximation error.
problem Minimizing Maximum Mean Discrepancy (MMD) for probability measure quantization.
method Iterative algorithms including kernel herding, greedy MMD minimization, and Sequential Bayesian Quadrature (SBQ).
result The greedy algorithms have a lower approximation error than SBQ, but are significantly faster.
EVI-MMD approximates target distributions via MMD minimization with adaptive kernel.
problem Approximating target distributions using kernel discrepancy methods.
method EVI-MMD uses Maximum Mean Discrepancy (MMD) to minimize kernel discrepancy, solving ODEs with implicit Euler scheme and L-BFGS optimization.
result EVI-MMD with adaptive bandwidth selection significantly improves performance in sampling problems.
New MMD estimators detect differences in missing paired data.
problem Handling missing data in matched pairs with complex distributions.
method Maximum mean discrepancy (MMD) estimators for complex data with missing values.
result Valid and consistent estimators detect differences in data distributions.
New tools evaluate and optimize conditional sequence models in bioinformatics.
problem Evaluating and optimizing conditional sequence models in bioinformatics.
method Kernel-based discrepancy measure (ACMMD) to estimate model fit and tune hyperparameters.
result Rejects the hypothesis that ProteinMPNN fits its data for various protein families and optimizes model temperature.
ConvMMD improves inference in noisy data.
problem Inference degradation due to measurement error in noisy data.
method Convolutional Maximum Mean Discrepancy (convMMD) for inference with noisy, heteroscedastic observations.
result Established consistency and asymptotic normality of the convMMD-based estimator.
Enhances generative models stability and accuracy with BNPL, WMMD, and triple model.
problem Overfitting in GANs and noisy samples in VAEs.
method Bayesian non-parametric learning framework, integrating Wasserstein distance and maximum mean discrepancy.
result Superior performance across various generative tasks.
We propose a framework for synthesis of geological images based on an exemplar image. We synthesize new realizations such that the discrepancy in the patch distribution between the realizations and the exemplar image is minimized. Such discrepancy is quantified using a kernel method for two-sample test called maximum m…
Paper tackles model vulnerabilities by reconstructing training data.
problem Reconstructing training data from model parameters poses a security risk.
method Developed a mathematical framework and score matching method for both Bayesian and non-Bayesian models.
result First score matching framework for reconstructing data in Bayesian models.
A method to select validation data from a dataset using statistical criteria.
problem Selecting a validation basis from a full dataset for machine learning model validation.
method Adopting a 'design of experiments' point of view and using statistical criteria, particularly Maximum Mean Discrepancy criteria.
result The 'support points' concept is particularly relevant for selecting validation data.
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.
Deep learning model approximates stochastic responses.
problem Approximating stochastic responses using neural networks.
method Generative neural network with conditional maximum mean discrepancy (CMMD) loss.
result Excellent performance on benchmark problems.
New method improves neural spike train models by minimizing divergence directly, leading to better performance.
problem Poor performance and divergence issues in spike train models using maximum likelihood estimation.
method Directly minimize maximum mean discrepancy using spike train kernels and stochastic optimization.
result The proposed method generates well-behaved models with better control over feature trade-offs.
We characterize the asymptotic performance of nonparametric goodness of fit testing. The exponential decay rate of the type-II error probability is used as the asymptotic performance metric, and a test is optimal if it achieves the maximum rate subject to a constant level constraint on the type-I error probability. We …
A new deep generative model uses BSDEs for high-dimensional data generation.
problem Generating high-dimensional complex data, especially images.
method Combines BSDEs with deep neural networks for training with MMD loss.
result BSDE-Gen effectively generates high-dimensional data with stochasticity.
When maximum likelihood estimation is infeasible, one often turns to score matching, contrastive divergence, or minimum probability flow to obtain tractable parameter estimates. We provide a unifying perspective of these techniques as minimum Stein discrepancy estimators, and use this lens to design new diffusion kerne…
In this paper, we bound the error induced by using a weighted skeletonization of two data sets for computing a two sample test with kernel maximum mean discrepancy. The error is quantified in terms of the speed in which heat diffuses from those points to the rest of the data, as well as how at the weights on the refere…
Stein discrepancy improves UDA performance in low-data scenarios.
problem Improving model performance on unlabeled target domains with limited data.
method Proposes a novel UDA framework using Stein discrepancy, an asymmetric measure that depends on the target distribution through its score function.
result Consistently outperforms prior UDA approaches under limited target data across multiple benchmarks.
We construct a Wasserstein gradient flow of the maximum mean discrepancy (MMD) and study its convergence properties. The MMD is an integral probability metric defined for a reproducing kernel Hilbert space (RKHS), and serves as a metric on probability measures for a sufficiently rich RKHS. We obtain conditions for conv…
New method for MMD with unequal sample sizes improves test power.
problem Existing MMD methods assume equal sample sizes, discarding valuable data.
method Extended generalized U-statistics to handle unequal sample sizes.
result New asymptotic distributions and power optimization for MMD with unequal sample sizes.