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.
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.
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…
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.
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.
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.
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.
sig-MMD tests compare path distributions using kernel methods.
problem Comparing path distributions in stochastic processes.
method Signature kernel for path space valued distributions.
result sig-MMD can lead to Type 2 errors in limited data settings.
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.
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.
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.
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 test for comparing function samples using MMD.
problem Testing if two functional data samples come from the same distribution.
method Maximum Mean Discrepancy (MMD) for functional data, with theoretical scaling analysis.
result The proposed test is effective and robust to functional reconstructions.
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…
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.
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 finds points for approximating distributions faster.
problem Approximating target probability distributions using finite points.
method Stationary MMD points computed via MMD gradient flows.
result Stationary MMD points converge faster than global minimizers.
MMD-B-Fair learns fair representations by minimizing MMD test power.
problem Learning fair representations of data while preserving target attributes.
method Kernel two-sample testing and block testing schemes.
result Minimizing MMD test power allows hiding sensitive attribute information.
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 new MMD-based test combines kernels for two-sample testing without splitting data.
problem Efficiently testing if two datasets come from the same distribution without splitting data.
method Proposes a novel statistic based on Maximum Mean Discrepancy (MMD) that combines kernels, proving concentration bounds and showing data-dependent kernel selection.
result Exponential concentration bounds and improved test power compared to existing methods.
Unified method for MMD variance estimation improves accuracy and computational efficiency.
problem Variance estimation for MMD in nonparametric testing.
method Unified finite-sample characterization of MMD variance through U-statistic and Hoeffding decomposition; exact acceleration method for univariate case.
result Unified estimators improve accuracy and computational efficiency for MMD variance.
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.
This thesis improves kernel-based distances for statistical inference and integration.
problem Efficiently measuring distances between probability distributions for robust and smooth modeling.
method Kernel-based distances, focusing on maximum mean discrepancy (MMD) and novel kernel quantile discrepancies.
result Improved MMD estimators for simulation-based inference and conditional expectations.
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.
A new measure scales MMD to assess distribution closeness.
problem Testing statistical significance of distribution closeness.
method Norm-adaptive MMD (NAMMD) for distributional discrepancy.
result NAMMD-based DCT has higher test power than MMD-based DCT.
We propose a method to optimize the representation and distinguishability of samples from two probability distributions, by maximizing the estimated power of a statistical test based on the maximum mean discrepancy (MMD). This optimized MMD is applied to the setting of unsupervised learning by generative adversarial ne…
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.
The Maximum Mean Discrepancy (MMD) has found numerous applications in statistics and machine learning, most recently as a penalty in the Wasserstein Auto-Encoder (WAE). In this paper we compute closed-form expressions for estimating the Gaussian kernel based MMD between a given distribution and the standard multivariat…
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.
Gradient descent on MMD GAN parameter space converges globally to target distribution.
problem Convergence of gradient descent in Maximum Mean Discrepancy (MMD) GANs.
method Proposes a parametric kernelized gradient flow that mimics the min-max game in gradient regularized MMD GAN.
result Gradient descent on the generator's parameter space in gradient regularized MMD GAN is globally convergent to the target distribution under certain conditions.
This paper refines MMD for domain adaptation by balancing intra-class and inter-class distances.
problem Balancing intra-class and inter-class distances for better feature discriminability in domain adaptation.
method The paper theoretically proves two facts about MMD and proposes a novel discriminative MMD method to balance intra-class and inter-class distances.
result The proposed method improves feature discriminability and outperforms state-of-the-art methods.
BDC compresses both sample size and dimensionality of large datasets.
problem Large datasets in both sample size and dimensionality.
method Two-stage framework using Decoded MMD, Reconstruction MMD, and Encoded MMD.
result BDC achieves comparable or superior performance with lower cost and higher compression rates.
"Which Generative Adversarial Networks (GANs) generates the most plausible images?" has been a frequently asked question among researchers. To address this problem, we first propose an \emph{incomplete} U-statistics estimate of maximum mean discrepancy MMDinc to measure the distribution discrepancy betwee…
Efficiently tests two distributions using Nyström approximation of MMD.
problem Testing whether two sets of data are from the same distribution in large-scale scenarios.
method Nyström approximation of maximum mean discrepancy (MMD) for scalable testing.
result Finite-sample bound on power of the test for sufficiently separated distributions.
Proposes a semi-Bayesian nonparametric estimator for MMD in GOF tests and GANs.
problem Challenges in goodness-of-fit testing for intractable models.
method Semi-Bayesian nonparametric estimator of MMD.
result Outperforms frequentist MMD-based methods in false rejection and acceptance rates.
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 …
This note optimizes distributions using kernel mean embeddings with a new parameterization.
problem Optimizing distributions using kernel mean embeddings is challenging due to the difficulty of characterizing probability distribution vectors.
method Proposes a new parameterization of positive functions using kernel sums-of-squares to fit distributions in the MMD geometry.
result Distributions with kernel sum-of-squares densities are dense in the MMD geometry, allowing optimization in the finite-sample setting.
Paper improves MMD estimation for analytical mean embeddings.
problem Improving MMD estimation for distributions with analytical mean embeddings.
method Proposes a tighter concentration result for MMD estimation under semi-explicit settings and extends to unbounded kernels.
result Demonstrates efficiency in real-world applications like index replication and calibration.
New metrics improve probabilistic forecasting, especially for rare events.
problem Current evaluation frameworks for probabilistic forecasting assume independence and lack sensitivity to tail events.
method Proposed signature kernel-based metrics: Sig-MMD and CSig-MMD.
result These metrics capture complex dependencies and prioritize tail event prediction.
A new method improves Bayesian filtering in nonlinear systems.
problem Bayesian filtering in nonlinear dynamical systems with non-Gaussian posteriors.
method Transport maps with block-triangular structure and gradient flows for MMD minimization.
result Accurate approximation of non-Gaussian posteriors without particle collapse.
Dependent MMD coresets help compare multiple related datasets.
problem Comparing multiple related datasets for insights into model generalization.
method Dependent MMD coresets for collections of datasets.
result Dependent MMD coresets facilitate comparison and understanding of multiple related datasets.
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.
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.
In some misspecified settings, the posterior distribution in Bayesian statistics may lead to inconsistent estimates. To fix this issue, it has been suggested to replace the likelihood by a pseudo-likelihood, that is the exponential of a loss function enjoying suitable robustness properties. In this paper, we build a ps…
New method improves MMD estimation without convexity assumptions.
problem Lack of theoretical guarantees for MMD estimation algorithms.
method Preconditioned gradient descent (PGD) scheme for MMD optimization.
result PGD scheme converges globally under specific conditions.
New kernel improves MMDs with theoretical guarantees for gradient flows.
problem Non-smoothness of negative distance kernel in MMDs.
method Smoothed 1D absolute value function followed by fractional integral transform.
result Improved theoretical guarantees for Wasserstein gradient flows.
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 methods for Bayesian inference using mean shift particle systems.
problem Approximating expectations with unnormalized densities in Bayesian inference.
method Mean shift interacting particle systems that minimize maximum mean discrepancy (MMD).
result Mean shift interacting particle systems converge quickly and capture complex distributions.