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.
Study shows distance to boundary is always attained on varifolds with bounded curvature.
problem Understanding varifolds with bounded mean curvature in Riemannian manifolds.
method Proves a barrier principle at infinity using sharp maximum principles.
result Distance to boundary is always attained on varifolds with bounded curvature.
New distances measure mixtures of Gaussians, useful in machine learning.
problem Comparing distributions with disjoint supports.
method Schoenberg-Rao distances based on concave Rao's entropy.
result Closed-form distances for mixtures of Gaussians.
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.
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.
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.
New metrics improve quantum ensemble learning efficiency and power.
problem Quantum ensembles' distances poorly understood due to measurement constraints.
method Introduce MMD-k hierarchy of integral probability metrics for quantum ensembles. result MMD-k requires fewer samples for full discriminative power at higher k. A new metric compares true and learned causal graphs considering data and graph structure.
problem Comparing true and learned causal graphs accurately.
method Continuous Structural Intervention Distance (CSID) using conditional mean embeddings and maximum mean discrepancy.
result Validated the CSID with synthetic data, showing its effectiveness in comparing causal graphs.
New KQEs improve probability metrics without mean function constraints.
problem Improving probability metrics without relying on mean function representations.
method Kernel quantile embeddings (KQEs) to construct new distances.
result KQEs offer a competitive alternative to MMD with near-linear cost.
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…
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.
Proposes Mutual Regression Distance for better distribution comparison.
problem Lack of effective distance measures for manifold data.
method Constrained mutual regression problem to exploit manifold properties.
result Mutual Regression Distance (MRD) is a pseudometric effective for manifold data.
Validates economic scenarios using statistical tests on stochastic processes.
problem Ensuring the accuracy of real-world economic scenario models.
method Applies Chevyrev and Oberhauser's (2022) signature and maximum mean distance test to various stochastic processes.
result Demonstrates the test's effectiveness across different path properties relevant to financial modeling.
Some analysis on the Lorentzian distance in a spacetime with controlled sectional (or Ricci) curvatures is done. In particular, we focus on the study of the restriction of such distance to a spacelike hypersurface satisfying the Omori-Yau maximum principle. As a consequence, and under appropriate hypotheses on the (sec…
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 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.
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.
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.
The MEM method uses data-driven priors for linear inverse problems, proving convergence and estimating differences.
problem Linear inverse problems with approximate priors.
method Maximum Entropy on the Mean (MEM) method with data-driven priors.
result Empirical mean convergence and estimates for prior differences based on epigraphical distance.
Mean embeddings provide an extremely flexible and powerful tool in machine learning and statistics to represent probability distributions and define a semi-metric (MMD, maximum mean discrepancy; also called N-distance or energy distance), with numerous successful applications. The representation is constructed as the e…
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…
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.
This paper studies clustering of data sequences using the k-medoids algorithm. All the data sequences are assumed to be generated from \emph{unknown} continuous distributions, which form clusters with each cluster containing a composite set of closely located distributions (based on a certain distance metric between di…
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.
Unified meta algorithms estimate various distribution functionals in infinite-armed bandits.
problem Estimating various distribution functionals in infinite-armed bandits.
method Unified meta algorithms for offline and online settings, achieving optimal sample complexities.
result Online estimation offers significant advantage for certain distribution functionals.
In this paper we prove Hessian and Laplacian comparison theorems for the Lorentzian distance function in a spacetime with sectional (or Ricci) curvature bounded by a certain function by means of a comparison criterion for Riccati equations. Using these results, under suitable conditions, we are able to obtain some esti…
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.
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…
A new method for distribution regression using sliced Wasserstein distance.
problem Learning functions over spaces of probabilities.
method Proposes an OT-based estimator using the Sliced Wasserstein distance.
result Proves universal consistency and excess risk bounds for the proposed estimator.
Paper introduces GSPMs for robust probability metrics.
problem Lack of well-established convergence behavior for probability metrics.
method Introduces Generalized Sliced Probability Metrics (GSPMs) based on generalized Radon transform.
result GSPMs converge to global optimum under mild assumptions for generative modeling.
Proposes a new method to analyze the distributional effects of treatments.
problem Analyzing the full distributional impact of treatments beyond just the mean.
method Uses kernel conditional mean embeddings and U-statistic regression to investigate the CoDiTE.
result Demonstrates the effectiveness of the proposed method through experiments.
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.
Spectral clustering improves accuracy and efficiency for clustering discrete distributions.
problem Inaccurate clustering of discrete distributions using traditional methods.
method Spectral clustering combined with distribution affinity measures (MMD, Wasserstein distance) and linear optimal transport.
result Spectral clustering outperforms traditional methods in accuracy and efficiency.
The paper describes flows of MMD functionals with distance kernel and quantile functions.
problem Wasserstein gradient flows of MMD functionals with negative distance kernel.
method Characterization via Cauchy problem on L2(0,1), solution via subdifferential construction. result Flow invariance and smoothing properties on subsets of C(0,1), absolute continuity of initial measures. Plug-in robust NPE method adapts summaries independently of pretrained NPE.
problem Misspecification of neural posterior estimators under test data distribution.
method Minimum-distance summaries using maximum mean discrepancy (MMD).
result Substantial robustness gains with minimal additional overhead.
While likelihood-based inference and its variants provide a statistically efficient and widely applicable approach to parametric inference, their application to models involving intractable likelihoods poses challenges. In this work, we study a class of minimum distance estimators for intractable generative models, tha…
Study entropic regularization of Gaussian measures and processes on Hilbert space.
problem Regularizing 2-Wasserstein distance for infinite-dimensional Gaussian measures and processes.
method Minimum Mutual Information property, closed form formulas, Fréchet differentiability, Sinkhorn barycenter equation.
result Entropic 2-Wasserstein distance and Sinkhorn divergence are Fréchet differentiable in Hilbert space.
This paper investigates the utilization of maximum and average distance correlations for multivariate independence testing. We characterize their consistency properties in high-dimensional settings with respect to the number of marginally dependent dimensions, compare the advantages of each test statistic, examine thei…
Paper proposes a new algorithm for clustering financial market regimes.
problem Rapid and automated detection of distinct market regimes.
method Wasserstein k-means algorithm for clustering financial time-series.
result Wasserstein k-means algorithm outperforms traditional clustering methods.
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 method optimizes non-linear functionals over probability measures.
problem Optimizing non-linear functionals defined over probability measures.
method N-particle underdamped Langevin algorithm with spacetime discretization.
result Converges globally in total variation distance.
New method approximates MMD using pseudo-differential operators and singular values.
problem Approximating MMD with pseudo-differential operators and singular values.
method Corresponding pseudo-differential operators to Mercer kernels, approximating p(x,y) with its first r singular values. result The new MMD distance measures the difference of two distributions with respect to r∗ local moments, where r∗ depends on singular values decay rate. We study minimax convergence rates of nonparametric density estimation under a large class of loss functions called "adversarial losses", which, besides classical Lp losses, includes maximum mean discrepancy (MMD), Wasserstein distance, and total variation distance. These losses are closely related to the …
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…
A new distance metric compares probability distributions using kernel covariance operators.
problem Comparing probability distributions in machine learning tasks.
method Introduces a novel distance metric based on Schatten norm of kernel covariance operators.
result The new distance metric is more discriminative and robust to hyperparameters.
This work bridges outlier and drift detection by comparing inputs to a part of the reference distribution.
problem Monitoring machine learning models to ensure they operate within their validated distribution.
method Comparing a set of inputs to a chosen part of the reference distribution.
result A new approach that bridges outlier detection and drift detection.
Kernel embeddings of distributions and the Maximum Mean Discrepancy (MMD), the resulting distance between distributions, are useful tools for fully nonparametric two-sample testing and learning on distributions. However, it is rarely that all possible differences between samples are of interest -- discovered difference…
The paper presents new metrics to quantify and test for (i) the equality of distributions and (ii) the independence between two high-dimensional random vectors. We show that the energy distance based on the usual Euclidean distance cannot completely characterize the homogeneity of two high-dimensional distributions in …