Paper proposes Gini distance statistics for estimating feature-label dependence.
problem Identifying statistical dependence between features and categorical labels.
method Generalized Gini distance in RKHS for feature-label dependence estimation.
result Gini distance statistics converge faster and have tighter error bounds than distance covariance.
The paper introduces a statistical distance matrix for better feature representation and clustering.
problem Lack of detailed distance representation between feature elements.
method Extended traditional statistical distance to a matrix form (statistical distance matrix) and applied hierarchical clustering.
result The statistical distance matrix with clustering (Information Mandala) provides clearer and geometrically arranged feature representations.
Novel distances between distributions using conditional ground distances.
problem Quantifying distances between statistical multivariate distributions.
method Optimal transport with entropic regularization and ground distance on conditionals.
result Upper bounds for jointly convex distances and improved GMM learning.
This guide explains statistical distances for evaluating generative models.
problem Evaluating the quality of samples from generative models.
method Four statistical distances: SW, C2ST, MMD, FID.
result Different distances can yield varying results on similar data.
New statistical Minkowski distances for Gaussian mixtures with closed-form formulas.
problem Computing distances for Gaussian mixture models efficiently.
method Proposed novel statistical distances based on Minkowski's inequality for Gaussian mixtures.
result Closed-form formula for Gaussian mixture models with integer exponents.
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…
This paper connects Wasserstein distances to MMD norms for compressive statistical learning.
problem Comparing and controlling Wasserstein distances between probability distributions.
method Establishing conditions under which Wasserstein distances can be controlled by MMD norms.
result Introducing Wasserstein regularity for compressive statistical learning.
Valid inference method for DTW distance for abnormal time-series detection.
problem Statistical inference on DTW distance under uncertain conditions.
method Conditional selective inference framework to derive valid p-values.
result First method to provide valid p-values for DTW distance.
New method connects distance and kernel tests for better data structure.
problem Connecting distance and kernel methods for hypothesis testing.
method Proposes a new bijective transformation between metrics and kernels.
result Distance methods can be exactly the same as kernel methods for sample statistics and p-value.
New smoothing technique improves Wasserstein distance estimation in high dimensions.
problem Estimating statistical distances between high-dimensional distributions.
method Gaussian smoothing of p-Wasserstein distance and analysis of its asymptotic behavior. result Gaussian-smoothed p-Wasserstein distance converges at rate n−1/2, improving over n−1/d for unsmoothed distances. New adaptive tests improve statistical dependence detection.
problem Testing statistical dependence between multivariate variables.
method Adaptive nonlinear monotonic transformations of distances.
result Empirical tests outperform existing methods.
The paper uses Wasserstein distances for robust statistical learning.
problem Minimizing worst-case risk over ambiguity sets in statistical learning.
method Distributionally robust optimization with Wasserstein balls.
result Generalization bounds involving covering numbers of ERM problems.
This work proposes a model for geodesic distances and flows on manifolds.
problem Geodesic distances and flows on differentiable manifolds.
method Manifold-augmented Eikonal equation solutions.
result Geodesic flow provides globally length-minimizing curves.
High dimensional structured data such as text and images is often poorly understood and misrepresented in statistical modeling. The standard histogram representation suffers from high variance and performs poorly in general. We explore novel connections between statistical translation, heat kernels on manifolds and gra…
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, distances between embeddings of distributions to reproducing kernel Hilbert spaces (RKHS), as establ…
Generalizes robust statistics to various perturbations under Wasserstein distance.
problem Robust statistics for datasets corrupted by various perturbations.
method Generalizes robust statistics to any Wasserstein distance, showing robust estimation under certain perturbations.
result Generalized resilience property holds under moment or hypercontractive conditions, simplifying and improving known results.
The paper introduces a statistical test to assess and rank distance measures.
problem Assessing the relative information retained by different distance measures.
method Developed a statistical test to compare distance measures.
result Identifies the most informative distance measure among candidates.
This work improves understanding of projection robust optimal transport distances.
problem Understanding the behavior of minimum Wasserstein estimators in high-dimensional and misspecified models.
method Adopting projection robust (PR) optimal transport, establishing statistical properties, proposing IPRW distance, and providing asymptotic guarantees.
result Established fundamental statistical properties and proposed new distances that outperform Wasserstein distances empirically.
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.
Exact inference method for Wasserstein distance with finite-sample coverage.
problem Asymptotic approximation methods for Wasserstein distance lack finite-sample validity.
method Selective Inference inspired approach for exact inference.
result Valid confidence interval for Wasserstein distance with finite-sample coverage.
Unified framework for various probability distribution distances.
problem Handling diverse probability distribution distances in statistics.
method General framework covering density-based and distribution-function-based divergences.
result Unified approach to classical and modern statistical procedures.
The paper connects neural networks to Mahalanobis distance for interpretability.
problem Lack of interpretability in neural networks.
method Establishes a connection between neural network linear layers and Mahalanobis distance.
result Provides a foundation for more interpretable neural network models.
The article proposes modified Gower's coefficients for handling mixed type variables in nearest neighbor methods.
problem Handling mixed type variables in nearest neighbor methods, especially imputation and statistical matching.
method Suggests modifications to the Gower's distance for interval and ratio scaled variables to address unbalanced contributions and outlier sensitivity.
result Improved distance calculations reduce the unbalanced contribution of different variable types and attenuate outlier effects.
The paper uses distance covariance to improve fairness in machine learning models.
problem Improving fairness in machine learning models.
method Using conditional and distance covariance statistics to assess independence and add a penalty for fairness.
result The method effectively reduces the fairness gap in machine learning models.
This paper provides performance guarantees for neural estimation of statistical distances.
problem Developing performance guarantees for neural estimation of statistical distances.
method Non-asymptotic error bounds using function approximation theorems and empirical process theory.
result Established a fundamental tradeoff between approximation and estimation errors in neural estimation of statistical distances.
A new approach guarantees complete mode coverage in generative models.
problem Missing modes in generative models.
method Game-theoretic perspective and multiplicative weights update rule.
result Guaranteed complete mode coverage through generator mixture.
New RW distances improve GANs performance.
problem Wasserstein-1 distance limitations and slow training in GANs.
method Introducing Relaxed Wasserstein distances and applying them to GANs.
result RWGANs outperform other GANs on real images.
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.
New method speeds up computation of Sinkhorn distances for large datasets.
problem Quadratic time and memory requirements of standard Sinkhorn distance computation.
method Combining Nyström method and Sinkhorn scaling for faster approximations.
result Accurate approximations of Sinkhorn distances on massive datasets.
This work provides guaranteed bounds on the total variation distance for univariate mixtures.
problem Lack of closed-form expressions for total variation distance between mixtures.
method Two methods: information monotonicity for lower bounds and geometric envelopes for upper bounds.
result Demonstrated tightness of bounds on Gaussian, Gamma, and Rayleigh mixtures.
Paper proposes new metrics to compare asset pricing models, incorporating Bayesian insights.
problem Power problems of statistical tests and misuse of alpha-based statistics.
method Unified set of distance-based performance metrics derived from alphas and standard errors, Bayesian interpretation of model performance.
result Bayesian approach favors models with low alpha dispersion and high explanatory power, especially the momentum factor.
Survey on closed-form Fisher-Rao distance expressions.
problem Finding closed-form expressions for Fisher-Rao distance.
method Collect and present examples of closed-form expressions for Fisher-Rao distance of discrete and continuous distributions.
result Presentation of closed-form expressions for Fisher-Rao distance of various distributions.
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.
This work provides statistical guarantees for VAEs using PAC-Bayesian theory.
problem Theoretical properties of VAEs remain open questions.
method PAC-Bayesian theory to derive statistical guarantees.
result Upper bounds on Wasserstein distance between input and generative model.
Paper sets minimax bounds for Wasserstein distribution estimation.
problem Estimating a probability distribution using Wasserstein distance.
method Uses metric properties and weak moment assumptions.
result Upper and lower bounds on statistical minimax rates.
Method combines LD and Fermat Distance for neural network uncertainty.
problem Measuring uncertainty in neural network predictions.
method Statistical Depth (LD) combined with Fermat Distance.
result Effective uncertainty estimation without impacting original model performance.
New method robustifies topological data analysis against outliers.
problem Outliers make topological data analysis unstable.
method Proposed a robust distance function (MoM Dist) for persistent homology.
result MoM Dist sublevel filtrations and weighted filtrations are consistent estimators in adversarial settings.
The study examines Teichmüller distances in lattices and punctured tori.
problem Distribution of Teichmüller distances in moduli spaces.
method Uniform distribution of lattices, calculation of Teichmüller distances.
result Identifies distribution of distances in Teichmüller space.
A new ABC technique using Sliced-Wasserstein distance improves inference quality.
problem Intractable likelihood in generative models leads to loss of information in summary statistics.
method Proposes Sliced-Wasserstein ABC, a new ABC technique based on the Sliced-Wasserstein distance.
result Derives theoretical consistency results and demonstrates improved performance on synthetic and image denoising tasks.
The paper calculates expected distances on partially oriented flag manifolds.
problem Understanding distances on partially oriented flag manifolds.
method Computing expected distances on low-dimensional examples.
result Computed expected distances on partially oriented flag manifolds.
Proofs Fisher-Rao distance on Gaussian covariance manifold.
problem Proving Fisher-Rao distance on Gaussian covariance manifold.
method Basic Riemannian geometry.
result Proof of Fisher-Rao distance on covariance cone.
New measures quantify mutual dependence between multiple random vectors.
problem Measuring mutual dependence between multiple random vectors.
method Proposes three measures based on generalized distance covariance.
result Empirical and simplified empirical measures effectively test mutual independence.
New method improves robust point matching under probabilistic settings.
problem Insufficient theoretical understanding of existing point matching methods.
method Distance profiles and modified matching procedure.
result Improved robustness under probabilistic settings.
A new robust Wasserstein distance is proposed to handle outliers in probability distributions.
problem Outliers in probability distributions make Wasserstein distances sensitive and impractical.
method Introduces a new outlier-robust Wasserstein distance Wpε. result Achieves strong robust estimation guarantees under the Huber ε-contamination model. Improved computational efficiency for estimating Wasserstein distance.
problem Inefficient computation of Wasserstein distance for large samples.
method Developed Sample-Sketch-Solve paradigm using grid sketches.
result Approximates Wasserstein distance within ε error in ε^(-max(2, (d+1+o(1))/(1+α))) time.
The scaled complex Wishart distribution is a widely used model for multilook full polarimetric SAR data whose adequacy has been attested in the literature. Classification, segmentation, and image analysis techniques which depend on this model have been devised, and many of them employ some type of dissimilarity measure…
Generative model learns molecular geometry from graph representations.
problem Generating equilibrium states for molecular systems is computationally expensive.
method Probabilistic model based on Euclidean distance geometry.
result Generative model achieves state-of-the-art accuracy in molecular conformation generation.
BDC uses Distance Correlation for efficient Bayesian optimization of expensive functions.
problem Efficiently optimizing expensive black-box functions with Bayesian methods.
method Integrates Bayesian optimization with Distance Correlation for automatic exploration and exploitation.
result BDC performs similarly to popular BO methods on benchmark tests and real terrain optimization.