Cramming method evaluates learned policies from contextual bandits efficiently.
problem Evaluating final learned policies from contextual bandit algorithms.
method On-policy evaluation using a single pass of data, ensuring consistency and asymptotic normality.
result Cramming method reduces evaluation standard error by approximately 40% compared to off-policy methods.
New algorithms improve reinforcement learning for complex tasks.
problem Improving reinforcement learning for complex tasks.
method Developed new algorithms using distributional reinforcement learning and Cram{é}r distance.
result Proved asymptotic almost-sure convergence of new algorithms for neural networks.
Near-optimal confidence intervals for bounded data.
problem Online inference for sequential decision problems like A/B testing.
method Utilizing Bentkus' concentration results to improve on existing methods.
result Near-optimal confidence intervals confirmed favorable in synthetic and practical applications.
Study on ruin probabilities for Lévy processes with light-tailed jumps.
problem Determining bounds on ruin probabilities for Lévy processes.
method Analyzing the Laplace exponent of the Lévy process to find bounds on ruin probabilities.
result Identification of a new case not previously considered in the literature.
Paper introduces DLE for efficient inference of intractable models.
problem Intractable likelihood functions in model inference.
method DLE based on Kullback-Leibler divergence minimization and Stein operator.
result DLE can achieve Fisher efficiency under mild conditions.
We study the statistical properties of the recurrence intervals τ between successive trading volumes exceeding a certain threshold q. The recurrence interval analysis is carried out for the 20 liquid Chinese stocks covering a period from January 2000 to May 2009, and two Chinese indices from January 2003 to April 2…
Data selection boosts fact memorization in language models.
problem Language models struggle to accurately memorize factual knowledge.
method Formalizes fact memorization, proposes data selection schemes based on training loss.
result Data selection boosts fact accuracy to model capacity and improves performance.
Energy markets and the associated energy futures markets play a crucial role in global economies. We investigate the statistical properties of the recurrence intervals of daily volatility time series of four NYMEX energy futures, which are defined as the waiting times τ between consecutive volatilities exceeding a gi…
Three methods detect informed trading on prediction markets, each focusing on different aspects.
problem Detecting informed trading in decentralized prediction markets.
method Composite screen, event-level sign-randomization test, and Information Leakage Score (ILS) framework.
result Different methods detect informed trading on prediction markets, each focusing on different aspects.
The paper tightens bounds on distances between Reeb graphs.
problem Certifying quasi-universality of distances between Reeb graphs.
method Establishes tight bi-Lipschitz bounds for various distances.
result Proves strict universality of the functional contortion distance for contour trees and coincides with interleaving distance for merge trees.
Paper defines new GSW distances for probability measures.
problem Computational simplicity and similarity to Wasserstein distance.
method Generalized Radon transform to define GSW distances.
result GSW and max-GSW distances are distances under certain conditions.
Paper calculates Gromov-Hausdorff distance between simplexes and 2-distance spaces.
problem Calculating Gromov-Hausdorff distance between simplexes and 2-distance spaces.
method Formulas derived for clique covering number and chromatic number of graphs.
result Complete solution to generalized Borsuk problem for 2-distance spaces.
Extends Teichmüller distance concept to non-distance maps.
problem Defining distance metrics for non-distance functions.
method Generalizes horofunction compactification to non-distance maps.
result Defines horofunction counterpart to Teichmüller distance.
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.
New network distance based on Laplacian flow captures structure.
problem Measuring similarity between network objects.
method Introducing Laplacian flow to define a new diffusion distance.
result Demonstrated utility and advantage over existing distances.
Calculates Gordian distances using algebraic methods.
problem Determining when Alexander polynomials can't be realized by matrices with Gordian distance one.
method Using Blanchfield pairings and quadratic equations with integer solutions.
result Shows that certain Alexander polynomials cannot be realized by matrices with Gordian distance one.
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.
There have lately been several suggestions for parametrized distances on a graph that generalize the shortest path distance and the commute time or resistance distance. The need for developing such distances has risen from the observation that the above-mentioned common distances in many situations fail to take into ac…
Graph neural network learns graph distances effectively.
problem Maintaining graph distance metric properties.
method GRAPH-BERT based semi-supervised distance metric learning.
result GB-DISTANCE outperforms existing methods.
The paper studies stable mappings of plane curves using distance-squared functions.
problem Stability of mappings of plane curves.
method Investigation of compositions of plane curves and generic distance-squared mappings.
result Stable mappings of plane curves are explored.
New toolkit for directed distances improves flexibility of OT problems.
problem Optimal transport problems with constraints.
method Directed distances between quantile functions.
result Flexibility in solving OT problems enhanced.
A new robust metric compares distributions more accurately than existing methods.
problem Sensitivity to outliers and sampling discrepancy in Wasserstein distances.
method Introducing k-RPW, a partial p-Wasserstein distance.
result k-RPW converges faster to true distance and is more robust to outliers.
A new metric HCP distance for comparing distributions.
problem Comparing high-dimensional probability distributions efficiently.
method Hilbert curve projection to low-dimensional coupling, followed by transport distance calculation.
result HCP distance is a proper metric for probability measures with bounded supports.
Formula for interleaving distance of rectangle persistence modules.
problem Calculating distances between rectangle persistence modules.
method Formulas based on rectangle geometry, extended to decomposable modules.
result Closed formulas for interleaving and bottleneck distances.
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 distances for comparing multivariate normal distributions.
problem Comparing multivariate normal distributions efficiently and accurately.
method Approximated Fisher-Rao distance and pullback SPD cone distances.
result Efficient computation of distances between normal distributions.
The paper introduces a new Wasserstein distance for approximating posteriors in inverse problems.
problem Approximating posterior measures in inverse problems using conditional Wasserstein distances.
method Introduces a conditional Wasserstein distance with restricted couplings and derives its dual.
result Shows that conditional Wasserstein GANs can yield favorable properties for posterior sampling.
Finite mapping class groups for Heegaard splittings with distance ≥ 3, but not for distance 2.
problem Finiteness of mapping class groups for Heegaard splittings.
method Analysis of Heegaard splittings with distances 1, 2, and 3.
result Mapping class groups are finite for Heegaard splittings with distance ≥ 3, but not for distance 2.
Framework uses Minimax distances for unsupervised feature extraction.
problem Extracting features from unlabeled data.
method Develops a framework for computing Minimax distances and embedding them into a vector space.
result Minimax distances effectively capture underlying patterns and structures in data.
The paper studies horofunction compactifications of symmetric cones under Finsler distances.
problem Understanding horofunction compactifications of symmetric cones under Finsler distances.
method Establishing a correspondence between horofunction compactifications of symmetric cones and normed spaces, using Thompson and Hilbert distances.
result Explicit extensions of the exponential map and characterizations of horofunctions for Thompson and Hilbert distances.
A new supervised tree-Wasserstein distance improves document classification.
problem Measuring document similarity efficiently and accurately.
method Rewriting Wasserstein distance on tree metric, using contrastive loss for optimization.
result The Supervised Tree-Wasserstein (STW) distance improves document classification accuracy.
CADM proposes a cluster-specific distance metric for categorical data clustering.
problem Inadequate distance metrics for categorical data, especially varying within clusters.
method Cluster-customized adaptive distance metric for categorical data.
result Achieved competitive performance in categorical data clustering.
Estimates manifold distances using graph Laplacian, proving consistency.
problem Estimating distances in compact Riemannian manifolds.
method Graph Laplacian estimates of the Laplace-Beltrami operator, bounding errors.
result Proof of consistency for manifold distances.
Transforms distance-based outlier scores into interpretable probabilistic estimates.
problem Difficult interpretation of distance-based outlier scores.
method Generic transformation of scores into probabilistic estimates using distance probability distributions.
result Probabilistic transformation improves interpretability without impacting detection performance.
Paper proves rigidity of inversive distance circle packings.
problem Proving rigidity of inversive distance circle packings.
method Variational principles and combinatorial curvature study.
result Global rigidity of inversive distance circle packings proved.
A new stable edit distance for Reeb graphs is shown to be universal.
problem Stability and comparability of Reeb graphs under function similarity.
method Defined and proved stability and universality of Reeb graph edit distance.
result Reeb graph edit distance is the most stable and universal among distances.
New distances defined on Legendrian spaces without positive loops.
problem Defining distances on Legendrian spaces without positive loops.
method Constructing unbounded invariant distances on Legendrian isotopy classes.
result Invariant distances on Legendrian isotopy classes are discrete.
Different distances on symmetrical domains in complex space.
problem Comparing distances on specific complex domains.
method Examined Carathéodory pseudo-distance and Kähler-Einstein metric distances.
result Found the distances differ on certain complex domains.
A method for fast estimation of Wasserstein distances using sliced Wasserstein distances.
problem Efficiently computing Wasserstein distances for multiple pairs of distributions.
method Regression on sliced Wasserstein distances to predict true Wasserstein distances.
result The proposed method provides a better approximation of Wasserstein distance than state-of-the-art models, especially in low-data regimes.
Study compares distances for indoor WiFi mapping, finding Earth Mover's Distance effective.
problem Indoor localization and mapping using WiFi signals.
method Comparison of distance measures and kernel density estimation.
result Earth Mover's Distance is most beneficial for indoor localization.
A new warping-invariant distance improves nearest-neighbor classification efficiency.
problem dtw distance inconsistency and inefficiency in nearest-neighbor classification.
method Showed dtw is not warping-invariant, converted to twi distance.
result twi distance equivalent error rates to dtw, more efficient.
The study bounds distances in simplicial complexes and defines new invariants for 3-manifolds and handlebody-knots.
problem Estimating distances in simplicial complexes associated with low-dimensional manifolds.
method Obtained bounds on distances in simplicial complexes using topological conditions on vertices and curve complexes. Defined new invariants for 3-manifolds and handlebody-knots using splitting distances.
result Splitting distances in simplicial complexes are bounded from below under stabilizations, leading to converging invariants.
The distance function ϱ(p,q) (or d(p,q)) of a distance space (general metric space) is not differentiable in general. We investigate such distance spaces over Rn, whose distance functions are differentiable like in case of Finsler spaces. These spaces have several good properties, yet they are no F…
The paper explores selecting the parameter α for Fermat distance to balance geometry and noise.
problem Choosing the optimal parameter α for Fermat distance to navigate geometry and noise.
method Theoretical and simulation studies to determine the best α value.
result An optimal α value is identified to balance geometry and noise.
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.
Paper finds the best way to estimate neural net distance from samples.
problem Estimating the neural net distance from samples.
method Developed minimax lower and upper bounds for the neural net distance.
result Lower and upper bounds match, validating the empirical neural net distance.
New method estimates Wasserstein distances more efficiently.
problem Efficient estimation of Wasserstein distances.
method Orthogonal coupling in Monte Carlo estimation.
result Proposes a new variant of sliced Wasserstein distance.
Learning a distance function or metric on a given data manifold is of great importance in machine learning and pattern recognition. Many of the previous works first embed the manifold to Euclidean space and then learn the distance function. However, such a scheme might not faithfully preserve the distance function if t…