Extends L2-norm LDA to 2D inputs using Bhattacharyya bound.
problem L2-norm LDA loses useful image information for 2D inputs.
method 2DBLDA maximizes matrix-based between-class distance and minimizes within-class distance, optimizing Bhattacharyya error bound.
result 2DBLDA improves image recognition and face reconstruction.
Combines distance measures and dimension reduction for comparing distributions.
problem Comparing different entities' distributions and their similarities.
method Marriage between Bhattacharyya distance and Johnson-Lindenstrauss Lemma for dimension reduction.
result Demonstrates relationship between covariance and distance measures.
New algorithm clusters multiple samples from hidden distributions.
problem Traditional clustering algorithms cannot handle multiple samples from non-Gaussian distributions.
method Proposes a general framework for multiple sample clustering, generating various algorithms.
result Sufficient statistics improve clustering accuracy and stability.
Novel L1-norm and L2-norm LDA methods improve discriminant analysis.
problem Improving linear discriminant analysis for robustness and adaptability.
method Proposes L1BLDA and L2BLDA using Bhattacharyya error bound, maximizing between-class scatters and minimizing within-class scatters.
result Proposed methods avoid SSS and have no rank limit, demonstrating robust performance and effectiveness.
New properties for density-based dissimilarity measures in hybrid clustering are proposed and evaluated.
problem Choosing the right dissimilarity measure for hybrid clustering.
method Six data-independent properties for density-based dissimilarity measures are proposed and evaluated.
result A new dissimilarity measure based on Kullback-Leibler information is introduced and shown to satisfy all proposed properties.
Paper connects rejection learning to Bhattacharyya divergence.
problem Learning models to abstain from predictions.
method Developed a link between rejection and thresholding different statistical divergences, focusing on Bhattacharyya divergence.
result Rejector obtained by joint ideal distribution corresponds to thresholding of skewed Bhattacharyya divergence.
New divergences introduced in dually flat spaces with properties.
problem Measuring discrepancy between probability distributions in dually flat spaces.
method Introducing two types of divergences based on affine coordinates and potentials, and deriving relational equations.
result Generalization of the law of cosines and new inequalities between divergences.
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…
Images obtained with coherent illumination, as is the case of sonar, ultrasound-B, laser and Synthetic Aperture Radar -- SAR, are affected by speckle noise which reduces the ability to extract information from the data. Specialized techniques are required to deal with such imagery, which has been modeled by the G0 dist…
Study on error probability for classification of heavy-tailed renewal processes.
problem Error probability in classification of heavy-tailed renewal processes.
method Asymptotic expressions for Bhattacharyya bound on misclassification error probabilities.
result Obtained asymptotic expressions for misclassification error probabilities.
In many machine learning problems, labeled training data is limited but unlabeled data is ample. Some of these problems have instances that can be factored into multiple views, each of which is nearly sufficent in determining the correct labels. In this paper we present a new algorithm for probabilistic multi-view lear…
In data science, it is often required to estimate dependencies between different data sources. These dependencies are typically calculated using Pearson's correlation, distance correlation, and/or mutual information. However, none of these measures satisfy all the Granger's axioms for an "ideal measure". One such ideal…
Detects anomalies in sensor data using entropy changes.
problem Identifying unusual measurements in sensor data.
method Estimates probability density function and entropy, detects anomalies based on entropy changes.
result Method detects subtle anomalies not covered by previous work.
Estimates mixture entropy using pairwise distances.
problem Computing mixture entropy is challenging due to lack of closed-form solutions.
method Proposes a family of estimators based on pairwise distances.
result The proposed estimators are efficient, differentiable, and provide tight bounds on mixture entropy.
Market microstructure studies aim to reduce frictions in financial markets by analyzing price, volume, and volatility.
problem Reducing frictions in financial markets to improve efficiency and reduce costs.
method Application of Bhattacharyya distance and Johnson Lindenstrauss Lemma for comparing distributions of financial variables.
result Different markets or securities have distinct measures of their distributions, aiding in diversification or finding similar assets.
Efficient unsupervised training and inference in deep generative models remains a challenging problem. One basic approach, called Helmholtz machine, involves training a top-down directed generative model together with a bottom-up auxiliary model used for approximate inference. Recent results indicate that better genera…
A framework for disentangling class-related and class-independent factors in data.
problem Learning disentangled representations in variational autoencoders.
method Attention mechanism in latent space, mixture models, Bhattacharyya coefficient, semi-supervised training.
result Disentangles class-related and class-independent factors of variation.
Algorithm learns latent simplex from perturbed points in input-sparsity time.
problem Learning a latent k-vertex simplex from noisy data. method Input-sparsity time algorithm using low-rank approximation and adaptive selection.
result Algorithm achieves O(extrmnnz(A)) time complexity, avoiding k⋅extrmnnz(A). Geometrically refines Cramér-Rao bound using extrinsic manifold curvature.
problem Improving estimator efficiency in non-asymptotic settings.
method Incorporates curvature-aware corrections based on extrinsic geometry of statistical model manifold.
result Meaningful tightening of estimator variance bounds.
New CRB derived for curved models using extrinsic geometry.
problem Estimate curved statistical families accurately.
method Vector generalization of CRB with curvature correction using SDP and SOS relaxations.
result Directional curvature correction provides more accurate estimation.
Article provides Bernstein gradient estimates for heat equations with potential terms.
problem Gradient estimates for heat equations with potential terms on weighted Riemannian manifolds.
method Derived Bernstein type gradient estimates for two systems of heat equations with linear, exponential, and combined potentials.
result Resolves part of the problem raised by Bhattacharyya et al. in \cite{SB-1}.
The space of probability distributions on a given sample space possesses natural geometric properties. For example, in the case of a smooth parametric family of probability distributions on the real line, the parameter space has a Riemannian structure induced by the embedding of the family into the Hilbert space of squ…
GP-DRF model handles variable-sized input and learns deep features.
problem Scaling deep Gaussian processes for variable-sized data.
method GP-DRF model combining GPs and DRF layers for efficient inference.
result GP-DRF outperforms standard GP and DRF models across various datasets.
Study reconstructs hidden perfect matchings in random graphs with specific edge weights.
problem Reconstructing hidden perfect matchings in random weighted bipartite graphs.
method Analyzes the maximum likelihood estimator for matching reconstruction under different probability distributions of edge weights.
result Sharp threshold and infinite-order phase transition in reconstruction error for different probability distributions.
We propose a representation of graph as a functional object derived from the power iteration of the underlying adjacency matrix. The proposed functional representation is a graph invariant, i.e., the functional remains unchanged under any reordering of the vertices. This property eliminates the difficulty of handling e…
Efficiently learns polytrees with known skeleton in polynomial time and sample complexity.
problem Learning polytrees with known skeleton structure.
method Proposes an efficient algorithm for learning d-polytrees in polynomial time and sample complexity when the skeleton is known. result Establishes finite-sample guarantees for efficient learning of d-polytrees. Improves two-sample hypothesis testing using kernel divergences and scoring rules.
problem Two-sample hypothesis testing in machine learning.
method Proposes Kernel Scoring Rules and Divergences, including the Maximum Mean Discrepancy.
result Kernel Score provides more information about embedded distributions than Maximum Mean Discrepancy.
There has been a growing interest in mutual information measures due to their wide range of applications in Machine Learning and Computer Vision. In this paper, we present a generalized structured regression framework based on Shama-Mittal divergence, a relative entropy measure, which is introduced to the Machine Learn…
New algorithms SVCA and SSPA improve robustness to noise in nonnegative matrix factorization.
problem Estimating vertices from noisy data points in convex hull.
method Smoothed VCA (SVCA) and Smoothed SPA (SSPA) algorithms.
result Improved robustness to noise compared to existing methods.
Unified geometric interpretation of statistical estimation inequalities.
problem Curvature corrections in parametric statistical estimation.
method Cartan-geometric jet bundle formulation and jet prolongations.
result Unified geometric interpretation of higher-order information inequalities.
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.
Develops geometric framework for uncertainty-aware multi-class classification.
problem Silent failure of AI models when uncertain, especially in multi-class settings.
method Geometric framework treating probability vectors as points on the (c−1)-dimensional probability simplex, using Fisher--Rao metric for calibration and uncertainty quantification. result Empirical validation shows 72.5% of errors captured while deferring 34.5% of ambiguous predictions, reducing automated decision error rates from 16.8% to 6.9%.
The paper introduces a new risk measure for financial models with jumps.
problem The limitations of point-in-time risk measures in models with jumps.
method Proposes an intra-horizon expected shortfall for profit and loss processes.
result The intra-horizon expected shortfall is a coherent risk measure for various Lévy processes.
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.
Formula calculates distance between triangulations using arc graphs.
problem Calculating distances between triangulations efficiently.
method Proved a formula using projections into arc graphs.
result Distance formula for flip graph between triangulations.