Improved average distance classifier for HDLSS settings with multiple population differences.
problem Poor performance of average distance classifier in HDLSS settings with location and scale differences.
method Proposed transformations to the average distance classifier to handle multiple population differences.
result The proposed classifiers perform well even when populations differ in other aspects than location and scale.
New bounds for average graph distance using curvature and centrality.
problem Finding bounds for average graph distance.
method Using weighted average Ollivier curvature with edge betweenness centrality.
result Equality in bounds achieved for specific reflective graphs.
Optimal posterior distributions improve SVM classifiers and parameter selection.
problem Improving SVM classifiers and selecting optimal regularization parameters.
method PAC-Bayesian approach with optimal posterior identification for stochastic classifiers.
result Optimal posteriors yield tight risk bounds and improved SVM performance.
In this work, we addressed the issue of combining linear classifiers using their score functions. The value of the scoring function depends on the distance from the decision boundary. Two score functions have been tested and four different combination strategies were investigated. During the experimental study, the pro…
A simple method flags images as out-of-distribution based on their distance to nearest neighbors.
problem Detecting images not aligned with a trained model's in-distribution data.
method Flag images as OOD if their average distance to K nearest neighbors is large in the classifier's representation space.
result Simple methods can outperform more complex ones when considering learned representations.
DW-KNN improves KNN by integrating distance and neighbor reliability for better prediction accuracy.
problem Standard KNN assumes all neighbors are equally reliable, leading to unreliable predictions in heterogeneous feature spaces.
method DW-KNN integrates exponential distance with neighbor validity, providing instance-level interpretability and reducing hyperparameter sensitivity.
result DW-KNN achieves 0.8988 average accuracy, ranks 2nd among six methods, and has the lowest cross-validation variance.
The paper introduces tests for high-dimensional independence using maximum and average distance correlations.
problem Testing independence in high-dimensional data.
method Characterizes consistency properties, compares test statistics, examines null distributions, and presents a fast chi-square-based procedure.
result The proposed tests are non-parametric and applicable to various metrics.
tl;dr: no, it cannot, at least not on average on the standard archive problems. We assess whether using six smoothing algorithms (moving average, exponential smoothing, Gaussian filter, Savitzky-Golay filter, Fourier approximation and a recursive median sieve) could be automatically applied to time series classificatio…
Flexible classifier using Mahalanobis distances for non-elliptical distributions.
problem Classifying non-elliptical and multimodal distributions.
method Semiparametric classifier based on Mahalanobis distances and generalized additive models.
result The proposed classifiers outperform traditional methods in high-dimensional, low-sample-size scenarios.
Paper proposes a method to classify EEG signals with missing data.
problem Handling missing data in electroencephalogram (EEG) signals for classification.
method Uses an expectation-maximization algorithm with observed-data likelihood to compute covariance matrices, compares to imputed data and Riemannian averages.
result The proposed method generally performs better than existing methods on real EEG data.
We consider classifiers for high-dimensional data under the strongly spiked eigenvalue (SSE) model. We first show that high-dimensional data often have the SSE model. We consider a distance-based classifier using eigenstructures for the SSE model. We apply the noise reduction methodology to estimation of the eigenvalue…
We consider general non-Euclidean distance measures between real world objects that need to be classified. It is assumed that objects are represented by distances to other objects only. Conditions for zero-error dissimilarity based classifiers are derived. Additional conditions are given under which the zero-error deci…
WF distance measures time series similarity via spectral density displacement.
problem Measuring similarity between time series.
method Wasserstein-Fourier distance between normalised power spectral densities.
result WF establishes as a general-purpose metric for time series.
The paper classifies singularities of plane congruences and affine distance functions.
problem Classifying singularities of plane congruences and affine distance functions.
method Classification through 2-parameter plane congruences in \(\mathbb{R^4}\) and affine normal plane congruences.
result Generic singularities of plane congruences and affine distance functions are classified.
Study on predicting graph labels at nodes using local averaging and distance estimation.
problem Predicting graph labels at nodes given observations at other nodes.
method Local averaging and distance estimation methods for graph regression.
result Alternative methods can achieve standard nonparametric rates even when graph neighborhoods are too large or small.
Paper defines a new distance metric for comparing learning tasks.
problem Comparing difficulty of learning tasks between source and target.
method Information geometry, optimal transport, coupled transfer distance.
result Coupled transfer distance correlates with fine-tuning difficulty.
The k-nearest neighbour (k-NN) classifier is one of the oldest and most important supervised learning algorithms for classifying datasets. Traditionally the Euclidean norm is used as the distance for the k-NN classifier. In this thesis we investigate the use of alternative distances for the k-NN classifier. We …
Paper explains distance-based classifiers using neural network structures.
problem Making distance-based classifiers explainable.
method Uncovering latent neural network structures in distance-based classifiers.
result Novel explanation approach outperforms baselines.
A new classifier uses Fermat distance for semi-supervised learning in high dimensions.
problem Semi-supervised classification with limited labeled data in high-dimensional settings.
method Proposes weighted k-NN and MDS classifiers using Fermat distance.
result The weighted k-NN classifier is minimax optimal and outperforms other methods.
Paper proves CLTs for Q-learning with asynchronous updates.
problem Establishing convergence rates for Q-learning algorithms.
method Polyak-Ruppert averaging, non-asymptotic and functional CLTs.
result Convergence rates in Wasserstein distance for Q-learning.
RS-Del provides robustness for sequence classifiers against edit distance attacks.
problem Certifying robustness of discrete sequence classifiers against edit distance attacks.
method Randomized deletion (RS-Del) for discrete sequence classifiers, focusing on edit distance-bounded adversaries.
result Achieved a certified accuracy of 91% at an edit distance radius of 128 bytes on malware detection.
We present an information-theoretic framework for bounding the number of labeled samples needed to train a classifier in a parametric Bayesian setting. We derive bounds on the average Lp distance between the learned classifier and the true maximum a posteriori classifier, which are well-established surrogates for th…
This thesis uses Kantorovich-Rubinstein distance for classifying points based on their measures.
problem Classifying points based on their measures in a metric space.
method Using Kantorovich-Rubinstein distance as a metric in the space of measures to capture geometry and topology.
result A large Kantorovich-Rubinstein distance indicates the existence of a 1-Lipschitz classifier that well classifies the points.
Novel neural network approximates exact distance for robust classification.
problem Adversarial attacks on neural networks in safety-critical systems.
method Signed Distance Classifiers (SDCs) and Unitary-Gradient Neural Network.
result Approximates exact distance from classification boundary for certifiable predictions.
In his seminal work, Schapire (1990) proved that weak classifiers could be improved to achieve arbitrarily high accuracy, but he never implied that a simple majority-vote mechanism could always do the trick. By comparing the asymptotic misclassification error of the majority-vote classifier with the average individual …
Clusters of financial market states identified over 2006-2019.
problem Understanding the statistical properties of financial markets.
method Clustering analysis of correlation matrices constructed from sliding epochs.
result Financial markets can be classified into distinct states with transitions indicating precursors to catastrophic events.
We introduce a new metric to evaluate corruption robustness of ML classifiers.
problem Evaluating corruption robustness of machine learning classifiers.
method We propose a test data augmentation method using minimal class separation distance to derive a robustness distance ε and a metric MSCR.
result The MSCR metric allows interpretable comparison of classifier robustness on different datasets.
Single particle reconstruction (SPR) from cryo-electron microscopy (EM) is a technique in which the 3D structure of a molecule needs to be determined from its contrast transfer function (CTF) affected, noisy 2D projection images taken at unknown viewing directions. One of the main challenges in cryo-EM is the typically…
Adversarial robustness has become an important research topic given empirical demonstrations on the lack of robustness of deep neural networks. Unfortunately, recent theoretical results suggest that adversarial training induces a strict tradeoff between classification accuracy and adversarial robustness. In this paper,…
Time series classification is an increasing research topic due to the vast amount of time series data that are being created over a wide variety of fields. The particularity of the data makes it a challenging task and different approaches have been taken, including the distance based approach. 1-NN has been a widely us…
In this paper we study the geometry of metric spheres in the curve complex of a surface, with the goal of determining the "average" distance between points on a given sphere. Averaging is not technically possible because metric spheres in the curve complex are countably infinite and do not support any invariant probabi…
We define generalized distance-squared mappings, and we concentrate on the plane to plane case. We classify generalized distance-squared mappings of the plane into the plane in a recognizable way.
This paper provides new insight into maximizing F1 scores in the context of binary classification and also in the context of multilabel classification. The harmonic mean of precision and recall, F1 score is widely used to measure the success of a binary classifier when one class is rare. Micro average, macro average, a…
Proposes a non-convex optimization method for a parsimonious weighted naive Bayes classifier.
problem Improving naïve Bayes classifier performance with a large number of input variables.
method Sparse regularization of model log-likelihood for direct estimation of variable weights.
result Optimization-based weighted naïve Bayes classifiers achieve equivalent performance to averaging-based classifiers.
The dynamic time warping (dtw) distance fails to satisfy the triangle inequality and the identity of indiscernibles. As a consequence, the dtw-distance is not warping-invariant, which in turn results in peculiarities in data mining applications. This article converts the dtw-distance to a semi-metric and shows that its…
Proposes a new scoring function for linear classifiers to improve object positioning in feature space.
problem Lack of information about relative positions of recognized objects in feature space.
method Calculates a scoring function based on object distance from decision boundary and class centroid.
result Demonstrates effectiveness of the proposed method compared to other ensemble algorithms on multiple datasets.
New fairness criteria for algorithmic recourse actions that consider causal relationships.
problem Fairness of recourse actions in algorithmic classification.
method Proposes two new fairness criteria at group and individual levels, explicitly accounting for causal relationships.
result Fairness of recourse is complementary to fairness of prediction, and can be enforced by altering the classifier.
Revises Bayesian model averaging for foundation models.
problem Ensemble pre-trained and lightly-finetuned foundation models for improved classification performance.
method Introduces trainable linear classifiers and computationally cheaper model averaging scheme (OMA).
result Ensembled models can better predict on various datasets.
Mahalanobis distance detects anomalies well, but not for classification.
problem Detecting anomalies in neural classifier outputs.
method Analyzes Mahalanobis distance-based anomaly detection method, revealing its reliance on information not useful for classification.
result Combining Mahalanobis and ODIN methods improves anomaly detection performance and robustness.
Proposes MFSWB for marginal fairness in SWB, improving efficiency and performance.
problem Achieving marginal fairness in SWB averaging.
method Defining MFSWB as a constrained SWB problem, proposing two surrogate problems and a new slicing distribution.
result Surrogate MFSWB problems effectively minimize distances to marginals and encourage marginal fairness.
A clustering procedure, based on the Hausdorff distance, is introduced and tested on the financial time series of the Dow Jones Industrial Average (DJIA) index.
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.
If a simple 3-manifold M admits a reducible and a toroidal Dehn filling, the distance between the filling slopes is known to be bounded by three. In this paper, we classify all manifolds which admit a reducible Dehn filling and a toroidal Dehn filling with distance 3.
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.
Model tracks structural changes in Brownian particle configurations on a sphere.
problem Tracking structural changes in Brownian particle configurations on a sphere.
method Introduces Frustrated Distance Matrix (FDM) model for dynamic distance matrices on S^2.
result Preserves static BBS template with dynamics as redistributed spectral mass.
The nearest neighbor classifier fails in high dimensions, leading to this study.
problem Failure of nearest neighbor classifier in high-dimensional data.
method Discussed and proposed new methods to address the issue.
result The proposed methods improve performance in high-dimensional data.
We prove that S^2 x S^2 satisfies an intermediate condition between having metrics with positive Ricci and positive sectional curvature. Namely, there exist metrics for which the average of the sectional curvatures of any two planes tangent at the same point, but separated by a minimum distance in the 2-Grassmannian, i…
Detecting adversarial examples is as hard as classifying them.
problem The difficulty of detecting adversarial examples in machine learning models.
method Proved a general hardness reduction between detection and classification of adversarial examples.
result The hardness reduction implies that detecting adversarial examples is computationally infeasible.