arXiv research

Local and global classifications of Einstein submanifolds in Euclidean space.

The paper shows over-confidence in models isn't just due to over-parametrization.

In recent years, many non-traditional classification methods, such as Random Forest, Boosting, and neural network, have been widely used in applications. Their performance is typically measured in terms of classification accuracy. While the classification error rate and the like are important, they do not address a fun…

Study magnetic curves in Sasakian manifolds, classifying and parametrizing them.

New model for time series classification from single example.

Simpler GNNs with low-rank non-parametric aggregators perform well on graph benchmarks.

IB-GAN improves multivariate time series classification under imbalance.

The model interpretation is essential in many application scenarios and to build a classification model with a ease of model interpretation may provide useful information for further studies and improvement. It is common to encounter with a lengthy set of variables in modern data analysis, especially when data are coll…

The paper studies binary classification and aims at estimating the underlying regression function which is the conditional expectation of the class labels given the inputs. The regression function is the key component of the Bayes optimal classifier, moreover, besides providing optimal predictions, it can also assess t…

Convolutional neural networks converge quickly with gradient descent.

We propose a new constrained-optimization formulation for deep ordinal classification, in which uni-modality of the label distribution is enforced implicitly via a set of inequality constraints over all the pairs of adjacent labels. Based on (c-1) constraints for c labels, our model is non-parametric and, therefore, mo…

We introduce a framework, twisted parametrized stable homotopy theory, for describing semi-infinite homotopy types. A twisted parametrized spectrum is a section of a bundle whose fibre is the category of spectra. We define these bundles in terms of modules over a stack of parametrized spectra and in terms of diagrams o…

Improved DNN calibration without sacrificing accuracy.

Study reveals differences in label shift problem difficulty in supervised vs. unsupervised settings.

Proposes a multi-resolution model for prostate cancer classification using mpMRI.

Several classification methods assume that the underlying distributions follow tree-structured graphical models. Indeed, trees capture statistical dependencies between pairs of variables, which may be crucial to attain low classification errors. The resulting classifier is linear in the log-transformed univariate and b…

Graph convolutional neural networks (GCNN) have been successfully applied to many different graph based learning tasks including node and graph classification, matrix completion, and learning of node embeddings. Despite their impressive performance, the techniques have a limited capability to incorporate the uncertaint…

The Neyman-Pearson (NP) paradigm in binary classification seeks classifiers that achieve a minimal type II error while enforcing the prioritized type I error controlled under some user-specified level $α$. This paradigm serves naturally in applications such as severe disease diagnosis and spam detection, where people h…

SMD outperforms SGD in over-parametrized linear models for certain data distributions.

In this article we characterize all biharmonic curves of the Cartan-Vranceanu 3-dimensional spaces and we give their explicit parametrizations.

Many applications of classification methods not only require high accuracy but also reliable estimation of predictive uncertainty. However, while many current classification frameworks, in particular deep neural networks, achieve high accuracy, they tend to incorrectly estimate uncertainty. In this paper, we propose a …

We consider the problems of clustering, classification, and visualization of high-dimensional data when no straightforward Euclidean representation exists. Typically, these tasks are performed by first reducing the high-dimensional data to some lower dimensional Euclidean space, as many manifold learning methods have b…

Probabilistic Quantum Memory (PQM) is a data structure that computes the distance from a binary input to all binary patterns stored in superposition on the memory. This data structure allows the development of heuristics to speed up artificial neural networks architecture selection. In this work, we propose an improved…

Adversarially robust machine learning has received much recent attention. However, prior attacks and defenses for non-parametric classifiers have been developed in an ad-hoc or classifier-specific basis. In this work, we take a holistic look at adversarial examples for non-parametric classifiers, including nearest neig…

The paper classifies and analyzes the stability of elastic curves with fixed endpoints.

Researchers classify cmc surfaces using Jacobi elliptic functions.

Theoretical and empirical taxonomy of imbalance in binary classification.

Extends Demographic Parity for fairer wage predictions with expert knowledge.

Novel nonparametric method for GLMs improves prediction and inference performance.

Classifies ancient ovals in higher dimensional mean curvature flow.

We show that every rational knot $K$ of crossing number $N$ admits a polynomial parametrization $x=T_a(t), y = T_b(t), z = C(t)$ where $T_k(t)$ are the Chebyshev polynomials, $a=3$ and $b+ °C = 3N.$ We show that every rational knot also admits a polynomial parametrization with $a=4$. If $C (t)= T_c(t)$ is a Chebyshev p…

Conventional techniques for supervised classification constrain the classification rules considered and use surrogate losses for classification 0-1 loss. Favored families of classification rules are those that enjoy parametric representations suitable for surrogate loss minimization, and low complexity properties suita…

Estimates classifier errors without ground truth using algebraic geometry.

Metric learning methods for dimensionality reduction in combination with k-Nearest Neighbors (kNN) have been extensively deployed in many classification, data embedding, and information retrieval applications. However, most of these approaches involve pairwise training data comparisons, and thus have quadratic computat…

One of the fundamental problems in supervised classification and in machine learning in general, is the modelling of non-parametric invariances that exist in data. Most prior art has focused on enforcing priors in the form of invariances to parametric nuisance transformations that are expected to be present in data. Le…

Study classifies special Hessian rank 2 hypersurfaces in 4D space.

Singularities of even smooth functions are studied. A classification of singular points which appear in typical parametric families of even functions with at most five parameters is given. Bifurcations of singular points near a caustic value of the parameter are also studied. A determinant for singularity types and con…

Study classifies ruled surfaces critical to Dirichlet energy.

We show that among the Euclidean submanifolds with codimension two the ones of rank two that are parabolic but nonruled are isometrically rigid. This generalizes the result in [10] that these submanifolds are genuinely rigid. In addition, we give a parametric classifications of all parabolic submanifolds.

Almost contact B-metric manifolds of dimension 3 are constructed by a two-parametric family of Lie groups. The class of these manifolds in a known classification of almost contact B-metric manifolds is determined as the direct sum of the main vertical classes. The type of the corresponding Lie algebras in the Bianchi c…

For any Engel 4-fold, we show that the scanning map from the space of Engel knots to the space of formal Engel knots is a weak homotopy equivalence when restricted to the complement of the orbits of the Engel kernel. This is a relative, parametric and close h-principle.

Information divergence functions play a critical role in statistics and information theory. In this paper we show that a non-parametric f-divergence measure can be used to provide improved bounds on the minimum binary classification probability of error for the case when the training and test data are drawn from the sa…

I propose a frequency domain adaptation of the Expectation Maximization (EM) algorithm to group a family of time series in classes of similar dynamic structure. It does this by viewing the magnitude of the discrete Fourier transform (DFT) of each signal (or power spectrum) as a probability density/mass function (pdf/pm…

Improves industry classification for diversified companies.

In this paper we give a complete local parametric classification of the hypersurfaces with dimension at least three of a space form that carry a totally geodesic foliation of codimension one. A classification under the assumption that the leaves of the foliation are complete was given in \cite{drt} for Euclidean hypers…

Study linear transformations' effects on data augmentation for improved estimation.

Paper tackles label noise in large datasets, purifying noisy data with a nonparametric framework.

This work tackles manifold regression onto hyperbolic space for tree classification and taxonomy extension.