arXiv research

New method assesses prediction intervals across different operating points.

Geometric analysis of ROC and PR curves for binary classification.

We propose a novel classifier accuracy metric: the Bayesian Area Under the Receiver Operating Characteristic Curve (CBAUC). The method estimates the area under the ROC curve and is related to the recently proposed Bayesian Error Estimator. The metric can assess the quality of a classifier using only the training datase…

Many problems that appear in biomedical decision making, such as diagnosing disease and predicting response to treatment, can be expressed as binary classification problems. The costs of false positives and false negatives vary across application domains and receiver operating characteristic (ROC) curves provide a visu…

Study predicts antimicrobial resistance in ICU patients quickly.

Throughout science and technology, receiver operating characteristic (ROC) curves and associated area under the curve (AUC) measures constitute powerful tools for assessing the predictive abilities of features, markers and tests in binary classification problems. Despite its immense popularity, ROC analysis has been su…

The paper proposes a test to assess rater accuracy while accounting for rater covariates.

Efficient algorithm for evaluating hierarchical classification methods at multiple operating points.

Machine learning methods may have the potential to significantly accelerate drug discovery. However, the increasing rate of new methodological approaches being published in the literature raises the fundamental question of how models should be benchmarked and validated. We reanalyze the data generated by a recently pub…

Receiver operating characteristic (ROC) analysis is widely used for evaluating diagnostic systems. Recent studies have shown that estimating an area under ROC curve (AUC) with standard cross-validation methods suffers from a large bias. The leave-pair-out (LPO) cross-validation has been shown to correct this bias. Howe…

The Receiver Operating Characteristic (ROC) curve is a representation of the statistical information discovered in binary classification problems and is a key concept in machine learning and data science. This paper studies the statistical properties of ROC curves and its implication on model selection. We analyze the …

We compute the Euler characteristics of the recently discovered series of Gothic Teichmüller curves. The main tool is the construction of 'Gothic' Hilbert modular forms vanishing at the images of these Teichmüller curves. Contrary to all previously known examples, the Euler characteristic is not proportional to the Eul…

We investigate the relationship among characteristic curves on developable surfaces. In case parameter curves coincide with these curves, we show that the base curve of a developable surface could be either a plane curve, a circular helix, a general helix or a slant helix.

Unified four trade-off curves for assessing generative model proximity.

The paper diagnoses factor models using characteristic axes and zero-curve restrictions.

The paper proves simplicial volume positivity for certain nonpositively curved 4-manifolds with nonzero Euler characteristic.

The paper diagnoses factor-model pricing errors using characteristic axes and bridge-alpha curves.

A new method QMS22 for semi-supervised anomaly detection outperforms existing methods.

We complete the remaining cases of the conjecture predicting existence of infinitely many rational curves on K3 surfaces in characteristic zero, prove almost all cases in positive characteristic and improve the proofs of the previously known cases. To achieve this, we introduce two new techniques in the deformation the…

Study Euler characteristic of manifolds with almost nonnegative curvature operator, showing nonnegativity under certain conditions.

We consider a $C^{1}$ smooth surface with prescribed $p$(or $H$)-mean curvature in the 3-dimensional Heisenberg group. Assuming only the prescribed $p$-mean curvature $H\in C^{0},$ we show that any characteristic curve is $C^{2}$ smooth and its (line) curvature equals $-H$ in the nonsingular domain$.$ By introducing ch…

LxCIM metric improves binary classification performance evaluation.

Modified AUC improves CNN training by considering model confidence.

Study Schrödinger evolution on surfaces in 3D contact sub-Riemannian manifolds.

We calculate the Euler characteristics of all of the Teichmuller curves in the moduli space of genus two Riemann surfaces which are generated by holomorphic one-forms with a single double zero. These curves can all be embedded in Hilbert modular surfaces and our main result is that the Euler characteristic of a Teichmu…

Neural network models improve ROC curve evaluation of biomarkers, focusing on age's role in physical activity-mortality association.

The study shows that nonpositively curved 4-manifolds with zero Euler characteristic have degenerating Ricci curvature.

We give a local integral formula, valid on general curved space-times, for the characteristic Cauchy problem for the Dirac equation with arbitrary spin using the method developed by Friedlander in his book "the wave equation on a curved spacetime" (1975). The results obtained by Penrose in the flat case in "Null hypers…

When sufficient labeled data are available, classical criteria based on Receiver Operating Characteristic (ROC) or Precision-Recall (PR) curves can be used to compare the performance of un-supervised anomaly detection algorithms. However , in many situations, few or no data are labeled. This calls for alternative crite…

Computes the Euler characteristic and rational homology of moduli spaces of multi-monopoles.

Proposes a new prior for VAEs to improve out-of-distribution detection.

The paper studies spectral properties of Jacobi operator for surfaces with nonpositive Euler characteristic.

The paper studies complex curves with translation structures from differential equations.

Worldsheet skein D-module for Hopf link conormal uniquely determines partition functions.

Formula conjectured for rational cuspidal curves in projective plane.

Formula proves Euler characteristic of singularized surfaces.

Study compatible and associated metrics for contact-symplectic structures, showing geodesic integral curves and minimal leaf properties.

Deep learning has significant potential for medical imaging. However, since the incident rate of each disease varies widely, the frequency of classes in a medical image dataset is imbalanced, leading to poor accuracy for such infrequent classes. One possible solution is data augmentation of infrequent classes using syn…

The study connects conic connections and torsion-free principal connections on G-structures.

The geometric Cauchy problem for a class of surfaces in a pseudo-Riemannian manifold of dimension 3 is to find the surface which contains a given curve with a prescribed tangent bundle along the curve. We consider this problem for constant negative Gauss curvature surfaces (pseudospherical surfaces) in Euclidean 3-spac…

We give conceptual proofs of some well known results concerning compact non-positively curved locally symmetric spaces. We discuss vanishing and non-vanishing of Pontrjagin numbers and Euler characteristics for these locally symmetric spaces. We also establish vanishing results for Stiefel-Whitney numbers of (finite co…

We describe and study the loci equidistant from finitely many points in the so-called complex hyperbolic geometry, i.e., in the geometry of a holomorphic $2$-ball $\Bbb B$. In particular, we show that the bisectors (= the loci equidistant from $2$ points) containing the (smooth real algebraic) curve equidistant from gi…

Electronic medical records (EMRs) supports the development of machine learning algorithms for predicting disease incidence, patient response to treatment, and other healthcare events. But insofar most algorithms have been centralized, taking little account of the decentralized, non-identically independently distributed…

We discuss a notion of integration with respect to the Euler characteristic in the projectivization $¶{\cal O}_{\C^n,0}$ of the ring ${\cal O}_{\C^n,0}$ of germs of functions on $C^n$ and show that the Alexander polynomial and the zeta-function of a plane curve singularity can be expressed as certain integrals over $¶{…

Optimal cutoff interval for risk scores improves binary classification accuracy.

Quadratic growth of intersecting curves on surfaces resolved.

Intensive care clinicians are presented with large quantities of patient information and measurements from a multitude of monitoring systems. The limited ability of humans to process such complex information hinders physicians to readily recognize and act on early signs of patient deterioration. We used machine learnin…

We study a generalization of constant Gauss curvature -1 surfaces in Euclidean 3-space, based on Lorentzian harmonic maps, that we call pseudospherical frontals. We analyze the singularities of these surfaces, dividing them into those of characteristic and non-characteristic type. We give methods for constructing all n…