Related papers: ROC curves for LDA classifiers
ROC analyses are considered under a variety of assumptions concerning the distributions of a measurement $X$ in two populations. These include the binormal model as well as nonparametric models where little is assumed about the form of…
Kernel alignment measures the degree of similarity between two kernels. In this paper, inspired from kernel alignment, we propose a new Linear Discriminant Analysis (LDA) formulation, kernel alignment LDA (kaLDA). We first define two…
We obtain a Bochner type formula and an estimate from below on the spectrum of the sublaplacian of a compact strictly pseudoconvex CR manifold.
A matrix polynomial is a polynomial in a complex variable $\lambda$ with coefficients in $n \times n$ complex matrices. The spectral curve of a matrix polynomial $P(\lambda)$ is the curve $\{ (\lambda, \mu) \in \mathbb{C}^2 \mid…
Free-response observer performance studies are of great importance for accuracy evaluation and comparison in tasks related to the detection and localization of multiple targets or signals. The free-response receiver operating characteristic…
We design an efficient algorithm that outputs tests for identifying predominantly homogeneous subcohorts of patients from large in-homogeneous datasets. Our theoretical contribution is a rounding technique, similar to that of Goemans and…
Linear resolutions and the stronger notion of linear quotients are important properties of monomial ideals. In this paper, we fully characterize linear quotients in terms of the lcm-lattice of monomial ideals. We also formulate an analogous…
When people evaluate the performance of a diagnostic test, it is important to control both True Positive Rate (TPR) and False Positive Rate (FPR). In the literature, most researchers propose the partial area under the ROC curve (pAUC) with…
We review the key steps of the construction of Levin-Wen type of models on lattices with boundaries and defects of codimension 1,2,3 in a joint work with Alexei Kitaev. We emphasize some universal properties, such as boundary-bulk duality…
It has been unknown whether Hirota's discrete Korteweg-de Vries equation and the lattice sine-Gordon equation have the consistency around a cube (CAC) property. In this paper, we show that they have the CAC property. Moreover, we also show…
We introduce an extension to local principal component analysis for learning symmetric manifolds. In particular, we use a spectral method to approximate the Lie algebra corresponding to the symmetry group of the underlying manifold. We…
Estimating average human performance has been performed inconsistently in research in diagnostic medicine. This has been particularly apparent in the field of medical artificial intelligence, where humans are often compared against AI…
We consider a subclass of the Cowen-Douglas class in which the problem of deciding whether two operators are similar becomes more manageable. A similarity criterion for Cowen-Douglas operators is known to be dependent on the trace of the…
For a Lie groupoid there is an analytic index morphism which takes values in the $K-$theory of the $C^*$-algebra associated to the groupoid. This is a good invariant but extracting numerical invariants from it, with the existent tools, is…
Whilst the size and complexity of ML models have rapidly and significantly increased over the past decade, the methods for assessing their performance have not kept pace. In particular, among the many potential performance metrics, the ML…
In this paper we obtain an explicit formula for the number of degree d curves in two dimensional complex projective space, passing through (d(d+3)/2 -k) generic points and having a codimension k singularity, where k is at most 7. In the…
Detecting cancers at early stages can dramatically reduce mortality rates. Therefore, practical cancer screening at the population level is needed. Here, we develop a comprehensive detection system to classify all common cancer types. By…
Motivated by the classical Euler elastic curves, David A. Singer posed in 1999 the problem of determining a plane curve whose curvature is given in terms of its position. We propound the same question in Lorentz-Minkowski plane, focusing on…
Prior to clinical applications, it is critical that risk prediction models are evaluated in independent studies that did not contribute to model development. While prospective cohort studies provide a natural setting for model validation,…
Accurate lymph node metastasis (LNM) assessment in rectal cancer is essential for treatment planning, yet current MRI-based evaluation shows unsatisfactory accuracy, leading to suboptimal clinical decisions. Developing automated systems…