Related papers: ROC curves for LDA classifiers

Using the compactified universal jacobian over the moduli space of stable marked curves, we give an expression in terms of natural classes of the zero section of the compactified universal jacobian the (rational) Chow ring. After extending…

We discuss two novel approaches to the classical two-sample problem. Our starting point are properly standardized and combined, very popular in several areas of statistics and data analysis, ordinal dominance and receiver characteristic…

The molecular characterization of tumor samples by multiple omics data sets of different types or modalities (e.g. gene expression, mutation, CpG methylation) has become an invaluable source of information for assessing the expected…

A new model validation and performance assessment tool is introduced, the sliding threshold of observation for numeric evaluation (STONE) curve. It is based on the relative operating characteristic (ROC) curve technique, but instead of…

Breast cancer is one of the leading causes of cancer-related mortality in women, and early detection is essential for improving outcomes. Magnetic resonance imaging (MRI) is a highly sensitive tool for breast cancer detection, particularly…

Geometry of holomorphic curves from point of view of open Toda systems is discussed. Parametrization of curves related this way to non-exceptional simple Lie algebras is given. This gives rise to explicit formulas for minimal surfaces in…

We review the following subjects: 1. Basic theory on algebraic curves and their moduli space, 2. Schottky uniformization theory of Riemann surfaces, and its extension called arithmetic uniformization theory, 3. Application to these theories…

The integration of multi-omics data has emerged as a promising approach for gaining comprehensive insights into complex diseases such as cancer. This paper proposes a novel approach to identify cancer subtypes through the integration of…

The Area Under the ROC Curve (AUC) is a crucial metric for machine learning, which evaluates the average performance over all possible True Positive Rates (TPRs) and False Positive Rates (FPRs). Based on the knowledge that a skillful…

In 2006, Kenyon and Okounkov computed the moduli space of Harnack curves of degree $d$ in $\mathbb{C}\mathbb{P}^2$. We generalize to any projective toric surface some of the techniques used there. More precisely, we show that the moduli…

The main goal of this paper is to compute the characteristic class of the Alekseev-Lachowska *-product on coadjoint orbits. We deduce an analogue of the Weyl dimension formula in the context of deformation quantization.

The ROC curve is widely used to assess binary classifiers. Yet for some applications, such as alert systems for monitoring hospitalized patients, conventional ROC analysis cannot meet two key deployment needs: enforcing a constraint on…

The Receiver Operating Characteristic (ROC) surface is a generalization of ROC curve and is widely used for assessment of the accuracy of diagnostic tests on three categories. A complication called the verification bias, meaning that not…

In this paper we deal with polarizations on a nodal curve $C$ with smooth components. Our aim is to study and characterize a class of polarizations, which we call "good", for which depth one sheaves on $C$ reflect some properties that hold…

We trained and evaluated a localization-based deep CNN for breast cancer screening exam classification on over 200,000 exams (over 1,000,000 images). Our model achieves an AUC of 0.919 in predicting malignancy in patients undergoing breast…

We study a Lorentzian version of the well-known Calder\'{o}n problem that is concerned with determination of lower order coefficients in a wave equation on a smooth Lorentzian manifold, given the associated Dirichlet-to-Neumann map. In the…

Breast cancer is one of the two cancers responsible for the most deaths in women, with about 42,000 deaths each year in the US. That there are over 300,000 breast cancers newly diagnosed each year suggests that only a fraction of the…

The `linear orbit' of a plane curve of degree d is its orbit in P^{d(d+3)/2} under the natural action of PGL(3). We classify curves with positive dimensional stabilizer, and we compute the degree of the closure of the linear orbits of…

In this paper, we present a new statistical approach to automatically identify cancer regions in pathological images. The proposed method is built from statistical theory in line with evidence-based medicine. The two core technologies are…

Deep learning (DL) has proven highly effective for ultrasound-based computer-aided diagnosis (CAD) of breast cancers. In an automaticCAD system, lesion detection is critical for the following diagnosis. However, existing DL-based methods…