相关论文: ROC curve analysis for functional markers

We observe two sequences of curve which are connected via an integral operator. Our model includes linear models as well as autoregressive models in Hilbert spaces. We wish to test the null hypothesis that the operator did not change during…

Continuous biomarkers are common for disease screening and diagnosis. To reach a dichotomous clinical decision, a threshold would be imposed to distinguish subjects with disease from non-diseased individuals. Among various performance…

Fractional integral operators connected with real-valued scalar functions of matrix argument are applied in problems of mathematics, statistics and natural sciences. In this article we start considering the case of a Gauss hypergeometric…

Multiple diagnostic tests are frequently used to determine the presence of a disease condition in patients. In this paper, we use bivariate copulas to examine the properties of receiver operating characteristic (ROC) curves formed when two…

We consider challenges that arise in the estimation of the mean outcome under an optimal individualized treatment strategy defined as the treatment rule that maximizes the population mean outcome, where the candidate treatment rules are…

The receiver operating characteristic (ROC) curve is an important graphic tool for evaluating a test in a wide range of disciplines. While useful, an ROC curve can cross the chance line, either by having an S-shape or a hook at the extreme…

This paper addresses the fundamental task of estimating covariance matrix functions for high-dimensional functional data/functional time series. We consider two functional factor structures encompassing either functional factors with scalar…

The choice of the location of controllers and observations is of great importance for designing control systems and improving the estimations in various practical problems. For time-varying systems in Hilbert spaces, the existence and…

Estimating covariance matrices is a problem of fundamental importance in multivariate statistics. In practice it is increasingly frequent to work with data matrices $X$ of dimension $n\times p$, where $p$ and $n$ are both large. Results…

This article deals with the problem of functional classification for L2-valued random covariates when some of the covariates may have missing or unobservable fragments. Here, it is allowed for both the training sample as well as the new…

Two different approaches to analysis of data from diagnostic biomarker studies are commonly employed. Logistic regression is used to fit models for probability of disease given marker values, while ROC curves and risk distributions are used…

A consistent functional calculus approach to the spectral theorem for strongly commuting normal operators on Hilbert spaces is presented. In contrast to the common approaches using projection-valued measures or multiplication operators,…

We introduce a formulation of optimal transport problem for distributions on function spaces, where the stochastic map between functional domains can be partially represented in terms of an (infinite-dimensional) Hilbert-Schmidt operator…

The goal of Inverse Optimal Control (IOC) is to identify the underlying objective function based on observed optimal trajectories. It provides a powerful framework to model expert's behavior, and a data-driven way to design an objective…

Area under the ROC curve, a.k.a. AUC, is a measure of choice for assessing the performance of a classifier for imbalanced data. AUC maximization refers to a learning paradigm that learns a predictive model by directly maximizing its AUC…

While the area under the ROC curve is perhaps the most common measure that is used to rank the relative performance of different binary classifiers, longstanding field folklore has noted that it can be a measure that ill-captures the…

Graph classification in medical imaging and drug discovery requires accuracy and robust uncertainty quantification. To address this need, we introduce Conditional Prediction ROC (CP-ROC) bands, offering uncertainty quantification for ROC…

When observations are curves over some natural time interval, the field of functional data analysis comes into play. Functional linear processes account for temporal dependence in the data. The prediction problem for functional linear…

Multivariate spatial field data are increasingly common and whose modeling typically relies on building cross-covariance functions to describe cross-process relationships. An alternative viewpoint is to model the matrix of spectral…

This is a tutorial introduction to the functional analysis mathematics needed in many physical problems, such as in waves in continuous media. Functional analysis takes us beyond finite matrices, allowing us to work with infinite sets of…