相关论文: ROC curve analysis for functional markers

We provide a comprehensive theory of conducting in-sample statistical inference about receiver operating characteristic (ROC) curves that are based on predicted values from a first stage model with estimated parameters (such as a logit…

Researchers in functional neuroimaging mostly use activation coordinates to formulate their hypotheses. Instead, we propose to use the full statistical images to define regions of interest (ROIs). This paper presents two machine learning…

Risk stratification is most directly and informatively summarized as a risk distribution curve. From this curve the ROC curve, predictiveness curve, and other curves depicting risk stratification can be derived, demonstrating that they…

Supervised operator learning centers on the use of training data, in the form of input-output pairs, to estimate maps between infinite-dimensional spaces. It is emerging as a powerful tool to complement traditional scientific computing,…

As with classic statistics, functional regression models are invaluable in the analysis of functional data. While there are now extensive tools with accompanying theory available for linear models, there is still a great deal of work to be…

Spectral discretizations of fractional derivative operators are examined, where the approximation basis is related to the set of Jacobi polynomials. The pseudo-spectral method is implemented by assuming that the grid, used to represent the…

The Kendall plot ($\K$-plot) is a plot measuring dependence between the components of a bivariate random variable. The $\K$-plot graphs the Kendall distribution function against the distribution function of $VU$, where $V$ and $U$ are…

Rationing of healthcare resources has emerged as an important issue, which has been discussed by medical experts, policy-makers, and the general public. We consider a rationing problem where medical units are to be allocated to patients.…

We consider four main goals when fitting spatial linear models: 1) estimating covariance parameters, 2) estimating fixed effects, 3) kriging (making point predictions), and 4) block-kriging (predicting the average value over a region). Each…

We here introduce indicator functions, which identify regions of a given density in order to characterize the density dependence of clustering. After a general introduction to this tool, we show that indicator-function power spectra are…

Due to the increasing recording capability, functional data analysis has become an important research topic. For functional data the study of outlier detection and/or the development of robust statistical procedures has started recently.…

Let ${\mbox{$\mbox{\boldmath $f$}$}}$ be a square-integrable, zero-mean, random vector with observable realizations in a Hilbert space $H$, and let ${\mbox{$\mbox{\boldmath $g$}$}}$ be an associated square-integrable, zero-mean, random…

Autonomous exploration is a complex task where the robot moves through an unknown environment with the goal of mapping it. The desired output of such a process is a sequence of paths that efficiently and safely minimise the uncertainty of…

Classical spectral theory provides powerful tools for analyzing linear operators, but does not extend naturally to nonlinear or compositional settings. In particular, there is no general way to transport spectral invariants in a functorial…

Many applications of AI involve scoring individuals using a learned function of their attributes. These predictive risk scores are then used to take decisions based on whether the score exceeds a certain threshold, which may vary depending…

Functional data analysis is a fast evolving branch of statistics. Estimation procedures for the popular functional linear model either suffer from lack of robustness or are computationally burdensome. To address these shortcomings, a…

Individualized treatment rules aim to identify if, when, which, and to whom treatment should be applied. A globally aging population, rising healthcare costs, and increased access to patient-level data have created an urgent need for…

We encounter a bottleneck when we try to borrow the strength of classical classifiers to classify functional data. The major issue is that functional data are intrinsically infinite dimensional, thus classical classifiers cannot be applied…

We formulate a supervised learning problem, referred to as continuous ranking, where a continuous real-valued label Y is assigned to an observable r.v. X taking its values in a feature space $\mathcal{X}$ and the goal is to order all…

We consider linear models with scalar responses and covariates from a separable Hilbert space. The aim is to detect change points in the error distribution, based on sequential residual empirical distribution functions. Expansions for those…