Related papers: ROC curve analysis for functional markers
Radio frequency (RF) signals have facilitated the development of non-contact human monitoring tasks, such as vital signs measurement, activity recognition, and user identification. In some specific scenarios, an RF signal analysis framework…
The authors study statistical linear inverse problems in Hilbert spaces. Approximate solutions are sought within a class of linear one-parameter regularization schemes, and the parameter choice is crucial to control the root mean squared…
Elastic Riemannian metrics have been used successfully in the past for statistical treatments of functional and curve shape data. However, this usage has suffered from an important restriction: the function boundaries are assumed fixed and…
This paper deals with analyzing structural breaks in the covariance operator of sequentially observed functional data. For this purpose, procedures are developed to segment an observed stretch of curves into periods for which second-order…
The functional linear model extends the notion of linear regression to the case where the response and covariates are iid elements of an infinite dimensional Hilbert space. The unknown to be estimated is a Hilbert-Schmidt operator, whose…
We develop methodology for the estimation of the functional mean and the functional principal components when the functions form a spatial process. The data consist of curves $X(\mathbf{s}_k;t),t\in[0,T],$ observed at spatial locations…
In the framework of scalar-on-function regression models, in which several functional variables are employed to predict a scalar response, we propose a methodology for selecting relevant functional predictors while simultaneously providing…
Learning a nonparametric system of ordinary differential equations from trajectories in a $d$-dimensional state space requires learning $d$ functions of $d$ variables. Explicit formulations often scale quadratically in $d$ unless additional…
Function-on-function linear regression is important for understanding the relationship between the response and the predictor that are both functions. In this article, we propose a reproducing kernel Hilbert space approach to…
We present a Representer Theorem result for a large class of weak formulation problems. We provide examples of applications of our formulation both in traditional machine learning and numerical methods as well as in new and emerging…
In this paper we present a nonparametric method for extending functional regression methodology to the situation where more than one functional covariate is used to predict a functional response. Borrowing the idea from Kadri et al.…
There has been a split in the statistics community about the need for taking covariates into account in the design phase of a clinical trial. There are many advocates of using stratification and covariate-adaptive randomization to promote…
In this paper we consider the problems of supervised classification and regression in the case where attributes and labels are functions: a data is represented by a set of functions, and the label is also a function. We focus on the use of…
We introduce a new model of linear regression for random functional inputs taking into account the first order derivative of the data. We propose an estimation method which comes down to solving a special linear inverse problem. Our…
The development of a metric for structural data is a long-term problem in pattern recognition and machine learning. In this paper, we develop a general metric for comparing nonlinear dynamical systems that is defined with Perron-Frobenius…
Receiver Operating Characteristic (ROC) curves are plots of true positive rate versus false positive rate which are useful for evaluating binary classification models, but difficult to use for learning since the Area Under the Curve (AUC)…
Individualized treatment rules (ITRs) are considered a promising recipe to deliver better policy interventions. One key ingredient in optimal ITR estimation problems is to estimate the average treatment effect conditional on a subject's…
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…
Multidimensional function data arise from many fields nowadays. The covariance function plays an important role in the analysis of such increasingly common data. In this paper, we propose a novel nonparametric covariance function estimation…
Koopman operator describes evolution of observables in the phase space, which could be used to extract characteristic dynamical features of a nonlinear system. Here, we show that it is possible to carry out interesting symbolic partitions…