Related papers: On functional logistic regression: some conceptual…
We revisit the problem of the existence of the maximum likelihood estimate for multi-class logistic regression. We show that one method of ensuring its existence is by assigning positive probability to every class in the sample dataset. The…
Consider the nonparametric logistic regression problem. In the logistic regression, we usually consider the maximum likelihood estimator, and the excess risk is the expectation of the Kullback-Leibler (KL) divergence between the true and…
Previous analysis of regularized functional linear regression in a reproducing kernel Hilbert space (RKHS) typically requires the target function to be contained in this kernel space. This paper studies the convergence performance of…
Classical regression analysis relates the expectation of a response variable to a linear combination of explanatory variables. In this article, we propose a covariance regression model that parameterizes the covariance matrix of a…
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…
We address the problem of {\it adaptivity} in the framework of reproducing kernel Hilbert space (RKHS) regression. More precisely, we analyze estimators arising from a linear regularization scheme $g_\lam$. In practical applications, an…
Longitudinal studies with binary or ordinal responses are widely encountered in various disciplines, where the primary focus is on the temporal evolution of the probability of each response category. Traditional approaches build from the…
The paper considers linear regression problems where the number of predictor variables is possibly larger than the sample size. The basic motivation of the study is to combine the points of view of model selection and functional regression…
Functional data that are nonnegative and have a constrained integral can be considered as samples of one-dimensional density functions. Such data are ubiquitous. Due to the inherent constraints, densities do not live in a vector space and,…
Classical functional linear regression models the relationship between a scalar response and a functional covariate, where the coefficient function is assumed to be identical for all subjects. In this paper, the classical model is extended…
The aim of this study is to present a good modernistic strategy for solving some well-known classes of Lane-Emden type singular differential equations. The proposed approach is based on the reproducing kernel Hilbert space (RKHS) and…
An asymptotic theory is established for linear functionals of the predictive function given by kernel ridge regression, when the reproducing kernel Hilbert space is equivalent to a Sobolev space. The theory covers a wide variety of linear…
The logistic regression model is one of the most powerful statistical methods for the analysis of binary data. The logistic regression allows to use a set of covariates to explain the binary responses. The mixture of logistic regression…
Learning in the reproducing kernel Hilbert space (RKHS) such as the support vector machine has been recognized as a promising technique. It continues to be highly effective and competitive in numerous prediction tasks, particularly in…
Over the last decade, kernel methods for nonlinear processing have successfully been used in the machine learning community. The primary mathematical tool employed in these methods is the notion of the Reproducing Kernel Hilbert Space.…
We consider the problem of consistently estimating the conditional distribution $P(Y \in A |X)$ of a functional data object $Y=(Y(t): t\in[0,1])$ given covariates $X$ in a general space, assuming that $Y$ and $X$ are related by a functional…
A conventional linear model for functional data involves expressing a response variable $Y$ in terms of the explanatory function $X(t)$, via the model: $Y=a+\int_I b(t)X(t)dt+\hbox{error}$, where $a$ is a scalar, $b$ is an unknown function…
We present a unified theoretical and computational framework for constructing reproducing kernels tailored to transport equations and adapted to Koopman eigenfunctions of nonlinear dynamical systems. These eigenfunctions satisfy a…
Additive models form a widely popular class of regression models which represent the relation between covariates and response variables as the sum of low-dimensional transfer functions. Besides flexibility and accuracy, a key benefit of…
Modern machine learning models with high accuracy are often miscalibrated -- the predicted top probability does not reflect the actual accuracy, and tends to be over-confident. It is commonly believed that such over-confidence is mainly due…