Related papers: Functional Linear Regression of Cumulative Distrib…
The function-on-function linear regression model in which the response and predictors consist of random curves has become a general framework to investigate the relationship between the functional response and functional predictors.…
We propose dual regression as an alternative to the quantile regression process for the global estimation of conditional distribution functions under minimal assumptions. Dual regression provides all the interpretational power of the…
Optimal experimental design seeks to determine the most informative allocation of experiments to infer an unknown statistical quantity. In this work, we investigate the optimal design of experiments for {\em estimation of linear functionals…
Learning the multivariate distribution of data is a core challenge in statistics and machine learning. Traditional methods aim for the probability density function (PDF) and are limited by the curse of dimensionality. Modern neural methods…
Federated reinforcement learning (FedRL) enables collaborative learning while preserving data privacy by preventing direct data exchange between agents. However, many existing FedRL algorithms assume that all agents operate in identical…
We consider the problem of estimating the slope parameter in circular functional linear regression, where scalar responses Y1,...,Yn are modeled in dependence of 1-periodic, second order stationary random functions X1,...,Xn. We consider an…
We propose a framework for hypothesis testing on conditional probability distributions, which we then use to construct statistical tests of functionals of conditional distributions. These tests identify the inputs where the functionals…
Many statistical estimands of interest (e.g., in regression or causality) are functions of the joint distribution of multiple random variables. But in some applications, data is not available that measures all random variables on each…
The functional generalized additive model (FGAM) provides a more flexible nonlinear functional regression model than the well-studied functional linear regression model. This paper restricts attention to the FGAM with identity link and…
We study the model-based reward-free reinforcement learning with linear function approximation for episodic Markov decision processes (MDPs). In this setting, the agent works in two phases. In the exploration phase, the agent interacts with…
Considering the case where the response variable is a categorical variable and the predictor is a random function, two novel functional sufficient dimensional reduction (FSDR) methods are proposed based on mutual information and square loss…
We consider nonparametric estimation of the mean and covariance functions for functional/longitudinal data. Strong uniform convergence rates are developed for estimators that are local-linear smoothers. Our results are obtained in a unified…
The focus of this paper is to extend Fisher's linear discriminant analysis (LDA) to both densely re-corded functional data and sparsely observed longitudinal data for general $c$-category classification problems. We propose an efficient…
Approximation of scattered geometric data is often a task in many engineering problems. The Radial Basis Function (RBF) approximation is appropriate for large scattered (unordered) datasets in d-dimensional space. This method is useful for…
Reinforcement learning utilizing kernel ridge regression to predict the expected value function represents a powerful method with great representational capacity. This setting is a highly versatile framework amenable to analytical results.…
The research is about a systematic investigation on the following issues. First, we construct different outcome regression-based estimators for conditional average treatment effect under, respectively, true (oracle), parametric,…
In regression problems where there is no known true underlying model, conformal prediction methods enable prediction intervals to be constructed without any assumptions on the distribution of the underlying data, except that the training…
We consider the task of low-multilinear-rank functional regression, i.e., learning a low-rank parametric representation of functions from scattered real-valued data. Our first contribution is the development and analysis of an efficient…
Work in machine learning and statistics commonly focuses on building models that capture the vast majority of data, possibly ignoring a segment of the population as outliers. However, there does not often exist a good model on the whole…
Conformal prediction is a general distribution-free approach for constructing prediction sets combined with any machine learning algorithm that achieve valid marginal or conditional coverage in finite samples. Ordinal classification is…