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Found 13 papers, 3 papers with code
Smoothness Adaptive Hypothesis Transfer Learning
We first prove that employing the misspecified fixed bandwidth Gaussian kernel in target-only KRR learning can achieve minimax optimality and derive an adaptive procedure to the unknown Sobolev smoothness.
Pure Differential Privacy for Functional Summaries via a Laplace-like Process
Many existing mechanisms to achieve differential privacy (DP) on infinite-dimensional functional summaries often involve embedding these summaries into finite-dimensional subspaces and applying traditional DP techniques.
FAStEN: an efficient adaptive method for feature selection and estimation in high-dimensional functional regressions
Functional regression analysis is an established tool for many contemporary scientific applications.
Shape And Structure Preserving Differential Privacy
It is common for data structures such as images and shapes of 2D objects to be represented as points on a manifold.
On Hypothesis Transfer Learning of Functional Linear Models
We study the transfer learning (TL) for the functional linear regression (FLR) under the Reproducing Kernel Hilbert Space (RKHS) framework, observing the TL techniques in existing high-dimensional linear regression is not compatible with the truncation-based FLR methods as functional data are intrinsically infinite-dimensional and generated by smooth underlying processes.
A Highly-Efficient Group Elastic Net Algorithm with an Application to Function-On-Scalar Regression
Feature Selection and Functional Data Analysis are two dynamic areas of research, with important applications in the analysis of large and complex data sets.
Modern Non-Linear Function-on-Function Regression
We introduce a new class of non-linear function-on-function regression models for functional data using neural networks.
Non-linear Functional Modeling using Neural Networks
We introduce a new class of non-linear models for functional data based on neural networks.
Modern Multiple Imputation with Functional Data
This work considers the problem of fitting functional models with sparsely and irregularly sampled functional data.
An Efficient Semi-smooth Newton Augmented Lagrangian Method for Elastic Net
Our new algorithm exploits both the sparsity induced by the Elastic Net penalty and the sparsity due to the second order information of the augmented Lagrangian.
Fast and Fair Simultaneous Confidence Bands for Functional Parameters
Quantifying uncertainty using confidence regions is a central goal of statistical inference.
Methodology Statistics Theory Statistics Theory
KNG: The K-Norm Gradient Mechanism
This paper presents a new mechanism for producing sanitized statistical summaries that achieve \emph{differential privacy}, called the \emph{K-Norm Gradient} Mechanism, or KNG.
Benefits and Pitfalls of the Exponential Mechanism with Applications to Hilbert Spaces and Functional PCA
We study its extension to settings with summaries based on infinite dimensional outputs such as with functional data analysis, shape analysis, and nonparametric statistics.
