Related papers: Optimal differentially private kernel learning wit…
This paper considers the partially functional linear model (PFLM) where all predictive features consist of a functional covariate and a high dimensional scalar vector. Over an infinite dimensional reproducing kernel Hilbert space, the…
Devising mechanisms with good beyond-worst-case input-dependent performance has been an important focus of differential privacy, with techniques such as smooth sensitivity, propose-test-release, or inverse sensitivity mechanism being…
We consider a least-squares variational kernel-based method for numerical solution of second order elliptic partial differential equations on a multi-dimensional domain. In this setting it is not assumed that the differential operator is…
In this paper, we consider the parameter estimation in a bandwidth-constrained sensor network communicating through an insecure medium. The sensor performs a local quantization, and transmits a 1-bit message to an estimation center through…
We study the minimal error of the Empirical Risk Minimization (ERM) procedure in the task of regression, both in the random and the fixed design settings. Our sharp lower bounds shed light on the possibility (or impossibility) of adapting…
Motivated by the increasing deployment of reinforcement learning in the real world, involving a large consumption of personal data, we introduce a differentially private (DP) policy gradient algorithm. We show that, in this setting, the…
In this paper, we study the statistical limits of deep learning techniques for solving elliptic partial differential equations (PDEs) from random samples using the Deep Ritz Method (DRM) and Physics-Informed Neural Networks (PINNs). To…
In recent years, differential privacy has emerged as the de facto standard for sharing statistics of datasets while limiting the disclosure of private information about the involved individuals. This is achieved by randomly perturbing the…
We study efficient mechanisms for differentially private kernel density estimation (DP-KDE). Prior work for the Gaussian kernel described algorithms that run in time exponential in the number of dimensions $d$. This paper breaks the…
Empirical risk minimization is the main tool for prediction problems, but its extension to relational data remains unsolved. We solve this problem using recent ideas from graph sampling theory to (i) define an empirical risk for relational…
In recent years, multicalibration has emerged as a desirable learning objective for ensuring that a predictor is calibrated across a rich collection of overlapping subpopulations. Existing approaches typically achieve multicalibration by…
In recent years methods from optimal linear experimental design have been leveraged to obtain state of the art results for linear bandits. A design returned from an objective such as $G$-optimal design is actually a probability distribution…
We propose a novel sparse sliced inverse regression method based on random projections in a large $p$ small $n$ setting. Embedded in a generalized eigenvalue framework, the proposed approach finally reduces to parallel execution of…
We study the task of training regression models with the guarantee of label differential privacy (DP). Based on a global prior distribution on label values, which could be obtained privately, we derive a label DP randomization mechanism…
Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performances, these methods are supported by a well-developed theory.…
We consider the problem of estimating a regression function from anonymized data in the framework of local differential privacy. We propose a novel partitioning estimate of the regression function, derive a rate of convergence for the…
We present new differentially private algorithms for learning a large-margin halfspace. In contrast to previous algorithms, which are based on either differentially private simulations of the statistical query model or on private convex…
We consider the random design regression model with square loss. We propose a method that aggregates empirical minimizers (ERM) over appropriately chosen random subsets and reduces to ERM in the extreme case, and we establish sharp oracle…
With changes in privacy laws, there is often a hard requirement for client data to remain on the device rather than being sent to the server. Therefore, most processing happens on the device, and only an altered element is sent to the…
This paper proposes new methodologies for conducting practical differentially private (DP) estimation and inference in high-dimensional linear regression. We first introduce a DP Bayesian Information Criterion (DP-BIC) for selecting the…