相关论文: Extreme Points of the Local Differential Privacy P…
We present a private learner for halfspaces over an arbitrary finite domain $X\subset \mathbb{R}^d$ with sample complexity $mathrm{poly}(d,2^{\log^*|X|})$. The building block for this learner is a differentially private algorithm for…
We investigate convex polytopes of doubly stochastic matrices having special structures: symmetric, Hankel symmetric, centrosymmetric, and both symmetric and Hankel symmetric. We determine dimensions of these polytopes and classify their…
Bilevel optimization, in which one optimization problem is nested inside another, underlies many machine learning applications with a hierarchical structure -- such as meta-learning and hyperparameter optimization. Such applications often…
We present a necessary and sufficient condition for a finite dimensional density matrix to be an extreme point of the convex set of density matrices with positive partial transpose with respect to a subsystem. We also give an algorithm for…
We characterize the extreme points of the set of incentive-compatible mechanisms for screening problems with linear utility. Our framework subsumes problems with and without transfers, such as monopoly pricing, principal-optimal bilateral…
Privacy concerns with sensitive data are receiving increasing attention. In this paper, we study local differential privacy (LDP) in interactive decentralized optimization. By constructing random local aggregators, we propose a framework to…
Local differential privacy has recently surfaced as a strong measure of privacy in contexts where personal information remains private even from data analysts. Working in a setting where both the data providers and data analysts want to…
We investigate Dobrushin coefficients of discrete Markov kernels that have bounded pointwise maximal leakage (PML) with respect to all distributions with a minimum probability mass bounded away from zero by a constant $c>0$. This definition…
Differential privacy is a recently proposed notion of privacy that provides strong privacy guarantees without any assumptions on the adversary. The paper studies the problem of computing a differentially private solution to convex…
Eigenvalues of stochastic matrices have been studied from two complementary perspectives. The individual eigenvalues are characterised through the well-established Karpelevich regions. The spectrum as a whole has also been analysed,…
Minimizing a convex risk function is the main step in many basic learning algorithms. We study protocols for convex optimization which provably leak very little about the individual data points that constitute the loss function.…
Data publishing under privacy constraints can be achieved with mechanisms that add randomness to data points when released to an untrusted party, thereby decreasing the data's utility. In this paper, we analyze this privacy-utility tradeoff…
We study differentially private (DP) algorithms for stochastic convex optimization: the problem of minimizing the population loss given i.i.d. samples from a distribution over convex loss functions. A recent work of Bassily et al. (2019)…
The behaviour of periodic points of discrete Euler top is studied. We derive invariant varieties of periodic points explicitly. When the top is axially symmetric they are specified by some particular values of the angular velocity along the…
In this paper, we study the problem of precision matrix estimation when the dataset contains sensitive information. In the differential privacy framework, we develop a differentially private ridge estimator by perturbing the sample…
We show that one can enumerate the vertices of the convex hull of integer points in polytopes whose constraint matrices have bounded and nonzero subdeterminants, in time polynomial in the dimension and encoding size of the polytope. This…
In this paper, we provide three different ways to partition the polytope of doubly substochastic matrices into subpolytopes via the prescribed row and column sums, the sum of all elements and the sub-defect respectively. Then we…
We develop an algorithmic theory of convex optimization over discrete sets. Using a combination of algebraic and geometric tools we are able to provide polynomial time algorithms for solving broad classes of convex combinatorial…
Motivated by applications of large embedding models, we study differentially private (DP) optimization problems under sparsity of individual gradients. We start with new near-optimal bounds for the classic mean estimation problem but with…
We give a useful new characterization of the set of all completely positive, trace-preserving (i.e., stochastic) maps from 2x2 matrices to 2x2 matrices. These conditions allow one to easily check any trace-preserving map for complete…