Zobrazeno 1 - 10
of 254
pro vyhledávání: '"Vershynin, Roman"'
We investigate the best constant $J(n,d)$ such that Jackson's inequality \[ \inf_{\mathrm{deg}(g) \leq d} \|f - g\|_{\infty} \leq J(n,d) \, s(f), \] holds for all functions $f$ on the hypercube $\{0,1\}^n$, where $s(f)$ denotes the sensitivity of $f$
Externí odkaz:
http://arxiv.org/abs/2410.19949
The problem of detecting fake data inspires the following seemingly simple mathematical question. Sample a data point $X$ from the standard normal distribution in $\mathbb{R}^n$. An adversary observes $X$ and corrupts it by adding a vector $rt$, wher
Externí odkaz:
http://arxiv.org/abs/2410.18880
While differentially private synthetic data generation has been explored extensively in the literature, how to update this data in the future if the underlying private data changes is much less understood. We propose an algorithmic framework for stre
Externí odkaz:
http://arxiv.org/abs/2409.00322
Synthetic data are an attractive concept to enable privacy in data sharing. A fundamental question is how similar the privacy-preserving synthetic data are compared to the true data. Using metric privacy, an effective generalization of differential p
Externí odkaz:
http://arxiv.org/abs/2405.00329
We present a polynomial-time algorithm for online differentially private synthetic data generation. For a data stream within the hypercube $[0,1]^d$ and an infinite time horizon, we develop an online algorithm that generates a differentially private
Externí odkaz:
http://arxiv.org/abs/2402.08012
We show that every $(n,d,\lambda)$-graph contains a Hamilton cycle for sufficiently large $n$, assuming that $d\geq \log^{6}n$ and $\lambda\leq cd$, where $c=\frac{1}{70000}$. This significantly improves a recent result of Glock, Correia and Sudakov,
Externí odkaz:
http://arxiv.org/abs/2402.06177
Much of the research in differential privacy has focused on offline applications with the assumption that all data is available at once. When these algorithms are applied in practice to streams where data is collected over time, this either violates
Externí odkaz:
http://arxiv.org/abs/2401.14577
Autor:
Vershynin, Roman
We ask whether most Boolean functions are determined by their low frequencies. We show a partial result: for almost every function $f: \{-1,1\}^p \to \{-1,1\}$ there exists a function $f': \{-1,1\}^p \to (-1,1)$ that has the same frequencies as $f$ u
Externí odkaz:
http://arxiv.org/abs/2401.13143
We show that the minimal number of skewed hyperplanes that cover the hypercube $\{0,1\}^{n}$ is at least $\frac{n}{2}+1$, and there are infinitely many $n$'s when the hypercube can be covered with $n-\log_{2}(n)+1$ skewed hyperplanes. The minimal cov
Externí odkaz:
http://arxiv.org/abs/2310.13277