Sampling matrices from Harish-Chandra–Itzykson–Zuber densities with applications to Quantum inference and differential privacy

Enhanced Privacy Preserving for Social Networks Relational Data Based on Personalized Differential Privacy

“…Bichsel et al [15] proposed the DP-Finder method, which is a novel approach and system that automatically derives lower bounds on the differential privacy enforced by algorithms. Rubinstein et al [16] designed a sampler based on sensitivity sampling, which can automatically achieve random differential privacy. Leake et al [17] proposed a straightforward sampler for estimating sensitivity of non-private mechanisms, their sensitivity estimates hold with high probability, any mechanism that would be -differentially private under bounded global sensitivity automatically achieves -random differential privacy, Liu et al [18] proposed a local differential privacy model for social network publishing that preserves community structure information.…”

“…According to the sampling method, we delete the nodes that do not meet the privacy requirements and Perturbation method Mittal et al [8] , Fard et al [9] Cannot face the attacker with good knowledge background Anonymity method Cheng et al [10] , Ahmed et al [11] , Casas et al [12] , Zheleva et al [13] Cannot face the attacker with good knowledge background Differential privacy method Gao et al [14] , Bichsel et al [15] , Rubinstein et al [16] , Leake et al [17] , Liu et al [18] , Huang et al [19] Cannot provide personalized privacy protection in social network data protection…”

“…Leake et al . [ 17 ] proposed a straightforward sampler for estimating sensitivity of non‐private mechanisms, their sensitivity estimates hold with high probability, any mechanism that would be ‐differentially private under bounded global sensitivity automatically achieves ‐random differential privacy, Liu et al . [ 18 ] proposed a local differential privacy model for social network publishing that preserves community structure information.…”

Topological Expansion of Oscillatory BGW and HCIZ Integrals at Strong Coupling

“…Thus I (m) N may be viewed as an entire function of mN + 1 complex variables whose restriction to R mN +1 takes positive values, defining a true partition function in the sense of statistical physics. See [79] for some recent algorithmic results on sampling from the corresponding Gibbs measure in the case m = 2.…”

Statistical limits of dictionary learning: random matrix theory and the spectral replica method

“…Another one is to employ its asymptotic hydrodynamic description [79,80] but this is challenging too. The HCIZ formula can be evaluated exactly in very special cases (e.g., the uniform and Wigner cases below) or perturbatively (see Section 3), or approximated by using sampling techniques [88]. We wish to point out that an easy and nice application of the HCIZ formula is to check that the asymptotic mutual information obtained in Conjecture 2 is the same for a signal S or its centered (trace-less) version S − I d,N N −1 TrS (where I d,N is the identity of size N ); this can be checked using basic properties of determinants.…”