Compressive Privacy for a Linear Dynamical System

We consider a linear dynamical system in which the state vector consists of both public and private states. One or more sensors make measurements of the state vector and sends information to a fusion center, which performs the final state estimation. To achieve an optimal tradeoff between the utility of estimating the public states and protection of the private states, the measurements at each time step are linearly compressed into a lower dimensional space. Under the centralized setting where all measurements are collected by a single sensor, we propose an optimization problem and an algorithm to find the best compression matrix. Under the decentralized setting where measurements are made separately at multiple sensors, each sensor optimizes its own local compression matrix. We propose methods to separate the overall optimization problem into multiple sub-problems that can be solved locally at each sensor. We consider the cases where there is no message exchange between the sensors; and where each sensor takes turns to transmit messages to the other sensors. Simulations and empirical experiments demonstrate the efficiency of our proposed approach in allowing the fusion center to estimate the public states with good accuracy while preventing it from estimating the private states accurately

Context-Aware Generative Adversarial Privacy

Preserving the utility of published datasets while simultaneously providing provable privacy guarantees is a well-known challenge. On the one hand, context-free privacy solutions, such as differential privacy, provide strong privacy guarantees, but often lead to a significant reduction in utility. On the other hand, context-aware privacy solutions, such as information theoretic privacy, achieve an improved privacy-utility tradeoff, but assume that the data holder has access to dataset statistics. We circumvent these limitations by introducing a novel context-aware privacy framework called generative adversarial privacy (GAP). GAP leverages recent advancements in generative adversarial networks (GANs) to allow the data holder to learn privatization schemes from the dataset itself. Under GAP, learning the privacy mechanism is formulated as a constrained minimax game between two players: a privatizer that sanitizes the dataset in a way that limits the risk of inference attacks on the individuals' private variables, and an adversary that tries to infer the private variables from the sanitized dataset. To evaluate GAP's performance, we investigate two simple (yet canonical) statistical dataset models: (a) the binary data model, and (b) the binary Gaussian mixture model. For both models, we derive game-theoretically optimal minimax privacy mechanisms, and show that the privacy mechanisms learned from data (in a generative adversarial fashion) match the theoretically optimal ones. This demonstrates that our framework can be easily applied in practice, even in the absence of dataset statistics.Comment: Improved version of a paper accepted by Entropy Journal, Special Issue on Information Theory in Machine Learning and Data Scienc

O(\alpha_s) QCD Corrections to Spin Correlations in e−e+→ttˉe^- e^+ \to t \bar t process at the NLC

Using a Generic spin basis, we present a general formalism of one-loop radiative corrections to the spin correlations in the top quark pair production at the Next Linear Collider, and calculate the O(\alpha_s) QCD corrections under the soft gluon approximation. We find that: (a) in Off-diagonal basis, the $O(\alpha_s)$ QCD corrections to $e_L^- e^+$ ($e_R^- e^+$) scattering process increase the differential cross sections of the dominant spin component $t_{\uparrow}\bar{t}_{\downarrow}$ ($t_{\downarrow}\bar{t}_{\uparrow}$) by $\sim 30$ and $\sim (0.1$ depending on the scattering angle for $\sqrt{s}=400 GeV$ and 1 TeV, respectively; (b) in {Off-diagonal basis} (Helicity basis), the dominant spin component makes up 99.8% ($\sim 53$) of the total cross section at both tree and one-loop level for $\sqrt{s}=400 GeV$, and the Off-diagonal basis therefore remains to be the optimal spin basis after the inclusion of $O(\alpha_s)$ QCD corrections.Comment: 12 pages, 4 figures, revised version (a few print mistakes are corrected, some numerical results are modified, and Fig.4 is added

Rare decays Bs→l+l−B_s\to l^+l^- and B→Kl+l−B\to Kl^+l^- in \the topcolor-assisted technicolor model

We examine the rare decays $B_s\to l^+l^-$ and $B\to Kl^+l^-$ in the framework of the topcolor-assisted technicolor ($TC2$) model. The contributions of the new particles predicted by this model to these rare decay processes are evaluated. We find that the values of their branching ratios are larger than the standard model predictions by one order of magnitude in wide range of the parameter space. The longitudinal polarization asymmetry of leptons in $B_s \to l^+l^-$ can approach \ord(10^{-2}). The forward-backward asymmetry of leptons in $B \to Kl^+l^-$ is not large enough to be measured in future experiments. We also give some discussions about the branching ratios and the asymmetry observables related to these rare decay processes in the littlest Higgs model with T-parity.Comment: 29 pages, 9 figure, corrected typos, the version to appear in PR