arXiv subjects

Peter Kairouz

Publications and source records attributed to Peter Kairouz.

85 records · Page 5Linked to original sources

arXiv2019

On the Optimality of the Kautz-Singleton Construction in Probabilistic Group Testing

We consider the probabilistic group testing problem where $d$ random defective items in a large population of $N$ items are identified with high probability by applying binary tests. It is known that $Θ(d \log N)$ tests are necessary and sufficient to recover the defective set with vanishing probability of error when $d = O(N^α)$ for some $α\in (0, 1)$. However, to the best of our knowledge, there is no explicit (deterministic) construction achieving $Θ(d \log N)$ tests in general. In this work, we show that a famous construction introduced by Kautz and Singleton for the combinatorial group testing problem (which is known to be suboptimal for combinatorial group testing for moderate values of $d$) achieves the order optimal $Θ(d \log N)$ tests in the probabilistic group testing problem when $d = Ω(\log^2 N)$. This provides a strongly explicit construction achieving the order optimal result in the probabilistic group testing setting for a wide range of values of $d$. To prove the order-optimality of Kautz and Singleton's construction in the probabilistic setting, we provide a novel analysis of the probability of a non-defective item being covered by a random defective set directly, rather than arguing from combinatorial properties of the underlying code, which has been the main approach in the literature. Furthermore, we use a recursive technique to convert this construction into one that can also be efficiently decoded with only a log-log factor increase in the number of tests.

cs.IT↗

arXiv2019

Sparse Combinatorial Group Testing

In combinatorial group testing (CGT), the objective is to identify the set of at most $d$ defective items from a pool of $n$ items using as few tests as possible. The celebrated result for the CGT problem is that the number of tests $t$ can be made logarithmic in $n$ when $d=O(poly(\log n))$. However, state-of-the-art GT codes require the items to be tested $w=Ω(d\log n)$ times and tests to include $ρ=Ω(n/d)$ items (within log factors). In many applications, items can only participate in a limited number of tests and tests are constrained to include a limited number of items. In this paper, we study the "sparse" regime for the group testing problem where we restrict the number of tests each item can participate in by $w_{\max}$ or the number of items each test can include by $ρ_{\max}$ in both noiseless and noisy settings. These constraints lead to an unexplored regime where $t$ is a fractional power of $n$. Our results characterize the number of tests $t$ as a function of $w_{\max} (ρ_{\max})$ and show, for example, that $t$ decreases drastically when $w_{\max}$ is increased beyond a bare minimum. In particular, if $w_{\max}\leq d$, then we must have $t=n$, i.e., individual testing is optimal. We show that if $w_{\max}=d+1$, this decreases suddenly to $t=Θ(d\sqrt{n})$. The order-optimal construction is obtained via a modification of the Kautz-Singleton construction, which is known to be suboptimal for the classical GT problem. For more general case, when $w_{\max}=ld+1$ for $l>1$, the modified K-S construction requires $t=Θ(d n^{\frac{1}{l+1}})$ tests, which we prove to be near order-optimal. We show that our constructions have a favorable encoding and decoding complexity. We finally discuss an application of our results to the construction of energy-limited random access schemes for IoT networks, which provided the initial motivation for our work.

cs.IT↗

arXiv2018

Siamese Generative Adversarial Privatizer for Biometric Data

State-of-the-art machine learning algorithms can be fooled by carefully crafted adversarial examples. As such, adversarial examples present a concrete problem in AI safety. In this work we turn the tables and ask the following question: can we harness the power of adversarial examples to prevent malicious adversaries from learning identifying information from data while allowing non-malicious entities to benefit from the utility of the same data? For instance, can we use adversarial examples to anonymize biometric dataset of faces while retaining usefulness of this data for other purposes, such as emotion recognition? To address this question, we propose a simple yet effective method, called Siamese Generative Adversarial Privatizer (SGAP), that exploits the properties of a Siamese neural network to find discriminative features that convey identifying information. When coupled with a generative model, our approach is able to correctly locate and disguise identifying information, while minimally reducing the utility of the privatized dataset. Extensive evaluation on a biometric dataset of fingerprints and cartoon faces confirms usefulness of our simple yet effective method.

cs.CV↗

arXiv2018

Understanding Compressive Adversarial Privacy

Designing a data sharing mechanism without sacrificing too much privacy can be considered as a game between data holders and malicious attackers. This paper describes a compressive adversarial privacy framework that captures the trade-off between the data privacy and utility. We characterize the optimal data releasing mechanism through convex optimization when assuming that both the data holder and attacker can only modify the data using linear transformations. We then build a more realistic data releasing mechanism that can rely on a nonlinear compression model while the attacker uses a neural network. We demonstrate in a series of empirical applications that this framework, consisting of compressive adversarial privacy, can preserve sensitive information.

cs.LG↗

arXiv2018

On the Contractivity of Privacy Mechanisms

We present a novel way to compare the statistical cost of privacy mechanisms using their Dobrushin coefficient. Specifically, we provide upper and lower bounds for the Dobrushin coefficient of a privacy mechanism in terms of its maximal leakage and local differential privacy guarantees. Given the geometric nature of the Dobrushin coefficient, this approach provides some insights into the general statistical cost of these privacy guarantees. We highlight the strength of this method by applying our results to develop new bounds on the $\ell_2$-minimax risk in a distribution estimation setting under maximal leakage constraints. Specifically, we find its order with respect to the sample size and privacy level, allowing a quantitative comparison with the corresponding local differential privacy $\ell_2$-minimax risk.

cs.IT↗

arXiv2017

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.

cs.LG↗

arXiv2016

Hiding the Rumor Source

Anonymous social media platforms like Secret, Yik Yak, and Whisper have emerged as important tools for sharing ideas without the fear of judgment. Such anonymous platforms are also important in nations under authoritarian rule, where freedom of expression and the personal safety of message authors may depend on anonymity. Whether for fear of judgment or retribution, it is sometimes crucial to hide the identities of users who post sensitive messages. In this paper, we consider a global adversary who wishes to identify the author of a message; it observes either a snapshot of the spread of a message at a certain time, sampled timestamp metadata, or both. Recent advances in rumor source detection show that existing messaging protocols are vulnerable against such an adversary. We introduce a novel messaging protocol, which we call adaptive diffusion, and show that under the snapshot adversarial model, adaptive diffusion spreads content fast and achieves perfect obfuscation of the source when the underlying contact network is an infinite regular tree. That is, all users with the message are nearly equally likely to have been the origin of the message. When the contact network is an irregular tree, we characterize the probability of maximum likelihood detection by proving a concentration result over Galton-Watson trees. Experiments on a sampled Facebook network demonstrate that adaptive diffusion effectively hides the location of the source even when the graph is finite, irregular and has cycles.

cs.CR↗

arXiv2016

Discrete Distribution Estimation under Local Privacy

The collection and analysis of user data drives improvements in the app and web ecosystems, but comes with risks to privacy. This paper examines discrete distribution estimation under local privacy, a setting wherein service providers can learn the distribution of a categorical statistic of interest without collecting the underlying data. We present new mechanisms, including hashed K-ary Randomized Response (KRR), that empirically meet or exceed the utility of existing mechanisms at all privacy levels. New theoretical results demonstrate the order-optimality of KRR and the existing RAPPOR mechanism at different privacy regimes.

stat.ML↗

arXiv2015

The Composition Theorem for Differential Privacy

Sequential querying of differentially private mechanisms degrades the overall privacy level. In this paper, we answer the fundamental question of characterizing the level of overall privacy degradation as a function of the number of queries and the privacy levels maintained by each privatization mechanism. Our solution is complete: we prove an upper bound on the overall privacy level and construct a sequence of privatization mechanisms that achieves this bound. The key innovation is the introduction of an operational interpretation of differential privacy (involving hypothesis testing) and the use of new data processing inequalities. Our result improves over the state-of-the-art, and has immediate applications in several problems studied in the literature including differentially private multi-party computation.

cs.DS↗

arXiv2015

Extremal Mechanisms for Local Differential Privacy

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 maximize the utility of statistical analyses performed on the released data, we study the fundamental trade-off between local differential privacy and utility. This trade-off is formulated as a constrained optimization problem: maximize utility subject to local differential privacy constraints. We introduce a combinatorial family of extremal privatization mechanisms, which we call staircase mechanisms, and show that it contains the optimal privatization mechanisms for a broad class of information theoretic utilities such as mutual information and $f$-divergences. We further prove that for any utility function and any privacy level, solving the privacy-utility maximization problem is equivalent to solving a finite-dimensional linear program, the outcome of which is the optimal staircase mechanism. However, solving this linear program can be computationally expensive since it has a number of variables that is exponential in the size of the alphabet the data lives in. To account for this, we show that two simple privatization mechanisms, the binary and randomized response mechanisms, are universally optimal in the low and high privacy regimes, and well approximate the intermediate regime.

cs.IT↗

arXiv2015

Spy vs. Spy: Rumor Source Obfuscation

Anonymous messaging platforms, such as Secret and Whisper, have emerged as important social media for sharing one's thoughts without the fear of being judged by friends, family, or the public. Further, such anonymous platforms are crucial in nations with authoritarian governments; the right to free expression and sometimes the personal safety of the author of the message depend on anonymity. Whether for fear of judgment or personal endangerment, it is crucial to keep anonymous the identity of the user who initially posted a sensitive message. In this paper, we consider an adversary who observes a snapshot of the spread of a message at a certain time. Recent advances in rumor source detection shows that the existing messaging protocols are vulnerable against such an adversary. We introduce a novel messaging protocol, which we call adaptive diffusion, and show that it spreads the messages fast and achieves a perfect obfuscation of the source when the underlying contact network is an infinite regular tree: all users with the message are nearly equally likely to have been the origin of the message. Experiments on a sampled Facebook network show that it effectively hides the location of the source even when the graph is finite, irregular and has cycles. We further consider a stronger adversarial model where a subset of colluding users track the reception of messages. We show that the adaptive diffusion provides a strong protection of the anonymity of the source even under this scenario.

cs.SI↗

arXiv2014

Differentially Private Multi-party Computation: Optimality of Non-Interactive Randomized Response

We study the problem of interactive function computation by multiple parties possessing a single bit each in a differential privacy setting (i.e., there remains an uncertainty in any specific party's bit even when given the transcript of the interactions and all the other parties' bits). Each party is interested in computing a function, which could differ from party to party, and there could be a central observer interested in computing a separate function. Performance at each party and the central observer is measured via the accuracy of the function computed. We allow for an arbitrary cost function to measure the distortion between the true and the computed function value. Our main result is the exact optimality of a simple non-interactive protocol: each party randomizes (sufficiently) and publishes its own bit. In other words, non-interactive randomized response is exactly optimal. Each party and the central observer then separately compute their respective function to maximize the appropriate notion of their accuracy measure. The optimality is very general: it holds for all types of functions, heterogeneous privacy conditions on the parties, all types of cost metrics, and both average and worst-case (over the inputs) measures of accuracy. Finally, the optimality result is simultaneous, in terms of maximizing accuracy at each of the parties and the central observer.

cs.CR↗

arXiv2013

MIMO Communications over Multi-Mode Optical Fibers: Capacity Analysis and Input-Output Coupling Schemes

We consider multi-input multi-output (MIMO) communications over multi-mode fibers (MMFs). Current MMF standards, such as OM3 and OM4, use fibers with core radii of 50 μm, allowing hundreds of modes to propagate. Unfortunately, due to physical and computational complexity limitations, we cannot couple and detect hundreds of data streams into and out of the fiber. In order to circumvent this issue, we present input-output coupling schemes that allow the user to couple and extract a reasonable number of signals from a fiber with many modes. This approach is particularly attractive as it is scalable; i.e., the fibers do not have to be replaced every time the number of transmitters or receivers is increased, a phenomenon that is likely to happen in the near future. We present a statistical channel model that incorporates intermodal dispersion, chromatic dispersion, mode dependent losses, mode coupling, and input-output coupling. We show that the statistics of the fiber's frequency response are independent of frequency. This simplifies the computation of the average Shannon capacity of the fiber. We also provide an input-output coupling strategy that leads to an increase in the overall capacity. This strategy can be used whenever channel state information (CSI) is available at the transmitter. We show that the capacity of an Nt by Nt MIMO system over a fiber with M>>Nt modes can approach the capacity of an Nt-mode fiber with no mode-dependent losses. We finally present a statistical input-output coupling model in order to quantify the loss in capacity when CSI is not available at the transmitter. It turns out that the loss, relative to Nt-mode fibers, is minimal (less than 0.5 dB) for a wide range of signal-to-noise ratios (SNRs) and a reasonable range of MDLs.

cs.IT↗