arXiv subjects

Lalitha Sankar

Publications and source records attributed to Lalitha Sankar.

At least 91 records · Page 5Linked to original sources

arXiv2018

The Utility Cost of Robust Privacy Guarantees

Consider a data publishing setting for a data set with public and private features. The objective of the publisher is to maximize the amount of information about the public features in a revealed data set, while keeping the information leaked about the private features bounded. The goal of this paper is to analyze the performance of privacy mechanisms that are constructed to match the distribution learned from the data set. Two distinct scenarios are considered: (i) mechanisms are designed to provide a privacy guarantee for the learned distribution; and (ii) mechanisms are designed to provide a privacy guarantee for every distribution in a given neighborhood of the learned distribution. For the first scenario, given any privacy mechanism, upper bounds on the difference between the privacy-utility guarantees for the learned and true distributions are presented. In the second scenario, upper bounds on the reduction in utility incurred by providing a uniform privacy guarantee are developed.

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arXiv2018

Can Attackers with Limited Information Exploit Historical Data to Mount Successful False Data Injection Attacks on Power Systems?

This paper studies physical consequences of unobservable false data injection (FDI) attacks designed only with information inside a sub-network of the power system. The goal of this attack is to overload a chosen target line without being detected via measurements. To overcome the limited information, a multiple linear regression model is developed to learn the relationship between the external network and the attack sub-network from historical data. The worst possible consequences of such FDI attacks are evaluated by solving a bi-level optimization problem wherein the first level models the limited attack resources, while the second level formulates the system response to such attacks via DC optimal power flow (OPF). The attack model with limited information is reflected in the DC OPF formulation that only takes into account the system information for the attack sub-network. The vulnerability of this attack model is illustrated on the IEEE 24-bus RTS and IEEE 118-bus systems.

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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.

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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.

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arXiv2017

False Data Injection Attacks on Phasor Measurements That Bypass Low-rank Decomposition

This paper studies the vulnerability of phasor measurement units (PMUs) to false data injection (FDI) attacks. Prior work demonstrated that unobservable FDI attacks that can bypass traditional bad data detectors based on measurement residuals can be identified by detector based on low-rank decomposition (LD). In this work, a class of more sophisticated FDI attacks that captures the temporal correlation of PMU data is introduced. Such attacks are designed with a convex optimization problem and can always bypass the LD detector. The vulnerability of this attack model is illustrated on both the IEEE 24-bus RTS and the IEEE 118-bus systems.

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arXiv2017

Hypothesis Testing under Mutual Information Privacy Constraints in the High Privacy Regime

Hypothesis testing is a statistical inference framework for determining the true distribution among a set of possible distributions for a given dataset. Privacy restrictions may require the curator of the data or the respondents themselves to share data with the test only after applying a randomizing privacy mechanism. This work considers mutual information (MI) as the privacy metric for measuring leakage. In addition, motivated by the Chernoff-Stein lemma, the relative entropy between pairs of distributions of the output (generated by the privacy mechanism) is chosen as the utility metric. For these metrics, the goal is to find the optimal privacy-utility trade-off (PUT) and the corresponding optimal privacy mechanism for both binary and m-ary hypothesis testing. Focusing on the high privacy regime, Euclidean information-theoretic approximations of the binary and m-ary PUT problems are developed. The solutions for the approximation problems clarify that an MI-based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihoods.

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arXiv2017

Hypothesis Testing under Maximal Leakage Privacy Constraints

The problem of publishing privacy-guaranteed data for hypothesis testing is studied using the maximal leakage (ML) as a metric for privacy and the type-II error exponent as the utility metric. The optimal mechanism (random mapping) that maximizes utility for a bounded leakage guarantee is determined for the entire leakage range for binary datasets. For non-binary datasets, approximations in the high privacy and high utility regimes are developed. The results show that, for any desired leakage level, maximizing utility forces the ML privacy mechanism to reveal partial to complete knowledge about a subset of the source alphabet. The results developed on maximizing a convex function over a polytope may also of an independent interest.

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arXiv2016

Market Segmentation for Privacy Differentiated "Free" Services

The emerging marketplace for online free services in which service providers earn revenue from using consumer data in direct and indirect ways has lead to significant privacy concerns. This leads to the following question: can the online marketplace sustain multiple service providers (SPs) that offer privacy-differentiated free services? This paper studies the problem of market segmentation for the free online services market by augmenting the classical Hotelling model for market segmentation analysis to include the fact that for the free services market, a consumer values service not in monetized terms but by its quality of service (QoS) and that the differentiator of services is not product price but the privacy risk advertised by a SP. Building upon the Hotelling model, this paper presents a parametrized model for SP profit and consumer valuation of service for both the two- and multi-SP problems to show that: (i) when consumers place a high value on privacy, it leads to a lower use of private data by SPs (i.e., their advertised privacy risk reduces), and thus, SPs compete on the QoS; (ii) SPs that are capable of differentiating on services that do not directly target consumers gain larger market share; and (iii) a higher valuation of privacy by consumers forces SPs with smaller untargeted revenue to offer lower privacy risk to attract more consumers. The work also illustrates the market segmentation problem for more than two SPs and highlights the instability of such markets.

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arXiv2016

Privacy-guaranteed Two-Agent Interactions Using Information-Theoretic Mechanisms

This paper introduces a multi-round interaction problem with privacy constraints between two agents that observe correlated data. The agents alternately share data with one another for a total of K rounds such that each agent initiates sharing over K/2 rounds. The interactions are modeled as a collection of K random mechanisms (mappings), one for each round. The goal is to jointly design the K private mechanisms to determine the set of all achievable distortion-leakage pairs at each agent. Arguing that a mutual information-based leakage metric can be appropriate for streaming data settings, this paper: (i) determines the set of all achievable distortion- leakage tuples ; (ii) shows that the K mechanisms allow for precisely composing the total privacy budget over K rounds without loss; and (ii) develops conditions under which interaction reduces the net leakage at both agents and illustrates it for a specific class of sources. The paper then focuses on log-loss distortion to better understand the effect on leakage of using a commonly used utility metric in learning theory. The resulting interaction problem leads to a non-convex sum-leakage-distortion optimization problem that can be viewed as an interactive version of the information bottleneck problem. A new merge-and-search algorithm that extends the classical agglomerative information bottleneck algorithm to the interactive setting is introduced to determine a provable locally optimal solution. Finally, the benefit of interaction under log-loss is illustrated for specific source classes and the optimality of one-shot is proved for Gaussian sources under both mean-square and log-loss distortions constraints.

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arXiv2016

Hypothesis Testing in the High Privacy Limit

Binary hypothesis testing under the Neyman-Pearson formalism is a statistical inference framework for distinguishing data generated by two different source distributions. Privacy restrictions may require the curator of the data or the data respondents themselves to share data with the test only after applying a randomizing privacy mechanism. Using mutual information as the privacy metric and the relative entropy between the two distributions of the output (postrandomization) source classes as the utility metric (motivated by the Chernoff-Stein Lemma), this work focuses on finding an optimal mechanism that maximizes the chosen utility function while ensuring that the mutual information based leakage for both source distributions is bounded. Focusing on the high privacy regime, an Euclidean information-theoretic (E-IT) approximation to the tradeoff problem is presented. It is shown that the solution to the E-IT approximation is independent of the alphabet size and clarifies that a mutual information based privacy metric preserves the privacy of the source symbols in inverse proportion to their likelihood.

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arXiv2016

Evaluating Power System Vulnerability to False Data Injection Attacks via Scalable Optimization

Physical consequences to power systems of false data injection cyber-attacks are considered. Prior work has shown that the worst-case consequences of such an attack can be determined using a bi-level optimization problem, wherein an attack is chosen to maximize the physical power flow on a target line subsequent to re-dispatch. This problem can be solved as a mixed-integer linear program, but it is difficult to scale to large systems due to numerical challenges. Three new computationally efficient algorithms to solve this problem are presented. These algorithms provide lower and upper bounds on the system vulnerability measured as the maximum power flow subsequent to an attack. Using these techniques, vulnerability assessments are conducted for IEEE 118-bus system and Polish system with 2383 buses.

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arXiv2015

Designing Incentive Schemes For Privacy-Sensitive Users

Businesses (retailers) often wish to offer personalized advertisements (coupons) to individuals (consumers), but run the risk of strong reactions from consumers who want a customized shopping experience but feel their privacy has been violated. Existing models for privacy such as differential privacy or information theory try to quantify privacy risk but do not capture the subjective experience and heterogeneous expression of privacy-sensitivity. We propose a Markov decision process (MDP) model to capture (i) different consumer privacy sensitivities via a time-varying state; (ii) different coupon types (action set) for the retailer; and (iii) the action-and-state-dependent cost for perceived privacy violations. For the simple case with two states ("Normal" and "Alerted"), two coupons (targeted and untargeted) model, and consumer behavior statistics known to the retailer, we show that a stationary threshold-based policy is the optimal coupon-offering strategy for a retailer that wishes to minimize its expected discounted cost. The threshold is a function of all model parameters; the retailer offers a targeted coupon if their belief that the consumer is in the "Alerted" state is below the threshold. We extend this two-state model to consumers with multiple privacy-sensitivity states as well as coupon-dependent state transition probabilities. Furthermore, we study the case with imperfect (noisy) cost feedback from consumers and uncertain initial belief state.

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arXiv2015

Implication of Unobservable State-and-topology Cyber-physical Attacks

This paper studies the physical consequences of a class of unobservable state-and-topology cyber-physical attacks in which both state and topology data for a sub-network of the network are changed by an attacker to mask a physical attack. The problem is formulated as a two-stage optimization problem which aims to cause overload in a line of the network with limited attack resources. It is shown that unobservable state-and-topology cyber-physical attacks as studied in this paper can make the system operation more vulnerable to line outages and failures.

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arXiv2015

Vulnerability Analysis and Consequences of False Data Injection Attack on Power System State Estimation

An unobservable false data injection (FDI) attack on AC state estimation (SE) is introduced and its consequences on the physical system are studied. With a focus on understanding the physical consequences of FDI attacks, a bi-level optimization problem is introduced whose objective is to maximize the physical line flows subsequent to an FDI attack on DC SE. The maximization is subject to constraints on both attacker resources (size of attack) and attack detection (limiting load shifts) as well as those required by DC optimal power flow (OPF) following SE. The resulting attacks are tested on a more realistic non-linear system model using AC state estimation and ACOPF, and it is shown that, with an appropriately chosen sub-network, the attacker can overload transmission lines with moderate shifts of load.

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arXiv2014

Asymptotics and Non-asymptotics for Universal Fixed-to-Variable Source Coding

Universal fixed-to-variable lossless source coding for memoryless sources is studied in the finite blocklength and higher-order asymptotics regimes. Optimal third-order coding rates are derived for general fixed-to-variable codes and for prefix codes. It is shown that the non-prefix Type Size code, in which codeword lengths are chosen in ascending order of type class size, achieves the optimal third-order rate and outperforms classical Two-Stage codes. Converse results are proved making use of a result on the distribution of the empirical entropy and Laplace's approximation. Finally, the fixed-to-variable coding problem without a prefix constraint is shown to be essentially the same as the universal guessing problem.

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arXiv2014

Enabling Data Exchange in Interactive State Estimation under Privacy Constraints

Data collecting agents in large networks, such as the electric power system, need to share information (measurements) for estimating the system state in a distributed manner. However, privacy concerns may limit or prevent this exchange leading to a tradeoff between state estimation fidelity and privacy (referred to as competitive privacy). This paper builds upon a recent information-theoretic result (using mutual information to measure privacy and mean-squared error to measure fidelity) that quantifies the region of achievable distortion-leakage tuples in a two-agent network. The objective of this paper is to study centralized and decentralized mechanisms that can enable and sustain non-trivial data exchanges among the agents. A centralized mechanism determines the data sharing policies that optimize a network-wide objective function combining the fidelities and leakages at both agents. Using common-goal games and best-response analysis, the optimal policies allow for distributed implementation. In contrast, in the decentralized setting, repeated discounted games are shown to naturally enable data exchange without any central control nor economic incentives. The effect of repetition is modeled by a time-averaged payoff function at each agent which combines its fidelity and leakage at each interaction stage. For both approaches, it is shown that non-trivial data exchange can be sustained for specific fidelity ranges even when privacy is a limiting factor.

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arXiv2013

Utility-Privacy Tradeoff in Databases: An Information-theoretic Approach

Ensuring the usefulness of electronic data sources while providing necessary privacy guarantees is an important unsolved problem. This problem drives the need for an analytical framework that can quantify the safety of personally identifiable information (privacy) while still providing a quantifable benefit (utility) to multiple legitimate information consumers. This paper presents an information-theoretic framework that promises an analytical model guaranteeing tight bounds of how much utility is possible for a given level of privacy and vice-versa. Specific contributions include: i) stochastic data models for both categorical and numerical data; ii) utility-privacy tradeoff regions and the encoding (sanization) schemes achieving them for both classes and their practical relevance; and iii) modeling of prior knowledge at the user and/or data source and optimal encoding schemes for both cases.

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arXiv2012

Distributed Estimation in Multi-Agent Networks

A problem of distributed state estimation at multiple agents that are physically connected and have competitive interests is mapped to a distributed source coding problem with additional privacy constraints. The agents interact to estimate their own states to a desired fidelity from their (sensor) measurements which are functions of both the local state and the states at the other agents. For a Gaussian state and measurement model, it is shown that the sum-rate achieved by a distributed protocol in which the agents broadcast to one another is a lower bound on that of a centralized protocol in which the agents broadcast as if to a virtual CEO converging only in the limit of a large number of agents. The sufficiency of encoding using local measurements is also proved for both protocols.

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