arXiv subjects

Farhad Farokhi

Publications and source records attributed to Farhad Farokhi.

At least 73 records · Page 4Linked to original sources

arXiv2019

Information-Theoretic Privacy through Chaos Synchronization and Optimal Additive Noise

We study the problem of maximizing privacy of data sets by adding random vectors generated via synchronized chaotic oscillators. In particular, we consider the setup where information about data sets, queries, is sent through public (unsecured) communication channels to a remote station. To hide private features (specific entries) within the data set, we corrupt the response to queries by adding random vectors. We send the distorted query (the sum of the requested query and the random vector) through the public channel. The distribution of the additive random vector is designed to minimize the mutual information (our privacy metric) between private entries of the data set and the distorted query. We cast the synthesis of this distribution as a convex program in the probabilities of the additive random vector. Once we have the optimal distribution, we propose an algorithm to generate pseudo-random realizations from this distribution using trajectories of a chaotic oscillator. At the other end of the channel, we have a second chaotic oscillator, which we use to generate realizations from the same distribution. Note that if we obtain the same realizations on both sides of the channel, we can simply subtract the realization from the distorted query to recover the requested query. To generate equal realizations, we need the two chaotic oscillators to be synchronized, i.e., we need them to generate exactly the same trajectories on both sides of the channel synchronously in time. We force the two chaotic oscillators into exponential synchronization using a driving signal. Simulations are presented to illustrate our results.

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arXiv2019

The Value of Collaboration in Convex Machine Learning with Differential Privacy

In this paper, we apply machine learning to distributed private data owned by multiple data owners, entities with access to non-overlapping training datasets. We use noisy, differentially-private gradients to minimize the fitness cost of the machine learning model using stochastic gradient descent. We quantify the quality of the trained model, using the fitness cost, as a function of privacy budget and size of the distributed datasets to capture the trade-off between privacy and utility in machine learning. This way, we can predict the outcome of collaboration among privacy-aware data owners prior to executing potentially computationally-expensive machine learning algorithms. Particularly, we show that the difference between the fitness of the trained machine learning model using differentially-private gradient queries and the fitness of the trained machine model in the absence of any privacy concerns is inversely proportional to the size of the training datasets squared and the privacy budget squared. We successfully validate the performance prediction with the actual performance of the proposed privacy-aware learning algorithms, applied to: financial datasets for determining interest rates of loans using regression; and detecting credit card frauds using support vector machines.

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arXiv2019

A Game-Theoretic Approach to Adversarial Linear Support Vector Classification

In this paper, we employ a game-theoretic model to analyze the interaction between an adversary and a classifier. There are two classes (i.e., positive and negative classes) to which data points can belong. The adversary is interested in maximizing the probability of miss-detection for the positive class (i.e., false negative probability). The adversary however does not want to significantly modify the data point so that it still maintains favourable traits of the original class. The classifier, on the other hand, is interested in maximizing the probability of correct detection for the positive class (i.e., true positive probability) subject to a lower-bound on the probability of correct detection for the negative class (i.e., true negative probability). For conditionally Gaussian data points (conditioned on the class) and linear support vector machine classifiers, we rewrite the optimization problems of the adversary and the classifier as convex optimization problems and use best response dynamics to learn an equilibrium of the game. This results in computing a linear support vector machine classifier that is robust against adversarial input manipulations. We illustrate the framework on a synthetic dataset and a public Cardiovascular Disease dataset.

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arXiv2019

Secure and Private Implementation of Dynamic Controllers Using Semi-Homomorphic Encryption

This paper presents a secure and private implementation of linear time-invariant dynamic controllers using Paillier's encryption, a semi-homomorphic encryption method. To avoid overflow or underflow within the encryption domain, the state of the controller is reset periodically. A control design approach is presented to ensure stability and optimize performance of the closed-loop system with encrypted controller.

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arXiv2019

Non-Stochastic Hypothesis Testing with Application to Privacy Against Hypothesis-Testing Adversary

In this paper, we consider privacy against hypothesis testing adversaries within a non-stochastic framework. We develop a theory of non-stochastic hypothesis testing by borrowing the notion of uncertain variables from non-stochastic information theory. We define tests as binary-valued mappings on uncertain variables and prove a fundamental bound on the best performance of tests in non-stochastic hypothesis testing. We use this bound to develop a measure of privacy. We then construct reporting policies with prescribed privacy and utility guarantees. The utility of a reporting policy is measured by the distance between the reported and original values. We illustrate the effects of using such privacy-preserving reporting polices on a publicly-available practical dataset of preferences and demographics of young individuals, aged between 15-30, with Slovakian nationality.

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arXiv2019

Implementing Homomorphic Encryption Based Secure Feedback Control for Physical Systems

This paper is about an encryption based approach to the secure implementation of feedback controllers for physical systems. Specifically, Paillier's homomorphic encryption is used to digitally implement a class of linear dynamic controllers, which includes the commonplace static gain and PID type feedback control laws as special cases. The developed implementation is amenable to Field Programmable Gate Array (FPGA) realization. Experimental results, including timing analysis and resource usage characteristics for different encryption key lengths, are presented for the realization of an inverted pendulum controller; as this is an unstable plant, the control is necessarily fast.

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arXiv2019

State Estimation over Worst-Case Erasure and Symmetric Channels with Memory

Worst-case models of erasure and symmetric channels are investigated, in which the number of channel errors occurring in each sliding window of a given length is bounded. Upper and lower bounds on their zero-error capacities are derived, with the lower bounds revealing a connection with the topological entropy of the channel dynamics. Necessary and sufficient conditions for linear state estimation with bounded estimation errors via such channels are then obtained, by extending previous results for non-stochastic memoryless channels to those with finite memory. These estimation conditions involve the topological entropies of the linear system and the channel.

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arXiv2019

Development and Analysis of Deterministic Privacy-Preserving Policies Using Non-Stochastic Information Theory

A deterministic privacy metric using non-stochastic information theory is developed. Particularly, minimax information is used to construct a measure of information leakage, which is inversely proportional to the measure of privacy. Anyone can submit a query to a trusted agent with access to a non-stochastic uncertain private dataset. Optimal deterministic privacy-preserving policies for responding to the submitted query are computed by maximizing the measure of privacy subject to a constraint on the worst-case quality of the response (i.e., the worst-case difference between the response by the agent and the output of the query computed on the private dataset). The optimal privacy-preserving policy is proved to be a piecewise constant function in the form of a quantization operator applied on the output of the submitted query. The measure of privacy is also used to analyze the performance of $k$-anonymity methodology (a popular deterministic mechanism for privacy-preserving release of datasets using suppression and generalization techniques), proving that it is in fact not privacy-preserving.

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arXiv2018

On Privacy of Quantized Sensor Measurements through Additive Noise

We study the problem of maximizing privacy of quantized sensor measurements by adding random variables. In particular, we consider the setting where information about the state of a process is obtained using noisy sensor measurements. This information is quantized and sent to a remote station through an unsecured communication network. It is desired to keep the state of the process private; however, because the network is not secure, adversaries might have access to sensor information, which could be used to estimate the process state. To avoid an accurate state estimation, we add random numbers to the quantized sensor measurements and send the sum to the remote station instead. The distribution of these random variables is designed to minimize the mutual information between the sum and the quantized sensor measurements for a desired level of distortion -- how different the sum and the quantized sensor measurements are allowed to be. Simulations are presented to illustrate our results.

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arXiv2018

Ensuring Privacy with Constrained Additive Noise by Minimizing Fisher Information

The problem of preserving the privacy of individual entries of a database when responding to linear or nonlinear queries with constrained additive noise is considered. For privacy protection, the response to the query is systematically corrupted with an additive random noise whose support is a subset or equal to a pre-defined constraint set. A measure of privacy using the inverse of the trace of the Fisher information matrix is developed. The Cramer-Rao bound relates the variance of any estimator of the database entries to the introduced privacy measure. The probability density that minimizes the trace of the Fisher information (as a proxy for maximizing the measure of privacy) is computed. An extension to dynamic problems is also presented. Finally, the results are compared to the differential privacy methodology.

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arXiv2017

Scalable computation for optimal control of cascade systems with constraints

A method is devised for numerically solving a class of finite-horizon optimal control problems subject to cascade linear discrete-time dynamics. It is assumed that the linear state and input inequality constraints, and the quadratic measure of performance, are all separable with respect to the spatial dimension of the underlying cascade of sub-systems, as well as the temporal dimension of the dynamics. By virtue of this structure, the computation cost of an interior-point method for an equivalent quadratic programming formulation of the optimal control problem can be made to scale linearly with the number of sub-systems. However, the complexity of this approach grows cubically with the time horizon. As such, computational advantage becomes apparent in situations where the number of sub-systems is relatively large. In any case, the method is amenable to distributed computation with low communication overhead and only immediate upstream neighbour sharing of partial model data among processing agents. An example is presented to illustrate an application of the main results to model data for the cascade dynamics of an automated irrigation channel.

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arXiv2017

Integration of Information Patterns in the Modeling and Design of Mobility Management Services

Over the last decade, the rise of the mobile internet and the usage of mobile devices has enabled ubiquitous traffic information. With the increased adoption of specific smartphone applications, the number of users of routing applications has become large enough to disrupt traffic flow patterns in a significant manner. Similarly, but at a slightly slower pace, novel services for freight transportation and city logistics improve the efficiency of goods transportation and change the use of road infrastructure. The present article provides a general four-layer framework for modeling these new trends. The main motivation behind the development is to provide a unifying formal system description that can at the same time encompass system physics (flow and motion of vehicles) as well as coordination strategies under various information and cooperation structures. To showcase the framework, we apply it to the specific challenge of modeling and analyzing the integration of routing applications in today's transportation systems. In this framework, at the lowest layer (flow dynamics) we distinguish app users from non-app users. A distributed parameter model based on a non-local partial differential equation is introduced and analyzed. The second layer incorporates connected services (e.g., routing) and other applications used to optimize the local performance of the system. As inputs to those applications, we propose a third layer introducing the incentive design and global objectives, which are typically varying over the day depending on road and weather conditions, external events etc. The high-level planning is handled on the fourth layer taking social long-term objectives into account.

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arXiv2017

Preserving Privacy of Finite Impulse Response Systems

Adding input and output noises for increasing model identification error of finite impulse response (FIR) systems is considered. This is motivated by the desire to protect the model of the system as a trade secret by rendering model identification techniques ineffective. Optimal filters for constructing additive noises that maximizes the identification error subject to maintaining the closed-loop performance degradation below a limit are constructed. Furthermore, differential privacy is used for designing output noises that preserve the privacy of the model.

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arXiv2017

Private and Secure Coordination of Match-Making for Heavy-Duty Vehicle Platooning

A secure and private framework for inter-agent communication and coordination is developed. This allows an agent, in our case a fleet owner, to ask questions or submit queries in an encrypted fashion using semi-homomorphic encryption. The submitted query can be about the interest of the other fleet owners for using a road at a specific time of the day, for instance, for the purpose of collaborative vehicle platooning. The other agents can then provide appropriate responses without knowing the content of the questions or the queries. Strong privacy and security guarantees are provided for the agent who is submitting the queries. It is also shown that the amount of the information that this agent can extract from the other agent is bounded. In fact, with submitting one query, a sophisticated agent can at most extract the answer to two queries. This secure communication platform is used subsequently to develop a distributed coordination mechanisms among fleet owners.

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arXiv2016

Preserving Privacy of Agents in Participatory-Sensing Schemes for Traffic Estimation

A measure of privacy infringement for agents (or participants) travelling across a transportation network in participatory-sensing schemes for traffic estimation is introduced. The measure is defined to be the conditional probability that an external observer assigns to the private nodes in the transportation network, e.g., location of home or office, given all the position measurements that it broadcasts over time. An algorithm for finding an optimal trade-off between the measure of privacy infringement and the expected estimation error, captured by the number of the nodes over which the participant stops broadcasting its position, is proposed. The algorithm searches over a family of policies in which an agent stops transmitting its position measurements if its distance (in terms of the number of hops) to the privacy sensitive node is smaller than a prescribed threshold. Employing such symmetric policies are advantageous in terms of the resources required for implementation and the ease of computation. The results are expanded to more general policies. Further, the effect of the heterogeneity of the population density on the optimal policy is explored. Finally, the relationship between the betweenness measure of centrality and the optimal privacy-preserving policy of the agents is numerically explored.

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arXiv2016

Optimal State Estimation with Measurements Corrupted by Laplace Noise

Optimal state estimation for linear discrete-time systems is considered. Motivated by the literature on differential privacy, the measurements are assumed to be corrupted by Laplace noise. The optimal least mean square error estimate of the state is approximated using a randomized method. The method relies on that the Laplace noise can be rewritten as Gaussian noise scaled by Rayleigh random variable. The probability of the event that the distance between the approximation and the best estimate is smaller than a constant is determined as function of the number of parallel Kalman filters that is used in the randomized method. This estimator is then compared with the optimal linear estimator, the maximum a posteriori (MAP) estimate of the state, and the particle filter.

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arXiv2016

Budget-Constrained Contract Design for Effort-Averse Sensors in Averaging Based Estimation

Consider a group of effort-averse, or lazy, sensors that seek to minimize the effort invested to collect measurements of a variable. Increasing the effort invested by the sensors improves the quality of the measurements provided to the central planner but this incurs increased costs to the sensors. The central planner, which processes the sensor measurements, employs an averaging estimator. It also determines contracts for rewarding sensors based on the measurements obtained. The problem of designing a contract that yields an estimation-error based quality-of-service level in return for the reward extended to sensors is investigated in this paper. To this end, a game is formulated between the central planner and the sensors. Conditions for the existence and uniqueness of an equilibrium are identified. The equilibrium is constructed explicitly and its properties in response to a reward based contract are studied. It turns out that the central planner, while not being able to directly measure the effort invested by the sensors, can enhance the estimation quality by rewarding each sensor based on the distance of its measurements from the output of the averaging estimator. Ultimately, optimal contracts are designed from the perspective of the budget required for achieving a specified level of estimation error.

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arXiv2015

Faithful Implementations of Distributed Algorithms and Control Laws

When a distributed algorithm must be executed by strategic agents with misaligned interests, a social leader needs to introduce an appropriate tax/subsidy mechanism to incentivize agents to faithfully implement the intended algorithm so that a correct outcome is obtained. We discuss the incentive issues of implementing economically efficient distributed algorithms using the framework of indirect mechanism design theory. In particular, we show that indirect Groves mechanisms are not only sufficient but also necessary to achieve incentive compatibility. This result can be viewed as a generalization of the Green-Laffont theorem to indirect mechanisms. Then we introduce the notion of asymptotic incentive compatibility as an appropriate solution concept to faithfully implement distributed and iterative optimization algorithms. We consider two special types of optimization algorithms: dual decomposition algorithms for resource allocation and average consensus algorithms.

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