Energy big data: A survey <s> A. PRIVACY <s> Preface to the Second Edition. Preface to the First Edition. Acknowledgments for the Second Edition. Acknowledgments for the First Edition. 1. Introduction and Preview. 1.1 Preview of the Book. 2. Entropy, Relative Entropy, and Mutual Information. 2.1 Entropy. 2.2 Joint Entropy and Conditional Entropy. 2.3 Relative Entropy and Mutual Information. 2.4 Relationship Between Entropy and Mutual Information. 2.5 Chain Rules for Entropy, Relative Entropy, and Mutual Information. 2.6 Jensen's Inequality and Its Consequences. 2.7 Log Sum Inequality and Its Applications. 2.8 Data-Processing Inequality. 2.9 Sufficient Statistics. 2.10 Fano's Inequality. Summary. Problems. Historical Notes. 3. Asymptotic Equipartition Property. 3.1 Asymptotic Equipartition Property Theorem. 3.2 Consequences of the AEP: Data Compression. 3.3 High-Probability Sets and the Typical Set. Summary. Problems. Historical Notes. 4. Entropy Rates of a Stochastic Process. 4.1 Markov Chains. 4.2 Entropy Rate. 4.3 Example: Entropy Rate of a Random Walk on a Weighted Graph. 4.4 Second Law of Thermodynamics. 4.5 Functions of Markov Chains. Summary. Problems. Historical Notes. 5. Data Compression. 5.1 Examples of Codes. 5.2 Kraft Inequality. 5.3 Optimal Codes. 5.4 Bounds on the Optimal Code Length. 5.5 Kraft Inequality for Uniquely Decodable Codes. 5.6 Huffman Codes. 5.7 Some Comments on Huffman Codes. 5.8 Optimality of Huffman Codes. 5.9 Shannon-Fano-Elias Coding. 5.10 Competitive Optimality of the Shannon Code. 5.11 Generation of Discrete Distributions from Fair Coins. Summary. Problems. Historical Notes. 6. Gambling and Data Compression. 6.1 The Horse Race. 6.2 Gambling and Side Information. 6.3 Dependent Horse Races and Entropy Rate. 6.4 The Entropy of English. 6.5 Data Compression and Gambling. 6.6 Gambling Estimate of the Entropy of English. Summary. Problems. Historical Notes. 7. Channel Capacity. 7.1 Examples of Channel Capacity. 7.2 Symmetric Channels. 7.3 Properties of Channel Capacity. 7.4 Preview of the Channel Coding Theorem. 7.5 Definitions. 7.6 Jointly Typical Sequences. 7.7 Channel Coding Theorem. 7.8 Zero-Error Codes. 7.9 Fano's Inequality and the Converse to the Coding Theorem. 7.10 Equality in the Converse to the Channel Coding Theorem. 7.11 Hamming Codes. 7.12 Feedback Capacity. 7.13 Source-Channel Separation Theorem. Summary. Problems. Historical Notes. 8. Differential Entropy. 8.1 Definitions. 8.2 AEP for Continuous Random Variables. 8.3 Relation of Differential Entropy to Discrete Entropy. 8.4 Joint and Conditional Differential Entropy. 8.5 Relative Entropy and Mutual Information. 8.6 Properties of Differential Entropy, Relative Entropy, and Mutual Information. Summary. Problems. Historical Notes. 9. Gaussian Channel. 9.1 Gaussian Channel: Definitions. 9.2 Converse to the Coding Theorem for Gaussian Channels. 9.3 Bandlimited Channels. 9.4 Parallel Gaussian Channels. 9.5 Channels with Colored Gaussian Noise. 9.6 Gaussian Channels with Feedback. Summary. Problems. Historical Notes. 10. Rate Distortion Theory. 10.1 Quantization. 10.2 Definitions. 10.3 Calculation of the Rate Distortion Function. 10.4 Converse to the Rate Distortion Theorem. 10.5 Achievability of the Rate Distortion Function. 10.6 Strongly Typical Sequences and Rate Distortion. 10.7 Characterization of the Rate Distortion Function. 10.8 Computation of Channel Capacity and the Rate Distortion Function. Summary. Problems. Historical Notes. 11. Information Theory and Statistics. 11.1 Method of Types. 11.2 Law of Large Numbers. 11.3 Universal Source Coding. 11.4 Large Deviation Theory. 11.5 Examples of Sanov's Theorem. 11.6 Conditional Limit Theorem. 11.7 Hypothesis Testing. 11.8 Chernoff-Stein Lemma. 11.9 Chernoff Information. 11.10 Fisher Information and the Cram-er-Rao Inequality. Summary. Problems. Historical Notes. 12. Maximum Entropy. 12.1 Maximum Entropy Distributions. 12.2 Examples. 12.3 Anomalous Maximum Entropy Problem. 12.4 Spectrum Estimation. 12.5 Entropy Rates of a Gaussian Process. 12.6 Burg's Maximum Entropy Theorem. Summary. Problems. Historical Notes. 13. Universal Source Coding. 13.1 Universal Codes and Channel Capacity. 13.2 Universal Coding for Binary Sequences. 13.3 Arithmetic Coding. 13.4 Lempel-Ziv Coding. 13.5 Optimality of Lempel-Ziv Algorithms. Compression. Summary. Problems. Historical Notes. 14. Kolmogorov Complexity. 14.1 Models of Computation. 14.2 Kolmogorov Complexity: Definitions and Examples. 14.3 Kolmogorov Complexity and Entropy. 14.4 Kolmogorov Complexity of Integers. 14.5 Algorithmically Random and Incompressible Sequences. 14.6 Universal Probability. 14.7 Kolmogorov complexity. 14.9 Universal Gambling. 14.10 Occam's Razor. 14.11 Kolmogorov Complexity and Universal Probability. 14.12 Kolmogorov Sufficient Statistic. 14.13 Minimum Description Length Principle. Summary. Problems. Historical Notes. 15. Network Information Theory. 15.1 Gaussian Multiple-User Channels. 15.2 Jointly Typical Sequences. 15.3 Multiple-Access Channel. 15.4 Encoding of Correlated Sources. 15.5 Duality Between Slepian-Wolf Encoding and Multiple-Access Channels. 15.6 Broadcast Channel. 15.7 Relay Channel. 15.8 Source Coding with Side Information. 15.9 Rate Distortion with Side Information. 15.10 General Multiterminal Networks. Summary. Problems. Historical Notes. 16. Information Theory and Portfolio Theory. 16.1 The Stock Market: Some Definitions. 16.2 Kuhn-Tucker Characterization of the Log-Optimal Portfolio. 16.3 Asymptotic Optimality of the Log-Optimal Portfolio. 16.4 Side Information and the Growth Rate. 16.5 Investment in Stationary Markets. 16.6 Competitive Optimality of the Log-Optimal Portfolio. 16.7 Universal Portfolios. 16.8 Shannon-McMillan-Breiman Theorem (General AEP). Summary. Problems. Historical Notes. 17. Inequalities in Information Theory. 17.1 Basic Inequalities of Information Theory. 17.2 Differential Entropy. 17.3 Bounds on Entropy and Relative Entropy. 17.4 Inequalities for Types. 17.5 Combinatorial Bounds on Entropy. 17.6 Entropy Rates of Subsets. 17.7 Entropy and Fisher Information. 17.8 Entropy Power Inequality and Brunn-Minkowski Inequality. 17.9 Inequalities for Determinants. 17.10 Inequalities for Ratios of Determinants. Summary. Problems. Historical Notes. Bibliography. List of Symbols. Index. <s> BIB001 </s> Energy big data: A survey <s> A. PRIVACY <s> Global electrical grids are verging on the largest technological transformation since the introduction of electricity into the home. The antiquated infrastructure that delivers power to our homes and businesses is being replaced with a collection of digital systems called the smart grid. This grid is the modernization of the existing electrical system that enhances customers' and utilities' ability to monitor, control, and predict energy use. <s> BIB002 </s> Energy big data: A survey <s> A. PRIVACY <s> In this paper, we present a distributed incremental data aggregation approach, in which data aggregation is performed at all smart meters involved in routing the data from the source meter to the collector unit. With a carefully constructed aggregation tree, the aggregation route covers the entire local neighborhood or any arbitrary set of designated nodes with minimum overhead. To protect user privacy, homomorphic encryption is used to secure the data en route. Therefore, all the meters participate in the aggregation, without seeing any intermediate or final result. In this way, our approach supports efficient data aggregation in smart grids, while fully protecting user privacy. This approach is especially suitable for smart grids with repetitive routine data aggregation tasks. <s> BIB003 </s> Energy big data: A survey <s> A. PRIVACY <s> Smart grid privacy encompasses the privacy of information extracted by analysing smart metering data. In this paper, we suggest that home electrical power routing can be used to moderate the home's load signature in order to hide appliance usage information. In particular, 1) we introduce a power management model using a rechargeable battery, 2) we propose a power mixing algorithm, and 3) we evaluate its protection level by proposing three different privacy metrics: an information theoretic (relative entropy), a clustering classification, and a correlation/regression one; these are tested on different metering datasets. This paper sets the ground for further research on the subject of optimising home energy management with regards to hiding load signatures. <s> BIB004 </s> Energy big data: A survey <s> A. PRIVACY <s> We propose the first differentially private aggregation algorithm for distributed time-series data that offers good practical utility without any trusted server. This addresses two important challenges in participatory data-mining applications where (i) individual users collect temporally correlated time-series data (such as location traces, web history, personal health data), and (ii) an untrusted third-party aggregator wishes to run aggregate queries on the data. To ensure differential privacy for time-series data despite the presence of temporal correlation, we propose the Fourier Perturbation Algorithm (FPAk). Standard differential privacy techniques perform poorly for time-series data. To answer n queries, such techniques can result in a noise of Θ(n) to each query answer, making the answers practically useless if n is large. Our FPAk algorithm perturbs the Discrete Fourier Transform of the query answers. For answering n queries, FPAk improves the expected error from Θ(n) to roughly Θ(k) where k is the number of Fourier coefficients that can (approximately) reconstruct all the n query answers. Our experiments show that k To deal with the absence of a trusted central server, we propose the Distributed Laplace Perturbation Algorithm (DLPA) to add noise in a distributed way in order to guarantee differential privacy. To the best of our knowledge, DLPA is the first distributed differentially private algorithm that can scale with a large number of users: DLPA outperforms the only other distributed solution for differential privacy proposed so far, by reducing the computational load per user from O(U) to O(1) where U is the number of users. <s> BIB005 </s> Energy big data: A survey <s> A. PRIVACY <s> End-user privacy in smart meter measurements is a well-known challenge in the smart grid. The solutions offered thus far have been tied to specific technologies such as batteries or assumptions on data usage. Existing solutions have also not quantified the loss of benefit (utility) that results from any such privacy-preserving approach. Using tools from information theory, a new framework is presented that abstracts both the privacy and the utility requirements of smart meter data. This leads to a novel privacy-utility tradeoff problem with minimal assumptions that is tractable. Specifically for a stationary Gaussian Markov model of the electricity load, it is shown that the optimal utility-and-privacy preserving solution requires filtering out frequency components that are low in power, and this approach appears to encompass most of the proposed privacy approaches. <s> BIB006
The customer power consumption data collected from smart meters is a certain kind of privacy that showed be protected. From the detailed consumption information, an insight into a customer's behavior can be obtained. Smart grid stores customer privacy consequences and acts like an informationrich channel which is easy to exploit users' habits and offer intelligence service. As the history shows in BIB002 , a series of financial or political incentives boost the development of information mining and behavior learning technology. Terminal user's privacy is a well-known security problem about big data applied in power system. Many approaches have been proposed to solve the privacy problems during data access. Li et al. BIB003 presented a distributed incremental data aggregation approach by using neighborhood gateways. Kalogridis et al. BIB004 introduced a method to hide information contained in the energy consumption data by using battery storage. Rastogi and Nath BIB005 proposed a differential private aggregation algorithm for time-series data which offers good practical utility without any trusted server. Although these solutions manage to support the utility and privacy in various ways, they lack a robust theoretical basis from both utility and privacy. Rajagopalan et al. BIB006 proposed a theoretical framework which integrates most existing solutions of the trade-off and provides a universal model in smart meters. Such a theoretical framework is suitable for many current problems of the privacy-utility tradeoff using a technology-independent method. Assume that power consumption data is distributed normally, a data sequence {x k } is defined of random variables x k ∈ x, −∞ < k < ∞, which generated by stationary continuous valued sources with memory got via the autocorrelation function: C xx (m) = E[x k x k+m ], m = 0, ±1, ±2, · · · . Then, in order to estimate the privacy loss via the mutual information, authors would perturb data between two data sequences. Since continuous amplitude data transmission is lossy through finite capacity network links, a tested sequence of k-load measurements {x k } is usually quantized and compressed before the transmission. Therefore, data perturbation is needed to guarantee data privacy in some way. However, such a perturbation also needs encoding and decoding to maintain a desired level of fidelity. • Encoding: Assuming that a smart meter can collect n(n 1) measurements in a time interval before communication, and n is large enough to capture the memory of data sources. Then the encoding function performs a mapping of resulting source sequence X n = {X 1 , X 2 , · · · , X n }, where X k ∈ R, k = 1, 2, · · · , n, an index W i ∈ W n will be given by: where each index is a quantized sequence. • Decoding: The decoder at the data collector computes an output sequence X n = { X 2 , X 2 , · · · , X n }, X k ∈ R, for all X k , using the decoding function: 3852 VOLUME 4, 2016 FIGURE 5. Security branches and related solutions. The selection of the encoder should promote the input and output sequences to achieve a desired utility which is given by an average distortion constraint: and a constraint on the privacy leakage about the desired sequence {Y k } from the revealed one X k is quantized via the leakage function: where function E[·] computes the expectation and I(·) represents the mutual information. D n and L n are functions of the number of measurements n. When stationary sources converge to limiting values, the corresponding limiting values for utility can be given by D = lim n→∞ D n and L = lim n→∞ L n for privacy respectively BIB001 .