Privacy Funnel Research Articles

Graph Privacy Funnel: A Variational Approach for Privacy-Preserving Representation Learning on Graphs

Graph Privacy Funnel: A Variational Approach for Privacy-Preserving Representation Learning on Graphs

A Linearly Convergent Douglas-Rachford Splitting Solver for Markovian Information-Theoretic Optimization Problems

In this work, we propose solving the Information Bottleneck (IB) and Privacy Funnel (PF) problems with Douglas-Rachford Splitting methods (DRS). We study a general Markovian information-theoretic Lagrangian that includes IB and PF into a unified framework. We prove the linear convergence of the proposed solvers using the Kurdyka-Łojasiewicz inequality. Moreover, our analysis is beyond IB and PF and applies to any convex-weakly convex pair objectives. Based on the results, we develop two types of linearly convergent IB solvers, with one improves the performance of convergence over existing solvers while the other can be independent to the relevance-compression trade-off. Moreover, our results apply to PF, yielding a new class of linearly convergent PF solvers. Empirically, the proposed IB solvers IB obtain solutions that are comparable to the Blahut-Arimoto-based benchmark and is convergent for a wider range of the penalty coefficients than existing solvers. For PF, our non-greedy solvers can characterize the privacy-utility trade-off better than the clustering-based greedy solvers.

Bottlenecks CLUB: Unifying Information-Theoretic Trade-Offs Among Complexity, Leakage, and Utility

Bottleneck problems are an important class of optimization problems that have recently gained increasing attention in the domain of machine learning and information theory. They are widely used in generative models, fair machine learning algorithms, design of privacy-assuring mechanisms, and appear as information-theoretic performance bounds in various multi-user communication problems. In this work, we propose a general family of optimization problems, termed as <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">complexity-leakage-utility bottleneck (CLUB)</i> model, which (i) provides a unified theoretical framework that generalizes most of the state-of-the-art literature for the information-theoretic privacy models, (ii) establishes a new interpretation of the popular generative and discriminative models, (iii) constructs new insights for the generative compression models, and (iv) can be used to obtain fair generative models. We first formulate the CLUB model as a complexity-constrained privacy-utility optimization problem. We then connect it with the closely related bottleneck problems, namely information bottleneck (IB), privacy funnel (PF), deterministic IB (DIB), conditional entropy bottleneck (CEB), and conditional PF (CPF). We show that the CLUB model generalizes all these problems as well as most other information-theoretic privacy models. Then, we construct the deep variational CLUB (DVCLUB) models by employing neural networks to parameterize variational approximations of the associated information quantities. Building upon these information quantities, we present unified objectives of the <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">supervised</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">unsupervised</i> DVCLUB models. Leveraging the DVCLUB model in an unsupervised setup, we then connect it with state-of-the-art generative models, such as variational auto-encoders (VAEs), generative adversarial networks (GANs), as well as the Wasserstein GAN (WGAN), Wasserstein auto-encoder (WAE), and adversarial auto-encoder (AAE) models through the optimal transport (OT) problem. We then show that the DVCLUB model can also be used in fair representation learning problems, where the goal is to mitigate the undesired bias during the training phase of a machine learning model. We conduct extensive quantitative experiments on colored-MNIST and CelebA datasets.

Data privacy and utility trade-off based on mutual information neural estimator

In the era of big data and the Internet of Things (IoT), data owners need to share a large amount of data with the intended receivers in an insecure environment, posing a trade-off issue between user privacy and data utility. The privacy utility trade-off was facilitated through a privacy funnel based on mutual information. In this article, we propose a privacy funnel which is using mutual information neural estimator (MINE) to optimize the privacy utility trade-off by estimating mutual information. Firstly, we estimate mutual information in a training way for data with unknown distributions and make the result a measure of privacy and utility. Secondly, we optimize the privacy utility trade-off by optimizing the mutual information added noise as an encoding process and minimizing cross-entropy mutual information between published data and non-sensitive data as a decoding process. Finally, simulations are conducted comparing our methodology to the Kraskov, Stögbauer, and Grassberger (KSG) estimation obtained by k-nearest neighbor as well as information bottleneck in the traditional method. Our results clearly demonstrate that the designed framework has better performance and attains convergence quicker in the scenario where enormous volumes of data are handled, and the largest data utility obtained by the MINE for a given privacy threshold is even better.

A Survey on Statistical, Information, and Estimation—Theoretic Views on Privacy

Privacy has become an emerging challenge in both information theory and computer science due to massive (centralized) collection of user data. In this article, we overview privacy-preserving mechanisms and metrics from the lenses of information theory, and unify different privacy metrics, including f-divergences, Rényi divergences, and differential privacy (DP), in terms of the probability likelihood ratio (and its logarithm). We review recent progress on the design of privacy-preserving mechanisms according to the privacy metrics in computer science, where DP is the standard privacy notion which controls the output shift given small input perturbation, and information theory, where the privacy is guaranteed by minimizing information leakage. In particular, for DP, we include its important variants (e.g., Rényi DP, Pufferfish privacy) and properties, discuss its connections with information-theoretic quantities, and provide the operational interpretations of its additive noise mechanisms. For information-theoretic privacy, we cover notable frameworks, including the privacy funnel, originated from rate-distortion theory and information bottleneck, to privacy guarantee against statistical inference/guessing, and information obfuscation on samples and features. Finally, we discuss the implementations of these privacy-preserving mechanisms in current data-driven machine learning scenarios, including deep learning, information obfuscation, federated learning, and dataset sharing.

Secrecy by Design With Applications to Privacy and Compression

Secrecy by design is examined as an approach to information-theoretic secrecy. The main idea behind this approach is to design an information processing system from the ground up to be perfectly secure with respect to an explicit secrecy constraint. The principal technical contributions are decomposition bounds that allow the representation of a random variable <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> as a deterministic function of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$({S},{Z})$ </tex-math></inline-formula> , where <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> is a given fixed random variable and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$Z$ </tex-math></inline-formula> is constructed to be independent of <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> . Using the problems of privacy and lossless compression as examples, the utility cost of applying secrecy by design is investigated. Privacy is studied in the setting of the privacy funnel function previously introduced in the literature and new bounds for the regime of zero information leakage are derived. For the problem of lossless compression, it is shown that strong information-theoretic guarantees can be achieved using a reduced secret key size and a quantifiable penalty on the compression rate. The fundamental limits for both problems are characterized with matching lower and upper bounds when the secret <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$S$ </tex-math></inline-formula> is a deterministic function of the information source <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$X$ </tex-math></inline-formula> .

Bottleneck Problems: An Information and Estimation-Theoretic View.

Information bottleneck (IB) and privacy funnel (PF) are two closely related optimization problems which have found applications in machine learning, design of privacy algorithms, capacity problems (e.g., Mrs. Gerber’s Lemma), and strong data processing inequalities, among others. In this work, we first investigate the functional properties of IB and PF through a unified theoretical framework. We then connect them to three information-theoretic coding problems, namely hypothesis testing against independence, noisy source coding, and dependence dilution. Leveraging these connections, we prove a new cardinality bound on the auxiliary variable in IB, making its computation more tractable for discrete random variables. In the second part, we introduce a general family of optimization problems, termed “bottleneck problems”, by replacing mutual information in IB and PF with other notions of mutual information, namely f-information and Arimoto’s mutual information. We then argue that, unlike IB and PF, these problems lead to easily interpretable guarantees in a variety of inference tasks with statistical constraints on accuracy and privacy. While the underlying optimization problems are non-convex, we develop a technique to evaluate bottleneck problems in closed form by equivalently expressing them in terms of lower convex or upper concave envelope of certain functions. By applying this technique to a binary case, we derive closed form expressions for several bottleneck problems.

Variational approach for privacy funnel optimization on continuous data

Here we consider a common data encryption problem encountered by users who want to disclose some data to gain utility but preserve their private information. Specifically, we consider the inference attack, in which an adversary conducts inference on the disclosed data to gain information about users’ private data. Following privacy funnel (Makhdoumi et al., 2014), assuming that the original data X is transformed into Z before disclosing and the log loss is used for both privacy and utility metrics, then the problem can be modeled as finding a mapping X→Z that maximizes mutual information between X and Z subject to a constraint that the mutual information between Z and private data S is smaller than a predefined threshold ϵ. In contrast to the original study (Makhdoumi et al., 2014), which only focused on discrete data, we consider the more general and practical setting of continuous and high-dimensional disclosed data (e.g., image data). Most previous work on privacy-preserving representation learning is based on adversarial learning or generative adversarial networks, which has been shown to suffer from the vanishing gradient problem, and it is experimentally difficult to eliminate the relationship with private data Y when Z is constrained to retain more information about X. Here we propose a simple but effective variational approach that does not rely on adversarial training. Our experimental results show that our approach is stable and outperforms previous methods in terms of both downstream task accuracy and mutual information estimation.

Extended Gray–Wyner System With Complementary Causal Side Information

We establish the rate region of an extended Gray–Wyner system (EGW) for 2-DMS $(X,Y)$ with two additional decoders having complementary causal side information. We show that the 5-D rate region of the EGW system is equivalent to the 3-D mutual information region consisting of the set of all triples of the form $(I(X;U),\,I(Y;U),\,I(X,Y;U))$ for some $p_{U|X,Y}$ . This correspondence greatly simplifies the exploration of the the extreme points of the rate region. In addition to the operationally significant extreme points of the original Gray–Wyner rate region, which include Wyner’s common information, Gacs-Korner common information, and the information bottleneck, the extreme points of the rate region for the EGW system also include the Korner graph entropy, the privacy funnel and excess functional information, as well as three new quantities of potential interest. We further show that projections of the mutual information region yield the rate regions for many settings involving a two discrete memoryless source (2-DMS), including lossless source coding with causal side information, distributed channel synthesis, and lossless source coding with a helper. To further motivate the mutual information region itself, we draw analogies between set operations and its extreme points. This allows us to find random variables that can be considered as intersection, difference, and symmetric difference of two random variables. Finally, we establish the rate regions for two related setups to the EGW system, namely, the noncausal EGW system and the lossy EGW system.

A Compressive Privacy approach to Generalized Information Bottleneck and Privacy Funnel problems

This paper explores a Compressive Privacy (CP) methodology for optimal tradeoff between utility gain and privacy loss. CP represents a dimension-reduced subspace design of optimally desensitized query that may be safely shared with the public. Built upon the information and estimation theory, this paper proposes a “differential mutual information” (DMI) criterion to safeguard the privacy protection (PP). Algorithmically, DMI-optimal solutions can be derived via the Discriminant Component Analysis (DCA). Moreover, DCA has two machine learning variants (one in the original space and another is the kernel space) good for supervised learning applications. By extending the notion of DMI to the utility gain and privacy loss, CP unifies the conventional Information Bottleneck (IB) and Privacy Funnel (PF) and lead to two constrained optimizers, named Generalized Information Bottleneck (GIB) and Generalized Privacy Funnel (GPF). In the supervised learning environments, DCA can be further extended to a DUCA machine learning variant to reach an optimal tradeoff between utility gain and privacy loss. Finally, for fast convergence, a golden-section iterative method is developed particularly for solving the two constrained optimization problems: GIB and GPF.