Differential privacy (DP) allows the quantification of privacy loss when the data of individuals is subjected to algorithmic processing such as machine learning, as well as the provision of objective privacy guarantees. However, while techniques such as individual R\'enyi DP (RDP) allow for granular, per-person privacy accounting, few works have investigated the impact of each input feature on the individual's privacy loss. Here we extend the view of individual RDP by introducing a new concept we call partial sensitivity, which leverages symbolic automatic differentiation to determine the influence of each input feature on the gradient norm of a function. We experimentally evaluate our approach on queries over private databases, where we obtain a feature-level contribution of private attributes to the DP guarantee of individuals. Furthermore, we explore our findings in the context of neural network training on synthetic data by investigating the partial sensitivity of input pixels on an image classification task.
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Distributional reinforcement learning (RL) -- in which agents learn about all the possible long-term consequences of their actions, and not just the expected value -- is of great recent interest. One of the most important affordances of a distributional view is facilitating a modern, measured, approach to risk when outcomes are not completely certain. By contrast, psychological and neuroscientific investigations into decision making under risk have utilized a variety of more venerable theoretical models such as prospect theory that lack axiomatically desirable properties such as coherence. Here, we consider a particularly relevant risk measure for modeling human and animal planning, called conditional value-at-risk (CVaR), which quantifies worst-case outcomes (e.g., vehicle accidents or predation). We first adopt a conventional distributional approach to CVaR in a sequential setting and reanalyze the choices of human decision-makers in the well-known two-step task, revealing substantial risk aversion that had been lurking under stickiness and perseveration. We then consider a further critical property of risk sensitivity, namely time consistency, showing alternatives to this form of CVaR that enjoy this desirable characteristic. We use simulations to examine settings in which the various forms differ in ways that have implications for human and animal planning and behavior.
Recent research in differential privacy demonstrated that (sub)sampling can amplify the level of protection. For example, for $\epsilon$-differential privacy and simple random sampling with sampling rate $r$, the actual privacy guarantee is approximately $r\epsilon$, if a value of $\epsilon$ is used to protect the output from the sample. In this paper, we study whether this amplification effect can be exploited systematically to improve the accuracy of the privatized estimate. Specifically, assuming the agency has information for the full population, we ask under which circumstances accuracy gains could be expected, if the privatized estimate would be computed on a random sample instead of the full population. We find that accuracy gains can be achieved for certain regimes. However, gains can typically only be expected, if the sensitivity of the output with respect to small changes in the database does not depend too strongly on the size of the database. We only focus on algorithms that achieve differential privacy by adding noise to the final output and illustrate the accuracy implications for two commonly used statistics: the mean and the median. We see our research as a first step towards understanding the conditions required for accuracy gains in practice and we hope that these findings will stimulate further research broadening the scope of differential privacy algorithms and outputs considered.
We consider sensitivity of a generic stochastic optimization problem to model uncertainty. We take a non-parametric approach and capture model uncertainty using Wasserstein balls around the postulated model. We provide explicit formulae for the first order correction to both the value function and the optimizer and further extend our results to optimization under linear constraints. We present applications to statistics, machine learning, mathematical finance and uncertainty quantification. In particular, we provide explicit first-order approximation for square-root LASSO regression coefficients and deduce coefficient shrinkage compared to the ordinary least squares regression. We consider robustness of call option pricing and deduce a new Black-Scholes sensitivity, a non-parametric version of the so-called Vega. We also compute sensitivities of optimized certainty equivalents in finance and propose measures to quantify robustness of neural networks to adversarial examples.
We introduce a universal framework for characterizing the statistical efficiency of a statistical estimation problem with differential privacy guarantees. Our framework, which we call High-dimensional Propose-Test-Release (HPTR), builds upon three crucial components: the exponential mechanism, robust statistics, and the Propose-Test-Release mechanism. Gluing all these together is the concept of resilience, which is central to robust statistical estimation. Resilience guides the design of the algorithm, the sensitivity analysis, and the success probability analysis of the test step in Propose-Test-Release. The key insight is that if we design an exponential mechanism that accesses the data only via one-dimensional robust statistics, then the resulting local sensitivity can be dramatically reduced. Using resilience, we can provide tight local sensitivity bounds. These tight bounds readily translate into near-optimal utility guarantees in several cases. We give a general recipe for applying HPTR to a given instance of a statistical estimation problem and demonstrate it on canonical problems of mean estimation, linear regression, covariance estimation, and principal component analysis. We introduce a general utility analysis technique that proves that HPTR nearly achieves the optimal sample complexity under several scenarios studied in the literature.
The arrival of Immersive Virtual and Augmented Reality hardware to the consumer market suggests seamless multi-modal communication between human participants and autonomous interactive characters is an achievable goal in the near future. This possibility is further reinforced by the rapid improvements in the automated analysis of speech, facial expressions and body language, as well as improvements in character animation and speech synthesis techniques. However, we do not have a formal theory that allows us to compare, on one side, interactive social scenarios among human users and autonomous virtual characters and, on the other side, pragmatic inference mechanisms as they occur in non-mediated communication. Grices' and Sperbers' model of inferential communication does explain the nature of everyday communication through cognitive mechanisms that support spontaneous inferences performed in pragmatic communication. However, such a theory is not based on a mathematical framework with a precision comparable to classical information theory. To address this gap, in this article we introduce a Mathematical Theory of Inferential Communication (MaTIC). MaTIC formalises some assumptions of inferential communication, it explores its theoretical consequences and outlines the practical steps needed to use it in different application scenarios.
Gaussian processes (GPs) are non-parametric Bayesian models that are widely used for diverse prediction tasks. Previous work in adding strong privacy protection to GPs via differential privacy (DP) has been limited to protecting only the privacy of the prediction targets (model outputs) but not inputs. We break this limitation by introducing GPs with DP protection for both model inputs and outputs. We achieve this by using sparse GP methodology and publishing a private variational approximation on known inducing points. The approximation covariance is adjusted to approximately account for the added uncertainty from DP noise. The approximation can be used to compute arbitrary predictions using standard sparse GP techniques. We propose a method for hyperparameter learning using a private selection protocol applied to validation set log-likelihood. Our experiments demonstrate that given sufficient amount of data, the method can produce accurate models under strong privacy protection.
Many video classification applications require access to personal data, thereby posing an invasive security risk to the users' privacy. We propose a privacy-preserving implementation of single-frame method based video classification with convolutional neural networks that allows a party to infer a label from a video without necessitating the video owner to disclose their video to other entities in an unencrypted manner. Similarly, our approach removes the requirement of the classifier owner from revealing their model parameters to outside entities in plaintext. To this end, we combine existing Secure Multi-Party Computation (MPC) protocols for private image classification with our novel MPC protocols for oblivious single-frame selection and secure label aggregation across frames. The result is an end-to-end privacy-preserving video classification pipeline. We evaluate our proposed solution in an application for private human emotion recognition. Our results across a variety of security settings, spanning honest and dishonest majority configurations of the computing parties, and for both passive and active adversaries, demonstrate that videos can be classified with state-of-the-art accuracy, and without leaking sensitive user information.
Train machine learning models on sensitive user data has raised increasing privacy concerns in many areas. Federated learning is a popular approach for privacy protection that collects the local gradient information instead of real data. One way to achieve a strict privacy guarantee is to apply local differential privacy into federated learning. However, previous works do not give a practical solution due to three issues. First, the noisy data is close to its original value with high probability, increasing the risk of information exposure. Second, a large variance is introduced to the estimated average, causing poor accuracy. Last, the privacy budget explodes due to the high dimensionality of weights in deep learning models. In this paper, we proposed a novel design of local differential privacy mechanism for federated learning to address the abovementioned issues. It is capable of making the data more distinct from its original value and introducing lower variance. Moreover, the proposed mechanism bypasses the curse of dimensionality by splitting and shuffling model updates. A series of empirical evaluations on three commonly used datasets, MNIST, Fashion-MNIST and CIFAR-10, demonstrate that our solution can not only achieve superior deep learning performance but also provide a strong privacy guarantee at the same time.
Alternating Direction Method of Multipliers (ADMM) is a widely used tool for machine learning in distributed settings, where a machine learning model is trained over distributed data sources through an interactive process of local computation and message passing. Such an iterative process could cause privacy concerns of data owners. The goal of this paper is to provide differential privacy for ADMM-based distributed machine learning. Prior approaches on differentially private ADMM exhibit low utility under high privacy guarantee and often assume the objective functions of the learning problems to be smooth and strongly convex. To address these concerns, we propose a novel differentially private ADMM-based distributed learning algorithm called DP-ADMM, which combines an approximate augmented Lagrangian function with time-varying Gaussian noise addition in the iterative process to achieve higher utility for general objective functions under the same differential privacy guarantee. We also apply the moments accountant method to bound the end-to-end privacy loss. The theoretical analysis shows that DP-ADMM can be applied to a wider class of distributed learning problems, is provably convergent, and offers an explicit utility-privacy tradeoff. To our knowledge, this is the first paper to provide explicit convergence and utility properties for differentially private ADMM-based distributed learning algorithms. The evaluation results demonstrate that our approach can achieve good convergence and model accuracy under high end-to-end differential privacy guarantee.
We detail a new framework for privacy preserving deep learning and discuss its assets. The framework puts a premium on ownership and secure processing of data and introduces a valuable representation based on chains of commands and tensors. This abstraction allows one to implement complex privacy preserving constructs such as Federated Learning, Secure Multiparty Computation, and Differential Privacy while still exposing a familiar deep learning API to the end-user. We report early results on the Boston Housing and Pima Indian Diabetes datasets. While the privacy features apart from Differential Privacy do not impact the prediction accuracy, the current implementation of the framework introduces a significant overhead in performance, which will be addressed at a later stage of the development. We believe this work is an important milestone introducing the first reliable, general framework for privacy preserving deep learning.
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