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The ratio of two Gaussians is useful in many contexts of statistical inference. We discuss statistically valid inference of the ratio estimator under Differential Privacy (DP). We use the delta method to derive the asymptotic distribution of the ratio estimator and use the Gaussian mechanism to provide $(\epsilon, \delta)$ privacy guarantees. Like many statistics, the quantities needed here can be re-written as functions of sums, and sums are easy to work with for many reasons. In the DP case, the sensitivity of a sum can be easily obtained. We focus on the coverage of 95\% confidence intervals (CIs). Our simulations shows that the no correction method, which ignores the noise mechanism, gives CIs that are too narrow to provide proper coverage for small samples. We propose two methods to mitigate the under-coverage issue, one based on Monte Carlo simulations and the other based on analytical correction. We show that the CIs of our methods have the right coverage with proper privacy budget. In addition, our methods can handle weighted data, where the weights are fixed and bounded.

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The age of information (AoI) performance metric for point-to-point wireless communication systems is analytically studied under Rician-faded channels and when the receiver is equipped with multiple antennas. The general scenario of a non-linear AoI function is considered, which includes the conventional linear AoI as a special case. The stop-and-wait transmission policy is adopted, where the source node samples and then transmits new data only upon the successful reception of previous data. This approach can serve as a performance benchmark for any queuing system used in practice. New analytical and closed-form expressions are derived with respect to the average AoI and average peak AoI for the considered system configuration. We particularly focus on the energy efficiency of the said mode of operation, whereas some useful engineering insights are provided.

Mendelian randomization is a widely-used method to estimate the unconfounded effect of an exposure on an outcome by using genetic variants as instrumental variables. Mendelian randomization analyses which use variants from a single genetic region (cis-MR) have gained popularity for being an economical way to provide supporting evidence for drug target validation. This paper proposes methods for cis-MR inference which use the explanatory power of many correlated variants to make valid inferences even in situations where those variants only have weak effects on the exposure. In particular, we exploit the highly structured nature of genetic correlations in single gene regions to reduce the dimension of genetic variants using factor analysis. These genetic factors are then used as instrumental variables to construct tests for the causal effect of interest. Since these factors may often be weakly associated with the exposure, size distortions of standard t-tests can be severe. Therefore, we consider two approaches based on conditional testing. First, we extend results of commonly-used identification-robust tests to account for the use of estimated factors as instruments. Secondly, we propose a test which appropriately adjusts for first-stage screening of genetic factors based on their relevance. Our empirical results provide genetic evidence to validate cholesterol-lowering drug targets aimed at preventing coronary heart disease.

Global Positioning Systems are now a standard module in mobile devices, and their ubiquity is fueling the rapid growth of location-based services (LBSs). This poses the risk of location privacy disclosure. Effective location privacy preservation is foremost for various mobile applications. Recently two strong privacy notions, geo-indistinguishability and expected inference error, are proposed based on statistical quantification. They are shown to be complementary for limiting the leakage of location information. In this paper, we argue that personalization means regionalization for geo-indistinguishability, and we propose a regionalized location obfuscation mechanism with personalized utility sensitivities. This substantially corrects the differential privacy problem of PIVE framework proposed by Yu, Liu and Pu on ISOC Network and Distributed System Security Symposium (NDSS) in 2017. Since PIVE fails to provide differential privacy guarantees on adaptive protection location set (PLS) as pointed in our previous work, we develop DPIVE with two phases. In Phase I, we determine disjoint sets by partitioning all possible positions such that different locations in the same set share the common PLS. In Phase II, we construct a probability distribution matrix by exponential mechanism in which the rows corresponding to the same PLS have their own sensitivity of utility (diameter of PLS). Moreover, we improve DPIVE with refined location partition and fine-grained personalization, in which each location has its own privacy level on two privacy control knobs, minimum inference error and differential privacy parameter. Experiments with two public datasets demonstrate that our mechanisms have the superior performance typically on skewed locations.

Ciphertexts of an order-preserving encryption (OPE) scheme preserve the order of their corresponding plaintexts. However, OPEs are vulnerable to inference attacks that exploit this preserved order. At another end, differential privacy has become the de-facto standard for achieving data privacy. One of the most attractive properties of DP is that any post-processing (inferential) computation performed on the noisy output of a DP algorithm does not degrade its privacy guarantee. In this paper, we propose a novel differentially private order preserving encryption scheme, OP$\epsilon$. Under OP$\epsilon$, the leakage of order from the ciphertexts is differentially private. As a result, in the least, OP$\epsilon$ ensures a formal guarantee (specifically, a relaxed DP guarantee) even in the face of inference attacks. To the best of our knowledge, this is the first work to combine DP with a property-preserving encryption scheme. We demonstrate OP$\epsilon$'s practical utility in answering range queries via extensive empirical evaluation on four real-world datasets. For instance, OP$\epsilon$ misses only around $4$ in every $10K$ correct records on average for a dataset of size $\sim732K$ with an attribute of domain size $\sim18K$ and $\epsilon= 1$.

We derive a consistency result, in the $L_1$-sense, for incomplete U-statistics in the non-standard case where the kernel at hand has infinite second-order moments. Assuming that the kernel has finite moments of order $p(\geq 1)$, we obtain a bound on the $L_1$ distance between the incomplete U-statistic and its Dirac weak limit, which allows us to obtain, for any fixed $p$, an upper bound on the consistency rate. Our results hold for most classical sampling schemes that are used to obtain incomplete U-statistics.

I construct and justify confidence intervals for longitudinal causal parameters estimated with machine learning. Longitudinal parameters include long term, dynamic, and mediated effects. I provide a nonasymptotic theorem for any longitudinal causal parameter estimated with any machine learning algorithm that satisfies a few simple, interpretable conditions. The main result encompasses local parameters defined for specific demographics as well as proximal parameters defined in the presence of unobserved confounding. Formally, I prove consistency, Gaussian approximation, and semiparametric efficiency. The rate of convergence is $n^{-1/2}$ for global parameters, and it degrades gracefully for local parameters. I articulate a simple set of conditions to translate mean square rates into statistical inference. A key feature of the main result is a new multiple robustness to ill posedness for proximal causal inference in longitudinal settings.

News recommendation aims to display news articles to users based on their personal interest. Existing news recommendation methods rely on centralized storage of user behavior data for model training, which may lead to privacy concerns and risks due to the privacy-sensitive nature of user behaviors. In this paper, we propose a privacy-preserving method for news recommendation model training based on federated learning, where the user behavior data is locally stored on user devices. Our method can leverage the useful information in the behaviors of massive number users to train accurate news recommendation models and meanwhile remove the need of centralized storage of them. More specifically, on each user device we keep a local copy of the news recommendation model, and compute gradients of the local model based on the user behaviors in this device. The local gradients from a group of randomly selected users are uploaded to server, which are further aggregated to update the global model in the server. Since the model gradients may contain some implicit private information, we apply local differential privacy (LDP) to them before uploading for better privacy protection. The updated global model is then distributed to each user device for local model update. We repeat this process for multiple rounds. Extensive experiments on a real-world dataset show the effectiveness of our method in news recommendation model training with privacy protection.

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.

Many applications require an understanding of an image that goes beyond the simple detection and classification of its objects. In particular, a great deal of semantic information is carried in the relationships between objects. We have previously shown that the combination of a visual model and a statistical semantic prior model can improve on the task of mapping images to their associated scene description. In this paper, we review the model and compare it to a novel conditional multi-way model for visual relationship detection, which does not include an explicitly trained visual prior model. We also discuss potential relationships between the proposed methods and memory models of the human brain.

Machine Learning is a widely-used method for prediction generation. These predictions are more accurate when the model is trained on a larger dataset. On the other hand, the data is usually divided amongst different entities. For privacy reasons, the training can be done locally and then the model can be safely aggregated amongst the participants. However, if there are only two participants in \textit{Collaborative Learning}, the safe aggregation loses its power since the output of the training already contains much information about the participants. To resolve this issue, they must employ privacy-preserving mechanisms, which inevitably affect the accuracy of the model. In this paper, we model the training process as a two-player game where each player aims to achieve a higher accuracy while preserving its privacy. We introduce the notion of \textit{Price of Privacy}, a novel approach to measure the effect of privacy protection on the accuracy of the model. We develop a theoretical model for different player types, and we either find or prove the existence of a Nash Equilibrium with some assumptions. Moreover, we confirm these assumptions via a Recommendation Systems use case: for a specific learning algorithm, we apply three privacy-preserving mechanisms on two real-world datasets. Finally, as a complementary work for the designed game, we interpolate the relationship between privacy and accuracy for this use case and present three other methods to approximate it in a real-world scenario.

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