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Register a new userDifferentially Private Bayesian Inference for Generalized Linear Models
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Added by
Tejas Kulkarni
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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Generalized linear models (GLMs) such as logistic regression are among the most widely used arms in data analysts repertoire and often used on sensitive datasets. A large body of prior works that investigate GLMs under differential privacy (DP) constraints provide only private point estimates of the regression coefficients, and are not able to quantify parameter uncertainty. In this work, with logistic and Poisson regression as running examples, we introduce a generic noise-aware DP Bayesian inference method for a GLM at hand, given a noisy sum of summary statistics. Quantifying uncertainty allows us to determine which of the regression coefficients are statistically significantly different from zero. We provide a previously unknown tight privacy analysis and experimentally demonstrate that the posteriors obtained from our model, while adhering to strong privacy guarantees, are close to the non-private posteriors.
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Economics and social science research often require analyzing datasets of sensitive personal information at fine granularity, with models fit to small subsets of the data. Unfortunately, such fine-grained analysis can easily reveal sensitive individual information. We study algorithms for simple linear regression that satisfy differential privacy, a constraint which guarantees that an algorithms output reveals little about any individual input data record, even to an attacker with arbitrary side information about the dataset. We consider the design of differentially private algorithms for simple linear regression for small datasets, with tens to hundreds of datapoints, which is a particularly challenging regime for differential privacy. Focusing on a particular application to small-area analysis in economics research, we study the performance of a spectrum of algorithms we adapt to the setting. We identify key factors that affect their performance, showing through a range of experiments that algorithms based on robust estimators (in particular, the Theil-Sen estimator) perform well on the smallest datasets, but that other more standard algorithms do better as the dataset size increases.
Bayesian neural network (BNN) allows for uncertainty quantification in prediction, offering an advantage over regular neural networks that has not been explored in the differential privacy (DP) framework. We fill this important gap by leveraging recent development in Bayesian deep learning and privacy accounting to offer a more precise analysis of the trade-off between privacy and accuracy in BNN. We propose three DP-BNNs that characterize the weight uncertainty for the same network architecture in distinct ways, namely DP-SGLD (via the noisy gradient method), DP-BBP (via changing the parameters of interest) and DP-MC Dropout (via the model architecture). Interestingly, we show a new equivalence between DP-SGD and DP-SGLD, implying that some non-Bayesian DP training naturally allows for uncertainty quantification. However, the hyperparameters such as learning rate and batch size, can have different or even opposite effects in DP-SGD and DP-SGLD. Extensive experiments are conducted to compare DP-BNNs, in terms of privacy guarantee, prediction accuracy, uncertainty quantification, calibration, computation speed, and generalizability to network architecture. As a result, we observe a new tradeoff between the privacy and the reliability. When compared to non-DP and non-Bayesian approaches, DP-SGLD is remarkably accurate under strong privacy guarantee, demonstrating the great potential of DP-BNN in real-world tasks.
Neural architecture search, which aims to automatically search for architectures (e.g., convolution, max pooling) of neural networks that maximize validation performance, has achieved remarkable progress recently. In many application scenarios, several parties would like to collaboratively search for a shared neural architecture by leveraging data from all parties. However, due to privacy concerns, no party wants its data to be seen by other parties. To address this problem, we propose federated neural architecture search (FNAS), where different parties collectively search for a differentiable architecture by exchanging gradients of architecture variables without exposing their data to other parties. To further preserve privacy, we study differentially-private FNAS (DP-FNAS), which adds random noise to the gradients of architecture variables. We provide theoretical guarantees of DP-FNAS in achieving differential privacy. Experiments show that DP-FNAS can search highly-performant neural architectures while protecting the privacy of individual parties. The code is available at https://github.com/UCSD-AI4H/DP-FNAS
Being able to efficiently and accurately select the top-$k$ elements with differential privacy is an integral component of various private data analysis tasks. In this paper, we present the oneshot Laplace mechanism, which generalizes the well-known Report Noisy Max mechanism to reporting noisy top-$k$ elements. We show that the oneshot Laplace mechanism with a noise level of $widetilde{O}(sqrt{k}/eps)$ is approximately differentially private. Compared to the previous peeling approach of running Report Noisy Max $k$ times, the oneshot Laplace mechanism only adds noises and computes the top $k$ elements once, hence much more efficient for large $k$. In addition, our proof of privacy relies on a novel coupling technique that bypasses the use of composition theorems. Finally, we present a novel application of efficient top-$k$ selection in the classical problem of ranking from pairwise comparisons.
This paper studies the relationship between generalization and privacy preservation in iterative learning algorithms by two sequential steps. We first establish an alignment between generalization and privacy preservation for any learning algorithm. We prove that $(varepsilon, delta)$-differential privacy implies an on-average generalization bound for multi-database learning algorithms which further leads to a high-probability bound for any learning algorithm. This high-probability bound also implies a PAC-learnable guarantee for differentially private learning algorithms. We then investigate how the iterative nature shared by most learning algorithms influence privacy preservation and further generalization. Three composition theorems are proposed to approximate the differential privacy of any iterative algorithm through the differential privacy of its every iteration. By integrating the above two steps, we eventually deliver generalization bounds for iterative learning algorithms, which suggest one can simultaneously enhance privacy preservation and generalization. Our results are strictly tighter than the existing works. Particularly, our generalization bounds do not rely on the model size which is prohibitively large in deep learning. This sheds light to understanding the generalizability of deep learning. These results apply to a wide spectrum of learning algorithms. In this paper, we apply them to stochastic gradient Langevin dynamics and agnostic federated learning as examples.
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