Empirical Calibration and Metric Differential Privacy in Language Models

NLP models trained with differential privacy (DP) usually adopt the DP-SGD framework, and privacy guarantees are often reported in terms of the privacy budget $\epsilon$. However, $\epsilon$ does not have any intrinsic meaning, and it is generally not possible to compare across variants of the framework. Work in image processing has therefore explored how to empirically calibrate noise across frameworks using Membership Inference Attacks (MIAs). However, this kind of calibration has not been established for NLP. In this paper, we show that MIAs offer little help in calibrating privacy, whereas reconstruction attacks are more useful. As a use case, we define a novel kind of directional privacy based on the von Mises-Fisher (VMF) distribution, a metric DP mechanism that perturbs angular distance rather than adding (isotropic) Gaussian noise, and apply this to NLP architectures. We show that, even though formal guarantees are incomparable, empirical privacy calibration reveals that each mechanism has different areas of strength with respect to utility-privacy trade-offs.

Comparing privacy notions for protection against reconstruction attacks in machine learning

Within the machine learning community, reconstruction attacks are a principal concern and have been identified even in federated learning (FL), which was designed with privacy preservation in mind. In response to these threats, the privacy community recommends the use of differential privacy (DP) in the stochastic gradient descent algorithm, termed DP-SGD. However, the proliferation of variants of DP in recent years\textemdash such as metric privacy\textemdash has made it challenging to conduct a fair comparison between different mechanisms due to the different meanings of the privacy parameters $\epsilon$ and $\delta$ across different variants. Thus, interpreting the practical implications of $\epsilon$ and $\delta$ in the FL context and amongst variants of DP remains ambiguous. In this paper, we lay a foundational framework for comparing mechanisms with differing notions of privacy guarantees, namely $(\epsilon,\delta)$-DP and metric privacy. We provide two foundational means of comparison: firstly, via the well-established $(\epsilon,\delta)$-DP guarantees, made possible through the R\'enyi differential privacy framework; and secondly, via Bayes' capacity, which we identify as an appropriate measure for reconstruction threats.

Bayes' capacity as a measure for reconstruction attacks in federated learning

Within the machine learning community, reconstruction attacks are a principal attack of concern and have been identified even in federated learning, which was designed with privacy preservation in mind. In federated learning, it has been shown that an adversary with knowledge of the machine learning architecture is able to infer the exact value of a training element given an observation of the weight updates performed during stochastic gradient descent. In response to these threats, the privacy community recommends the use of differential privacy in the stochastic gradient descent algorithm, termed DP-SGD. However, DP has not yet been formally established as an effective countermeasure against reconstruction attacks. In this paper, we formalise the reconstruction threat model using the information-theoretic framework of quantitative information flow. We show that the Bayes' capacity, related to the Sibson mutual information of order infinity, represents a tight upper bound on the leakage of the DP-SGD algorithm to an adversary interested in performing a reconstruction attack. We provide empirical results demonstrating the effectiveness of this measure for comparing mechanisms against reconstruction threats.

Directional Privacy for Deep Learning

Differentially Private Stochastic Gradient Descent (DP-SGD) is a key method for applying privacy in the training of deep learning models. This applies isotropic Gaussian noise to gradients during training, which can perturb these gradients in any direction, damaging utility. Metric DP, however, can provide alternative mechanisms based on arbitrary metrics that might be more suitable. In this paper we apply \textit{directional privacy}, via a mechanism based on the von Mises-Fisher (VMF) distribution, to perturb gradients in terms of \textit{angular distance} so that gradient direction is broadly preserved. We show that this provides $\epsilon d$-privacy for deep learning training, rather than the $(\epsilon, \delta)$-privacy of the Gaussian mechanism; and that experimentally, on key datasets, the VMF mechanism can outperform the Gaussian in the utility-privacy trade-off.

Locality Sensitive Hashing with Extended Differential Privacy

Extended differential privacy, a generalization of standard differential privacy (DP) using a general metric rather than the Hamming metric, has been widely studied to provide rigorous privacy guarantees while keeping high utility. However, existing works on extended DP focus on a specific metric such as the Euclidean metric, the $l_1$ metric, and the Earth Mover's metric, and cannot be applied to other metrics. Consequently, existing extended DP mechanisms are limited to a small number of applications such as location-based services and document processing. In this paper, we propose a mechanism providing extended DP with a wide range of metrics. Our mechanism is based on locality sensitive hashing (LSH) and randomized response, and can be applied to a wide variety of metrics including the angular distance (or cosine) metric, Jaccard metric, Earth Mover's metric, and $l_p$ metric. Moreover, our mechanism works well for personal data in a high-dimensional space. We theoretically analyze the privacy properties of our mechanism, introducing new versions of concentrated and probabilistic extended DP to explain the guarantees provided. Finally, we apply our mechanism to friend matching based on high-dimensional personal data with an angular distance metric in the local model. We show that existing local DP mechanisms such as the RAPPOR do not work in this application. We also show through experiments that our mechanism makes possible friend matching with rigorous privacy guarantees and high utility.

Generalised Differential Privacy for Text Document Processing

We address the problem of how to "obfuscate" texts by removing stylistic clues which can identify authorship, whilst preserving (as much as possible) the content of the text. In this paper we combine ideas from "generalised differential privacy" and machine learning techniques for text processing to model privacy for text documents. We define a privacy mechanism that operates at the level of text documents represented as "bags-of-words" - these representations are typical in machine learning and contain sufficient information to carry out many kinds of classification tasks including topic identification and authorship attribution (of the original documents). We show that our mechanism satisfies privacy with respect to a metric for semantic similarity, thereby providing a balance between utility, defined by the semantic content of texts, with the obfuscation of stylistic clues. We demonstrate our implementation on a "fan fiction" dataset, confirming that it is indeed possible to disguise writing style effectively whilst preserving enough information and variation for accurate content classification tasks.