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1. An Equivalence Between Private Classification and Online Prediction

   Bun, Mark ; Livni, Roi ; Moran, Shay ( January 2020 , 61st Annual IEEE Symposium on Foundations of Computer Science)

   null (Ed.)

   We prove that every concept class with finite Littlestone dimension can be learned by an (approximate) differentially-private algorithm. This answers an open question of Alon et al. (STOC 2019) who proved the converse statement (this question was also asked by Neel et al. (FOCS 2019)). Together these two results yield an equivalence between online learnability and private PAC learnability. We introduce a new notion of algorithmic stability called “global stability” which is essential to our proof and may be of independent interest. We also discuss an application of our results to boosting the privacy and accuracy parameters of differentially-private learners. 

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2. An Empirical Study of Rich Subgroup Fairness for Machine Learning

   https://doi.org/10.1145/3287560.3287592  

   Kearns, Michael ; Neel, Seth ; Roth, Aaron ; Wu, Zhiwei Steven ( January 2019 , ACM FAT* 2019)

   Kearns, Neel, Roth, and Wu [ICML 2018] recently proposed a notion of rich subgroup fairness intended to bridge the gap between statistical and individual notions of fairness. Rich subgroup fairness picks a statistical fairness constraint (say, equalizing false positive rates across protected groups), but then asks that this constraint hold over an exponentially or infinitely large collection of subgroups defined by a class of functions with bounded VC dimension. They give an algorithm guaranteed to learn subject to this constraint, under the condition that it has access to oracles for perfectly learning absent a fairness constraint. In this paper, we undertake an extensive empirical evaluation of the algorithm of Kearns et al. On four real datasets for which fairness is a concern, we investigate the basic convergence of the algorithm when instantiated with fast heuristics in place of learning oracles, measure the tradeoffs between fairness and accuracy, and compare this approach with the recent algorithm of Agarwal, Beygelzeimer, Dudik, Langford, and Wallach [ICML 2018], which implements weaker and more traditional marginal fairness constraints defined by individual protected attributes. We find that in general, the Kearns et al. algorithm converges quickly, large gains in fairness can be obtained with mild costs to accuracy, and that optimizing accuracy subject only to marginal fairness leads to classifiers with substantial subgroup unfairness. We also provide a number of analyses and visualizations of the dynamics and behavior of the Kearns et al. algorithm. Overall we find this algorithm to be effective on real data, and rich subgroup fairness to be a viable notion in practice 

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3. Private Everlasting Prediction

   Naor, Moni Naor ; Nissim, Kobbi Nissim ; Stemmer, Uri ; Yan, Chao ( December 2023 , proceedings of 37th NeurIPS 2023)

   A private learner is trained on a sample of labeled points and generates a hypothesis that can be used for predicting the labels of newly sampled points while protecting the privacy of the training set [Kasiviswannathan et al., FOCS 2008]. Past research uncovered that private learners may need to exhibit significantly higher sample complexity than non-private learners as is the case of learning of one-dimensional threshold functions [Bun et al., FOCS 2015, Alon et al., STOC 2019]. We explore prediction as an alternative to learning. A predictor answers a stream of classification queries instead of outputting a hypothesis. Earlier work has considered a private prediction model with a single classification query [Dwork and Feldman, COLT 2018]. We observe that when answering a stream of queries, a predictor must modify the hypothesis it uses over time, and in a manner that cannot rely solely on the training set. We introduce private everlasting prediction taking into account the privacy of both the training set and the (adaptively chosen) queries made to the predictor. We then present a generic construction of private everlasting predictors in the PAC model. The sample complexity of the initial training sample in our construction is quadratic (up to polylog factors) in the VC dimension of the concept class. Our construction allows prediction for all concept classes with finite VC dimension, and in particular threshold functions over infinite domains, for which (traditional) private learning is known to be impossible. 

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4. Private High-Dimensional Hypothesis Testing

   Narayanan, S. ( January 2022 , Conference on Learning Theory (COLT 2022))

   We provide improved differentially private algorithms for identity testing of high-dimensional distributions. Specifically, for d-dimensional Gaussian distributions with known covariance Σ, we can test whether the distribution comes from N(μ∗,Σ) for some fixed μ∗ or from some N(μ,Σ) with total variation distance at least α from N(μ∗,Σ) with (ε,0)-differential privacy, using only O~(d1/2α2+d1/3α4/3⋅ε2/3+1α⋅ε) samples if the algorithm is allowed to be computationally inefficient, and only O~(d1/2α2+d1/4α⋅ε) samples for a computationally efficient algorithm. We also provide a matching lower bound showing that our computationally inefficient algorithm has optimal sample complexity. We also extend our algorithms to various related problems, including mean testing of Gaussians with bounded but unknown covariance, uniformity testing of product distributions over {−1,1}d, and tolerant testing. Our results improve over the previous best work of Canonne et al.~\cite{CanonneKMUZ20} for both computationally efficient and inefficient algorithms, and even our computationally efficient algorithm matches the optimal \emph{non-private} sample complexity of O(d√α2) in many standard parameter settings. In addition, our results show that, surprisingly, private identity testing of d-dimensional Gaussians can be done with fewer samples than private identity testing of discrete distributions over a domain of size d \cite{AcharyaSZ18}, which refutes a conjectured lower bound of~\cite{CanonneKMUZ20}. 

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5. Black-Box Differential Privacy for Interactive ML

   Kaplan, Haim ; Mansour, Yishay ; Moran, Shay ; Nissim, Kobbi ; Stemmer, Uri ( December 2023 , 37th Conference on Neural Information Processing Systems (NeurIPS 2023))

   In this work we revisit an interactive variant of joint differential privacy, recently introduced by Naor et al. [2023], and generalize it towards handling online processes in which existing privacy definitions seem too restrictive. We study basic properties of this definition and demonstrate that it satisfies (suitable variants) of group privacy, composition, and post processing. In order to demonstrate the advantages of this privacy definition compared to traditional forms of differential privacy, we consider the basic setting of online classification. We show that any (possibly non-private) learning rule can be effectively transformed to a private learning rule with only a polynomial overhead in the mistake bound. This demonstrates a stark difference with traditional forms of differential privacy, such as the one studied by Golowich and Livni [2021], where only a double exponential overhead in the mistake bound is known (via an information theoretic upper bound). 

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