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Resampling methods for Private Statistical Inference
Feb 11, 2024
We consider the task of constructing confidence intervals with differential privacy. We propose two private variants of the non-parametric bootstrap, which privately compute the median of the results of multiple ``little'' bootstraps run on partitions of the data and give asymptotic bounds on the coverage error of the resulting confidence intervals. For a fixed differential privacy parameter $\epsilon$, our methods enjoy the same error rates as that of the non-private bootstrap to within logarithmic factors in the sample size $n$. We empirically validate the performance of our methods for mean estimation, median estimation, and logistic regression with both real and synthetic data. Our methods achieve similar coverage accuracy to existing methods (and non-private baselines) while providing notably shorter ($\gtrsim 10$ times) confidence intervals than previous approaches.
Differentially Private Heavy Hitter Detection using Federated Analytics
Jul 21, 2023
In this work, we study practical heuristics to improve the performance of prefix-tree based algorithms for differentially private heavy hitter detection. Our model assumes each user has multiple data points and the goal is to learn as many of the most frequent data points as possible across all users' data with aggregate and local differential privacy. We propose an adaptive hyperparameter tuning algorithm that improves the performance of the algorithm while satisfying computational, communication and privacy constraints. We explore the impact of different data-selection schemes as well as the impact of introducing deny lists during multiple runs of the algorithm. We test these improvements using extensive experimentation on the Reddit dataset~\cite{caldas2018leaf} on the task of learning the most frequent words.
Private optimization in the interpolation regime: faster rates and hardness results
Oct 31, 2022In non-private stochastic convex optimization, stochastic gradient methods converge much faster on interpolation problems -- problems where there exists a solution that simultaneously minimizes all of the sample losses -- than on non-interpolating ones; we show that generally similar improvements are impossible in the private setting. However, when the functions exhibit quadratic growth around the optimum, we show (near) exponential improvements in the private sample complexity. In particular, we propose an adaptive algorithm that improves the sample complexity to achieve expected error $\alpha$ from $\frac{d}{\varepsilon \sqrt{\alpha}}$ to $\frac{1}{\alpha^\rho} + \frac{d}{\varepsilon} \log\left(\frac{1}{\alpha}\right)$ for any fixed $\rho >0$, while retaining the standard minimax-optimal sample complexity for non-interpolation problems. We prove a lower bound that shows the dimension-dependent term is tight. Furthermore, we provide a superefficiency result which demonstrates the necessity of the polynomial term for adaptive algorithms: any algorithm that has a polylogarithmic sample complexity for interpolation problems cannot achieve the minimax-optimal rates for the family of non-interpolation problems.
Fine-tuning is Fine in Federated Learning
Aug 16, 2021
We study the performance of federated learning algorithms and their variants in an asymptotic framework. Our starting point is the formulation of federated learning as a multi-criterion objective, where the goal is to minimize each client's loss using information from all of the clients. We propose a linear regression model, where, for a given client, we theoretically compare the performance of various algorithms in the high-dimensional asymptotic limit. This asymptotic multi-criterion approach naturally models the high-dimensional, many-device nature of federated learning and suggests that personalization is central to federated learning. Our theory suggests that Fine-tuned Federated Averaging (FTFA), i.e., Federated Averaging followed by local training, and the ridge regularized variant Ridge-tuned Federated Averaging (RTFA) are competitive with more sophisticated meta-learning and proximal-regularized approaches. In addition to being conceptually simpler, FTFA and RTFA are computationally more efficient than its competitors. We corroborate our theoretical claims with extensive experiments on federated versions of the EMNIST, CIFAR-100, Shakespeare, and Stack Overflow datasets.
Accelerated, Optimal, and Parallel: Some Results on Model-Based Stochastic Optimization
Jan 07, 2021
We extend the Approximate-Proximal Point (aProx) family of model-based methods for solving stochastic convex optimization problems, including stochastic subgradient, proximal point, and bundle methods, to the minibatch and accelerated setting. To do so, we propose specific model-based algorithms and an acceleration scheme for which we provide non-asymptotic convergence guarantees, which are order-optimal in all problem-dependent constants and provide linear speedup in minibatch size, while maintaining the desirable robustness traits (e.g. to stepsize) of the aProx family. Additionally, we show improved convergence rates and matching lower bounds identifying new fundamental constants for "interpolation" problems, whose importance in statistical machine learning is growing; this, for example, gives a parallelization strategy for alternating projections. We corroborate our theoretical results with empirical testing to demonstrate the gains accurate modeling, acceleration, and minibatching provide.