arXiv subjects

Wei-Ning Chen

Publications and source records attributed to Wei-Ning Chen.

26 records · Page 2Linked to original sources

arXiv2022

The Fundamental Price of Secure Aggregation in Differentially Private Federated Learning

We consider the problem of training a $d$ dimensional model with distributed differential privacy (DP) where secure aggregation (SecAgg) is used to ensure that the server only sees the noisy sum of $n$ model updates in every training round. Taking into account the constraints imposed by SecAgg, we characterize the fundamental communication cost required to obtain the best accuracy achievable under $\varepsilon$ central DP (i.e. under a fully trusted server and no communication constraints). Our results show that $\tilde{O}\left( \min(n^2\varepsilon^2, d) \right)$ bits per client are both sufficient and necessary, and this fundamental limit can be achieved by a linear scheme based on sparse random projections. This provides a significant improvement relative to state-of-the-art SecAgg distributed DP schemes which use $\tilde{O}(d\log(d/\varepsilon^2))$ bits per client. Empirically, we evaluate our proposed scheme on real-world federated learning tasks. We find that our theoretical analysis is well matched in practice. In particular, we show that we can reduce the communication cost significantly to under $1.2$ bits per parameter in realistic privacy settings without decreasing test-time performance. Our work hence theoretically and empirically specifies the fundamental price of using SecAgg.

cs.LG↗

arXiv2022

Optimal Compression of Locally Differentially Private Mechanisms

Compressing the output of ε-locally differentially private (LDP) randomizers naively leads to suboptimal utility. In this work, we demonstrate the benefits of using schemes that jointly compress and privatize the data using shared randomness. In particular, we investigate a family of schemes based on Minimal Random Coding (Havasi et al., 2019) and prove that they offer optimal privacy-accuracy-communication tradeoffs. Our theoretical and empirical findings show that our approach can compress PrivUnit (Bhowmick et al., 2018) and Subset Selection (Ye et al., 2018), the best known LDP algorithms for mean and frequency estimation, to to the order of ε-bits of communication while preserving their privacy and accuracy guarantees.

cs.CR↗

arXiv2021

Pointwise Bounds for Distribution Estimation under Communication Constraints

We consider the problem of estimating a $d$-dimensional discrete distribution from its samples observed under a $b$-bit communication constraint. In contrast to most previous results that largely focus on the global minimax error, we study the local behavior of the estimation error and provide \emph{pointwise} bounds that depend on the target distribution $p$. In particular, we show that the $\ell_2$ error decays with $O\left(\frac{\lVert p\rVert_{1/2}}{n2^b}\vee \frac{1}{n}\right)$ (In this paper, we use $a\vee b$ and $a \wedge b$ to denote $\max(a, b)$ and $\min(a,b)$ respectively.) when $n$ is sufficiently large, hence it is governed by the \emph{half-norm} of $p$ instead of the ambient dimension $d$. For the achievability result, we propose a two-round sequentially interactive estimation scheme that achieves this error rate uniformly over all $p$. Our scheme is based on a novel local refinement idea, where we first use a standard global minimax scheme to localize $p$ and then use the remaining samples to locally refine our estimate. We also develop a new local minimax lower bound with (almost) matching $\ell_2$ error, showing that any interactive scheme must admit a $Ω\left( \frac{\lVert p \rVert_{{(1+δ)}/{2}}}{n2^b}\right)$ $\ell_2$ error for any $δ> 0$. The lower bound is derived by first finding the best parametric sub-model containing $p$, and then upper bounding the quantized Fisher information under this model. Our upper and lower bounds together indicate that the $\mathcal{H}_{1/2}(p) = \log(\lVert p \rVert_{{1}/{2}})$ bits of communication is both sufficient and necessary to achieve the optimal (centralized) performance, where $\mathcal{H}_{{1}/{2}}(p)$ is the Rényi entropy of order $2$. Therefore, under the $\ell_2$ loss, the correct measure of the local communication complexity at $p$ is its Rényi entropy.

cs.IT↗

arXiv2021

Breaking The Dimension Dependence in Sparse Distribution Estimation under Communication Constraints

We consider the problem of estimating a $d$-dimensional $s$-sparse discrete distribution from its samples observed under a $b$-bit communication constraint. The best-known previous result on $\ell_2$ estimation error for this problem is $O\left( \frac{s\log\left( {d}/{s}\right)}{n2^b}\right)$. Surprisingly, we show that when sample size $n$ exceeds a minimum threshold $n^*(s, d, b)$, we can achieve an $\ell_2$ estimation error of $O\left( \frac{s}{n2^b}\right)$. This implies that when $n>n^*(s, d, b)$ the convergence rate does not depend on the ambient dimension $d$ and is the same as knowing the support of the distribution beforehand. We next ask the question: ``what is the minimum $n^*(s, d, b)$ that allows dimension-free convergence?''. To upper bound $n^*(s, d, b)$, we develop novel localization schemes to accurately and efficiently localize the unknown support. For the non-interactive setting, we show that $n^*(s, d, b) = O\left( \min \left( {d^2\log^2 d}/{2^b}, {s^4\log^2 d}/{2^b}\right) \right)$. Moreover, we connect the problem with non-adaptive group testing and obtain a polynomial-time estimation scheme when $n = \tildeΩ\left({s^4\log^4 d}/{2^b}\right)$. This group testing based scheme is adaptive to the sparsity parameter $s$, and hence can be applied without knowing it. For the interactive setting, we propose a novel tree-based estimation scheme and show that the minimum sample-size needed to achieve dimension-free convergence can be further reduced to $n^*(s, d, b) = \tilde{O}\left( {s^2\log^2 d}/{2^b} \right)$.

stat.ML↗

arXiv2021

Breaking the Communication-Privacy-Accuracy Trilemma

Two major challenges in distributed learning and estimation are 1) preserving the privacy of the local samples; and 2) communicating them efficiently to a central server, while achieving high accuracy for the end-to-end task. While there has been significant interest in addressing each of these challenges separately in the recent literature, treatments that simultaneously address both challenges are still largely missing. In this paper, we develop novel encoding and decoding mechanisms that simultaneously achieve optimal privacy and communication efficiency in various canonical settings. In particular, we consider the problems of mean estimation and frequency estimation under $\varepsilon$-local differential privacy and $b$-bit communication constraints. For mean estimation, we propose a scheme based on Kashin's representation and random sampling, with order-optimal estimation error under both constraints. For frequency estimation, we present a mechanism that leverages the recursive structure of Walsh-Hadamard matrices and achieves order-optimal estimation error for all privacy levels and communication budgets. As a by-product, we also construct a distribution estimation mechanism that is rate-optimal for all privacy regimes and communication constraints, extending recent work that is limited to $b=1$ and $\varepsilon=O(1)$. Our results demonstrate that intelligent encoding under joint privacy and communication constraints can yield a performance that matches the optimal accuracy achievable under either constraint alone.

cs.LG↗

arXiv2020

Fisher information under local differential privacy

We develop data processing inequalities that describe how Fisher information from statistical samples can scale with the privacy parameter $\varepsilon$ under local differential privacy constraints. These bounds are valid under general conditions on the distribution of the score of the statistical model, and they elucidate under which conditions the dependence on $\varepsilon$ is linear, quadratic, or exponential. We show how these inequalities imply order optimal lower bounds for private estimation for both the Gaussian location model and discrete distribution estimation for all levels of privacy $\varepsilon>0$. We further apply these inequalities to sparse Bernoulli models and demonstrate privacy mechanisms and estimators with order-matching squared $\ell^2$ error.

cs.IT↗

arXiv2018

Anonymous Heterogeneous Distributed Detection: Optimal Decision Rules, Error Exponents, and the Price of Anonymity

We explore the fundamental limits of heterogeneous distributed detection in an anonymous sensor network with n sensors and a single fusion center. The fusion center collects the single observation from each of the n sensors to detect a binary parameter. The sensors are clustered into multiple groups, and different groups follow different distributions under a given hypothesis. The key challenge for the fusion center is the anonymity of sensors - although it knows the exact number of sensors and the distribution of observations in each group, it does not know which group each sensor belongs to. It is hence natural to consider it as a composite hypothesis testing problem. First, we propose an optimal test called mixture likelihood ratio test based on the ratio of the uniform mixture of all distributions under one hypothesis to that under the other. Optimality is shown by first arguing that symmetric tests are optimal, which do not depend on the order of observations across the sensors, and then proving that the mixture likelihood ratio test is optimal among all symmetric tests. Second, we focus on the Neyman-Pearson setting and characterize the error exponent of the worst-case type-II error probability as n tends to infinity, assuming the number of sensors in each group is proportional to n. Finally, we generalize our result to find the collection of all achievable type-I and type-II error exponents, where the boundary of the region can be obtained by solving a convex program. Our results elucidate the price of anonymity in heterogeneous distributed detection, and can be extended to M-ary hypothesis testing with heterogeneous observations generated according to hidden latent variables. The results are also applied to distributed detection under Byzantine attacks, which hints that the conventional approach based on simple hypothesis testing might be too pessimistic.

cs.IT↗

arXiv2015

Energy-Efficient Deterministic Adaptive Beamforming Algorithms for Distributed Sensor/Relay Networks

In this study, energy-efficient deterministic adaptive beamforming algorithms are proposed for distributed sensor/relay networks. Specifically, DBSA, D-QESA, D-QESA-E, and a hybrid algorithm, hybrid-QESA, that combines the benefits of both deterministic and random adaptive beamforming algorithms, are proposed. Rigorous convergence analyses are provided for all our proposed algorithms and convergence to the global optimal solution is shown for all our proposed algorithms. Through extensive numerical simulations, we demonstrate that superior performance is achieved by our proposed DBSA and D-QESA over random adaptive beamforming algorithms for static channels. Surprisingly, D-QESA is also more robust against random node removal than random adaptive beamforming algorithms. For time-varying channels, hybrid-QESA indeed achieves the best performance since it combines the benefits of both types of adaptive beamforming algorithms. In summary, our proposed deterministic algorithms demonstrate superior performance both in terms of convergence time and robustness against channel and network uncertainties.

cs.IT↗