On InstaHide, Phase Retrieval, and Sparse Matrix Factorization
In this work, we examine the security of InstaHide, a scheme recently proposed by [Huang, Song, Li and Arora, ICML'20] for preserving the security of private datasets in the context of distributed learning. To generate a synthetic training example to be shared among the distributed learners, InstaHide takes a convex combination of private feature vectors and randomly flips the sign of each entry of the resulting vector with probability 1/2. A salient question is whether this scheme is secure in any provable sense, perhaps under a plausible hardness assumption and assuming the distributions generating the public and private data satisfy certain properties. We show that the answer to this appears to be quite subtle and closely related to the average-case complexity of a new multi-task, missing-data version of the classic problem of phase retrieval. Motivated by this connection, we design a provable algorithm that can recover private vectors using only the public vectors and synthetic vectors generated by InstaHide, under the assumption that the private and public vectors are isotropic Gaussian.
Code (0)
등록된 구현이 없습니다.
Tasks
RetrievalSimilar Papers 제목 키워드 기반
Provable Burer-Monteiro factorization for a class of norm-constrained matrix problems
We study the projected gradient descent method on low-rank matrix problems with a strongly convex objective. We use the Burer-Monteiro factorization approach to implicitly enforce low-rankness; such factorization introdu…
LEMMAQuantum State TomographyRetrievalWhat Can Phase Retrieval Tell Us About Private Distributed Learning?
In this work, we examine the security of InstaHide, a scheme recently proposed by \cite{hsla20} for preserving the security of private datasets in the context of distributed learning. To generate a synthetic training exa…
RetrievalDictionary Learning Phase Retrieval from Noisy Diffraction Patterns
This paper proposes a novel algorithm for image phase retrieval, i.e., for recovering complex-valued images from the amplitudes of noisy linear combinations (often the Fourier transform) of the sought complex images. The…
Dictionary LearningregressionRetrievalSymmetry, Saddle Points, and Global Optimization Landscape of Nonconvex Matrix Factorization
We propose a general theory for studying the \xl{landscape} of nonconvex \xl{optimization} with underlying symmetric structures \tz{for a class of machine learning problems (e.g., low-rank matrix factorization, phase ret…
global-optimizationRetrievalApproximate Method of Variational Bayesian Matrix Factorization/Completion with Sparse Prior
We derive analytical expression of matrix factorization/completion solution by variational Bayes method, under the assumption that observed matrix is originally the product of low-rank dense and sparse matrices with addi…
Matrix Completion