8 research outputs found
Sublinear-Time Algorithms for Compressive Phase Retrieval
In the compressive phase retrieval problem, or phaseless compressed sensing,
or compressed sensing from intensity only measurements, the goal is to
reconstruct a sparse or approximately -sparse vector
given access to , where denotes the vector obtained from
taking the absolute value of coordinate-wise. In this paper
we present sublinear-time algorithms for different variants of the compressive
phase retrieval problem which are akin to the variants considered for the
classical compressive sensing problem in theoretical computer science. Our
algorithms use pure combinatorial techniques and near-optimal number of
measurements.Comment: The ell_2/ell_2 algorithm was substituted by a modification of the
ell_infty/ell_2 algorithm which strictly subsumes i
Improved Algorithms for Adaptive Compressed Sensing
In the problem of adaptive compressed sensing, one wants to estimate an approximately k-sparse vector x in R^n from m linear measurements A_1 x, A_2 x,..., A_m x, where A_i can be chosen based on the outcomes A_1 x,..., A_{i-1} x of previous measurements. The goal is to output a vector x^ for which |x-x^|_p 0 is an approximation factor. Indyk, Price and Woodruff (FOCS\u2711) gave an algorithm for p=q=2 for C = 1+epsilon with O((k/epsilon) loglog (n/k)) measurements and O(log^*(k) loglog (n)) rounds of adaptivity. We first improve their bounds, obtaining a scheme with O(k * loglog (n/k) + (k/epsilon) * loglog(1/epsilon)) measurements and O(log^*(k) loglog (n)) rounds, as well as a scheme with O((k/epsilon) * loglog (n log (n/k))) measurements and an optimal O(loglog (n)) rounds. We then provide novel adaptive compressed sensing schemes with improved bounds for (p,p) for every 0 < p < 2. We show that the improvement from O(k log(n/k)) measurements to O(k log log (n/k)) measurements in the adaptive setting can persist with a better epsilon-dependence for other values of p and q. For example, when (p,q) = (1,1), we obtain O(k/sqrt{epsilon} * log log n log^3 (1/epsilon)) measurements. We obtain nearly matching lower bounds, showing our algorithms are close to optimal. Along the way, we also obtain the first nearly-optimal bounds for (p,p) schemes for every 0 < p < 2 even in the non-adaptive setting
InstaHide: Instance-hiding Schemes for Private Distributed Learning
How can multiple distributed entities collaboratively train a shared deep net
on their private data while preserving privacy? This paper introduces
InstaHide, a simple encryption of training images, which can be plugged into
existing distributed deep learning pipelines. The encryption is efficient and
applying it during training has minor effect on test accuracy.
InstaHide encrypts each training image with a "one-time secret key" which
consists of mixing a number of randomly chosen images and applying a random
pixel-wise mask. Other contributions of this paper include: (a) Using a large
public dataset (e.g. ImageNet) for mixing during its encryption, which improves
security. (b) Experimental results to show effectiveness in preserving privacy
against known attacks with only minor effects on accuracy. (c) Theoretical
analysis showing that successfully attacking privacy requires attackers to
solve a difficult computational problem. (d) Demonstrating that use of the
pixel-wise mask is important for security, since Mixup alone is shown to be
insecure to some some efficient attacks. (e) Release of a challenge dataset
https://github.com/Hazelsuko07/InstaHide_Challenge
Our code is available at https://github.com/Hazelsuko07/InstaHideComment: ICML 202
Sublinear-time algorithms for compressive phase retrieval
In the compressive phase retrieval problem, the goal is to reconstruct a sparse or approximately k-sparse vector x ∈ R n given access to y = |Φ x |, where |v| denotes the vector obtained from taking the absolute value of v ∈ R n coordinatewise. In this paper we present sublinear-time algorithms for different variants of the compressive phase retrieval problem which are akin to the variants of the classical compressive sensing problem considered in theoretical computer science. Our algorithms use pure combinatorial techniques and achieve almost optimal number of measurements