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2021-05-05
Elvira, Clément, Herzet, Cédric.  2020.  Short and Squeezed: Accelerating the Computation of Antisparse Representations with Safe Squeezing. ICASSP 2020 - 2020 IEEE International Conference on Acoustics, Speech and Signal Processing (ICASSP). :5615—5619.
Antisparse coding aims at spreading the information uniformly over representation coefficients and can be expressed as the solution of an ℓ∞-norm regularized problem. In this paper, we propose a new methodology, coined "safe squeezing", accelerating the computation of antisparse representations. The idea consists in identifying saturated entries of the solution via simple tests and compacting their contribution to achieve some form of dimensionality reduction. Numerical experiments show that the proposed approach leads to significant computational gain.
2017-10-10
Yuan, Ganzhao, Yang, Yin, Zhang, Zhenjie, Hao, Zhifeng.  2016.  Convex Optimization for Linear Query Processing Under Approximate Differential Privacy. Proceedings of the 22Nd ACM SIGKDD International Conference on Knowledge Discovery and Data Mining. :2005–2014.

Differential privacy enables organizations to collect accurate aggregates over sensitive data with strong, rigorous guarantees on individuals' privacy. Previous work has found that under differential privacy, computing multiple correlated aggregates as a batch, using an appropriate strategy, may yield higher accuracy than computing each of them independently. However, finding the best strategy that maximizes result accuracy is non-trivial, as it involves solving a complex constrained optimization program that appears to be non-convex. Hence, in the past much effort has been devoted in solving this non-convex optimization program. Existing approaches include various sophisticated heuristics and expensive numerical solutions. None of them, however, guarantees to find the optimal solution of this optimization problem. This paper points out that under (ε, ཬ)-differential privacy, the optimal solution of the above constrained optimization problem in search of a suitable strategy can be found, rather surprisingly, by solving a simple and elegant convex optimization program. Then, we propose an efficient algorithm based on Newton's method, which we prove to always converge to the optimal solution with linear global convergence rate and quadratic local convergence rate. Empirical evaluations demonstrate the accuracy and efficiency of the proposed solution.