We have mentioned homomorphic encryption here on Nuit Blanche mostly because of Andrew McGregor et al's work on the subject (see references below). Today, we have a Machine Learning approach using this encoding strategy, which in effect is not really that far from the idea of homomorphic sketches or random projections for low dimensional manifolds. Without further ado:

A review of homomorphic encryption and software tools for encrypted statistical machine learning by Louis J. M. Aslett, Pedro M. Esperança, Chris C. Holmes

Encrypted statistical machine learning: new privacy preserving methods by Louis J. M. Aslett, Pedro M. Esperança, Chris C. Holmes

Recent advances in cryptography promise to enable secure statistical computation on encrypted data, whereby a limited set of operations can be carried out without the need to first decrypt. We review these homomorphic encryption schemes in a manner accessible to statisticians and machine learners, focusing on pertinent limitations inherent in the current state of the art. These limitations restrict the kind of statistics and machine learning algorithms which can be implemented and we review those which have been successfully applied in the literature. Finally, we document a high performance R package implementing a recent homomorphic scheme in a general framework.

Encrypted statistical machine learning: new privacy preserving methods by Louis J. M. Aslett, Pedro M. Esperança, Chris C. Holmes

We present two new statistical machine learning methods designed to learn on fully homomorphic encrypted (FHE) data. The introduction of FHE schemes following Gentry (2009) opens up the prospect of privacy preserving statistical machine learning analysis and modelling of encrypted data without compromising security constraints. We propose tailored algorithms for applying extremely random forests, involving a new cryptographic stochastic fraction estimator, and na\"{i}ve Bayes, involving a semi-parametric model for the class decision boundary, and show how they can be used to learn and predict from encrypted data. We demonstrate that these techniques perform competitively on a variety of classification data sets and provide detailed information about the computational practicalities of these and other FHE methods.An implementation in R is available here:

References:

- Videos and slides: Homomorphic Sketches: Shrinking Big Data without Sacrificing Structure

Andrew McGregor, University of Massachusetts - Homomorphic Sketches: Shrinking Big Data without Sacrificing Structure
- Slides: SPARC 2013, Coding, Complexity, and Sparsity Workshop

**Join the CompressiveSensing subreddit or the Google+ Community or the Facebook page and post there !**

Liked this entry ? subscribe to Nuit Blanche's feed, there's more where that came from. You can also subscribe to Nuit Blanche by Email, explore the Big Picture in Compressive Sensing or the Matrix Factorization Jungle and join the conversations on compressive sensing, advanced matrix factorization and calibration issues on Linkedin.

## No comments:

Post a Comment