3,505 research outputs found
Secure -ish Nearest Neighbors Classifier
In machine learning, classifiers are used to predict a class of a given query
based on an existing (classified) database. Given a database S of n
d-dimensional points and a d-dimensional query q, the k-nearest neighbors (kNN)
classifier assigns q with the majority class of its k nearest neighbors in S.
In the secure version of kNN, S and q are owned by two different parties that
do not want to share their data. Unfortunately, all known solutions for secure
kNN either require a large communication complexity between the parties, or are
very inefficient to run.
In this work we present a classifier based on kNN, that can be implemented
efficiently with homomorphic encryption (HE). The efficiency of our classifier
comes from a relaxation we make on kNN, where we allow it to consider kappa
nearest neighbors for kappa ~ k with some probability. We therefore call our
classifier k-ish Nearest Neighbors (k-ish NN).
The success probability of our solution depends on the distribution of the
distances from q to S and increase as its statistical distance to Gaussian
decrease.
To implement our classifier we introduce the concept of double-blinded
coin-toss. In a doubly-blinded coin-toss the success probability as well as the
output of the toss are encrypted. We use this coin-toss to efficiently
approximate the average and variance of the distances from q to S. We believe
these two techniques may be of independent interest.
When implemented with HE, the k-ish NN has a circuit depth that is
independent of n, therefore making it scalable. We also implemented our
classifier in an open source library based on HELib and tested it on a breast
tumor database. The accuracy of our classifier (F_1 score) were 98\% and
classification took less than 3 hours compared to (estimated) weeks in current
HE implementations
Momentum dependent light scattering in insulating cuprates
We investigate the problem of inelastic x-ray scattering in the spin
Heisenberg model on the square lattice. We first derive a momentum dependent
scattering operator for the and polarization geometries. On
the basis of a spin-wave analysis, including magnon-magnon interactions and
exact-diagonalizations, we determine the qualitative shape of the spectra. We
argue that our results may be relevant to help interpret inelastic x-ray
scattering experiments in the antiferromagnetic phase of the cuprates.Comment: 5 pages, 3 figures, to appear in PR
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