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Revisiting Differentially Private Regression: Lessons From Learning Theory and their Consequences
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Abstract: Private regression has received attention from both database and security
communities. Recent work by Fredrikson et al. (USENIX Security 2014) analyzed
the functional mechanism (Zhang et al. VLDB 2012) for training linear
regression models over medical data. Unfortunately, they found that model
accuracy is already unacceptable with differential privacy when $\varepsilon =
5$. We address this issue, presenting an explicit connection between
differential privacy and stable learning theory through which a ...
1
Entering edit mode
8 months ago
FrankS
▴
55
I am trying to implement algorithm 2 and would like to know a simple way to randomly sample points from the unit sphere in d-dimensional Euclidean space which I can code up in python.
2
Entering edit mode
8 months ago
Andy
46
Use a distibution that's symmetric around the origin and normalize the results so they lie on the sphere. E.g. you can use a Gaussian. Here's some code.
def sample_sphere_uniformly(d, n_samples):
"""Sample uniformly from d-sphere.
Args:
d: dimension of sphere
n: number of sample points to generate
Returns:
array of shape (n, d+1)
"""
import numpy as np
x = np.random.normal(0, 1, (n_samples, d+1))
return x / np.linalg.norm(x, axis=1, keepdims=True)
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