Digital presence in the world of online social media entails significant privacy risks [31, 56]. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i.e., commute times) or personalized PageRank scores. Using these similarities, the attacker seeks to infer as much information as possible about the network, including unknown pairwise node similarities and edges. For the effective resistance metric, we show that with just a small subset of measurements, one can learn a large fraction of edges in a social network. We also show that it is possible to learn a graph which accurately matches the underlying network on all other effective resistances.

Neural Information Processing Systems http://nips.cc/

We give the first algorithm for kernel Nyström approximation that runs in linear time in the number of training points and is provably accurate for all kernel matrices, without dependence on regularity or incoherence conditions.

Low-rank approximation is a common tool used to accelerate kernel methods: the n n kernel matrix K is approximated via a rank-k matrix K which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation.

Digital presence in the world of online social media entails significant privacy risks [31, 56]. In this work we consider a privacy threat to a social network in which an attacker has access to a subset of random walk-based node similarities, such as effective resistances (i.e., commute times) or personalized PageRank scores. Using these similarities, the attacker seeks to infer as much information as possible about the network, including unknown pairwise node similarities and edges. For the effective resistance metric, we show that with just a small subset of measurements, one can learn a large fraction of edges in a social network. We also show that it is possible to learn a graph which accurately matches the underlying network on all other effective resistances.

Low-rank approximation is a common tool used to accelerate kernel methods: the n n kernel matrix K is approximated via a rank-k matrix K which can be stored in much less space and processed more quickly. In this work we study the limits of computationally efficient low-rank kernel approximation.