Random maps

Compact Random Feature Maps

Kernel approximation using random feature maps has recently gained a lot of interest. This is mainly due to their applications in reducing training and testing times of kernel based learning algorithms. In this work, we identify that previous approaches for polynomial kernel approximation create maps that can be rank deficient, and therefore may not utilize the capacity of the projected feature...

Random Maps and Permutations

Proof Write Ck as the sum of indicator random variables 1γ , for γ a k-cycle. This means that 1γ(π) is 1 if γ is a cycle of π and 0 otherwise. Then E(Ck) = ∑ γ E(1γ). To determine E(1γ) we count the number of permutations having γ as a cycle. That number is (n− k)!. Thus, E(1γ) = (n − k)!/n!. Now, the number of possible γ is n(n − 1) · · · (n − k + 1)/k, since a k-cycle is an ordered selection ...

Random linear maps

Random Iterates of Monotone Maps

Multilinear Maps Using Random Matrix

Garg, Gentry and Halevi (GGH) described the first candidate multilinear maps using ideal lattices. However, Hu and Jia presented an efficient attack on GGH map, which breaks the GGH-based applications of multipartite key exchange (MPKE) and witness encryption (WE) based on the hardness of 3-exact cover problem. We describe a new construction of multilinear map using random matrix, which support...