Spectral Norm of Random Kernel Matrices with Applications to Privacy

Kernel methods are an extremely popular set of techniques used for many important machine learning and data analysis applications. In addition to having good practical performance, these methods are supported by a well-developed theory. Kernel methods use an implicit mapping of the input data into a high dimensional feature space defined by a kernel function, i.e., a function returning the inner product between the images of two data points in the feature space. Central to any kernel method is the kernel matrix, which is built by evaluating the kernel function on a given sample dataset. In this paper, we initiate the study of non-asymptotic spectral theory of random kernel matrices. These are n × n random matrices whose (i, j)th entry is obtained by evaluating the kernel function on xi and xj, where x1, . . . , xn are a set of n independent random high-dimensional vectors. Our main contribution is to obtain tight upper bounds on the spectral norm (largest eigenvalue) of random kerne...

• Type: Journal
• Year: 2015
• Where: APPROX
• Authors: Shiva Prasad Kasiviswanathan, Mark Rudelson
• Keywords: Algorithms, APPROX 2015