The Curse of Dimensionality for Local Kernel Machines

Consider an infinite sequence of equal mass m indexed by n in Z (each mass representing an atom)... Conclude that E(t) ≤ Ce −γt E(0) for any solution y(x, t) of the damped

It will be said, that a conclusion ought not to be drawn from the unthinking conduct of the great majority of an aristocratical body, against the capability of such a body for

One could clearly hope for stronger results, but the above are already strong indications that when the data lie on a high-dimensional and curved manifold, local learning methods

One might ask whether there are infinitely many primes in a given arithmetic progression; and since the arithmetic progression a (mod q) can be viewed as the values of the polynomial

In some applications (such as the one here), it suffices to bound the error term in the prime number theorem for the arithmetic progression a (mod q), averaging over q, for one

Conversely, it is easy to check that the latter condition implies that T a is bounded.. Moreover Λ is composed of eigenvalues λ associated with finite dimensional vector

We present a series of theoretical arguments supporting the claim that a large class of modern learning algorithms that rely solely on the smooth- ness prior – with similarity

A number of semi- supervised learning algorithms are based on the idea of propagating labels on the nodes of a neighbor- hood graph, starting from known labels, until some conver-