Learning from Infinite Data in Finite Time

We propose the following general method for scaling learning algorithms to arbitrarily large data sets. Upper-bound the loss L(Mii' M oo) between them as a function of ii, and then minimize the algorithm's time complexity f(ii) subject to the constraint that L(Moo, Mii) be at most f with probability at most 8. We apply this method to the EM algorithm for mixtures of Gaussians. Preliminary experiments on a series of large data sets provide evidence of the potential of this approach. On the other hand, they require large computational resources to learn from.