  We present a fast, accurate, robust and flexible method of accelerating
parameter estimation. This algorithm, called Pico, can compute the CMB power
spectrum and matter transfer function as well as any computationally expensive
likelihoods in a few milliseconds. By removing these bottlenecks from parameter
estimation codes, Pico decreases their computational time by 1 or 2 orders of
magnitude. Pico has several important properties. First, it is extremely fast
and accurate over a large volume of parameter space. Furthermore, its accuracy
can continue to be improved by using a larger training set. This method is
generalizable to an arbitrary number of cosmological parameters and to any
range of l-values in multipole space. Pico is approximately 3000 times faster
than CAMB for flat models, and approximately 2000 times faster then the WMAP 3
year likelihood code. In this paper, we demonstrate that using Pico to compute
power spectra and likelihoods produces parameter posteriors that are very
similar to those using CAMB and the official WMAP3 code, but in only a fraction
of the time. Pico and an interface to CosmoMC are made publicly available at
http://www.astro.uiuc.edu/~bwandelt/pico/.
