Experimental efforts of the last few decades have brought a golden age to mankind's endeavor to understand tine physical properties of the Universe throughout its history. Recent measurements of the cosmic microwave background (CMB) provide strong confirmation of the standard big bang paradigm, as well as introducing new mysteries, to unexplained by current physical models. In the following decades, even more ambitious scientific endeavours will begin to shed light on the new physics by looking at the detailed structure of the Universe both at very early and recent times. Modern data has allowed us to begins to test inflationary models of the early Universe, and the near future will bring higher precision data and much stronger tests.

Cracking the codes hidden in these cosmological observables is a difficult and computationally intensive problem. The challenges will continue to increase as future experiments bring larger and more precise data sets. Because of the complexity of the problem, we are forced to use approximate techniques and make simplifying assumptions to ease the computational workload. While this has been reasonably sufficient until now, hints of the limitations of our techniques have begun to come to light. For example, the likelihood approximation used for analysis of CMB data from the Wilkinson Microwave Anistropy Probe (WMAP) satellite was shown to have short falls, leading to pre-emptive conclusions drawn about current cosmological theories. Also it can be shown that an approximate method used by all current analysis codes to describe the recombination history of the Universe will not be sufficiently accurate for future experiments. With a new CMB satellite scheduled for launch in the coming months, it is vital that we develop techniques to improve the analysis of cosmological data. This work develops a novel technique of both avoiding the use of approximate computational codes as well as allowing the application of new, more precise analysis methods. These techniques will help in the understanding of new physics contained in current and future data sets as well as benefit the research efforts of the cosmology community.

Our idea is to shift the computationally intensive pieces of the parameter estimation framework to a parallel training step. We then provide a machine learning code that uses this training set to learn the relationship between the underlying cosmological parameters and the function we wish to compute. This code is very accurate and simple to evaluate. It can provide incredible speed-ups of parameter estimation codes. For some applications this provides the convenience of obtaining results faster, while in other cases this allows the use of codes that would be impossible to apply in the brute force setting. In this thesis we provide several examples where our method allows more accurate computation of functions important for data analysis than is currently possible. As the techniques developed in this work are very general, there are no doubt a wide array of applications both inside and outside of cosmology. We have already seen this interest as other scientists have presented ideas for using our algorithm to improve their computational work, indicating its importance as modern experiments push forward. In fact, our algorithm will play an important role in the parameter analysis of Planck, the next generation CMB space mission.