We present a neural net algorithm for parameter estimation in the context of large cosmological data sets. Cosmological data sets present a particular challenge to pattern-recognition algorithms since the input patterns (galaxy redshift surveys, maps of cosmic microwave background anisotropy) are not fixed templates overlaid with random noise, but rather are random realizations whose information ... [Show full abstract] content lies in the correlations between data points. We train a ``committee'' of neural nets to distinguish between Monte Carlo simulations at fixed parameter values. Sampling the trained networks using additional Monte Carlo simulations generated at intermediate parameter values allows accurate interpolation to parameter values for which the networks were never trained. The Monte Carlo samples automatically provide the probability distributions and truth tables required for either a frequentist or Bayseian analysis of the one observable sky. We demonstrate that neural networks provide unbiased parameter estimation with comparable precision as maximum-likelihood algorithms but significant computational savings. In the context of CMB anisotropies, the computational cost for parameter estimation via neural networks scales as N3/2. The results are insensitive to the noise levels and sampling schemes typical of large cosmological data sets and provide a desirable tool for the new generation of large, complex data sets.