  We describe a novel end-to-end approach using Machine Learning to reconstruct
the power spectrum of cosmological density perturbations at high redshift from
observed quasar spectra. State-of-the-art cosmological simulations of structure
formation are used to generate a large synthetic dataset of line-of-sight
absorption spectra paired with 1-dimensional fluid quantities along the same
line-of-sight, such as the total density of matter and the density of neutral
atomic hydrogen. With this dataset, we build a series of data-driven models to
predict the power spectrum of total matter density. We are able to produce
models which yield reconstruction to accuracy of about 1% for wavelengths $k
\leq 2 h Mpc^{-1}$, while the error increases at larger $k$. We show the size
of data sample required to reach a particular error rate, giving a sense of how
much data is necessary to reach a desired accuracy. This work provides a
foundation for developing methods to analyse very large upcoming datasets with
the next-generation observational facilities.
