Abstract: Cross-correlations between the Cosmic Microwave Background (CMB) and the large-scale structure (LSS) of the Universe provide a powerful avenue for extracting cosmological information. This thesis develops new statistical and machine-learning methods for analyzing CMB×LSS cross-correlations more efficiently, with a particular focus on the kinetic Sunyaev--Zel'dovich (kSZ) effect and local primordial non-Gaussianity. I introduce an optimal Bayesian framework for cosmic velocity reconstruction based on autodifferentiable likelihoods. I then present machine-learning methods for modeling the electron distribution and for estimating non-Gaussianity from LSS surveys. In addition, I develop an optimal method for large-scale power spectrum estimation in tomographic redshift surveys. I conclude by discussing how these methods can be combined to achieve state-of-the-art precision in constraining primordial non-Gaussianity using data from current CMB and LSS surveys