Explore a comprehensive lecture on obtaining compact representations of excited states from Quantum Monte Carlo (QMC) and their application in low-energy models. Delve into the advantages of variational Monte Carlo, various wave function ansatze, and the challenges of describing excited states. Learn about a novel penalty method for optimizing orbital, determinant, and Jastrow parameters independently for each state. Discover the density matrix downfolding technique for summarizing discrete excited states into effective models and interpolating QMC results to compute full spectra. Examine case studies including the hydrogen chain and bonzone molecule, and understand the fundamental principles behind model determination in quantum mechanics.