Remarkable progress has been made in increasing the complexity of quantum devices and improving their quality. Surprisingly, one of the central challenges for quantum technologies, is the search for useful applications of current quantum machines. In this talk, I will discuss how one can achieve robust quantum speedup in solving statistical inference problems by combining methods from classical machine learning and quantum computing. I will focus on two problems in particular: (i) model inference for nuclear magnetic resonance (NMR) spectroscopy, which is important for biological and medical research and (ii) Monte Carlo sampling, which forms the computational basis for unbiased Bayesian inference.