Efficient and Accurate Analysis of Two Classes of Transparent Generative Models

While widely used, generative models pose the challenging task of deriving and analyzing their underlying distribution. In this thesis, we focus on two classes of transparent genera- tive models and present new methods to tackle this task. Markov Population Processes use Continuous Time Markov Chains to describe the evolution of populations over time. Their analysis is often hindered by state-space explosion, tack- led with deterministic approximation or truncation techniques. We propose a method, Dynamic Boundary Projection, that couples an exact stochastic description of a subset of states and a deterministic approximation that dynamically shifts the subset across the state space. The resulting finite set of ODEs is asymptotically exact. We show that our method performs well in terms of accuracy and runtimes on challenging sys- tems. We also propose an extension that further reduces the number of equations while maintaining good accuracy. Probabilistic Programs leverage the power of programming languages to define probabilistic models; however, no one- fit-for-all solution exists to derive the posterior distribution. We define a family of approximating semantics, Gaussian Se- mantics, that leverages moment-matching and the approxi- mation power of Gaussian Mixtures to approximate the joint probability distribution over program variables. As the num- ber of the moments matched increases, Gaussian Semantics tends to the exact semantics. We implement an instance of Gaussian Semantics that matches the first two order moments and show that our implementation performs competitively with respect to other state-of-the-art inference methods and excellently on two classes of models taken from the literature.