Tutorial: Deep Generative Model for Inference

Introduction Generative model in estimation and inference problems The problem of generation and conditional generation Overview of neural network methods Mathematical background Partial differential equation (PDE) Stochastic differential equation (SDE) Langevin dynamics Continuity equation Samplers Diffusion model and ODE flow SDE and ODE approaches for normalizing flow Score matching Fokker Planck Equation and Transport Equation Deterministic and random backward process sampler Score-based and flow-based forward process Wasserstein gradient flow by flow network Neural ODE and continuous normalizing flow (CNF) From ResNet to CNF Computation of the exact likelihood The computational challenges in high-dimension Learning of interpolating distributions The problem of distribution interpolation from data Learning of dynamic Optimal Transport flow Density ratio estimation based on flow network Evaluation of generative models Differential comparison of distributions in high-dimensions Two-sample test Goodness-of-fit test Theoretical guarantee for kernel and neural network tests Applications Image generation: MNIST, CiFar Generative model for sequence data and adversarial samplers Uncertainty quantification for graph prediction using invertible graph neural networks (GNN)