TASK DEFINITION: In this task, you are given the abstract of a research paper. Your task is to generate a summary of this abstract. Your summary should not be very short, but it's better if it's not more than 30 words.
PROBLEM: We present a deep generative model, named Monge-Amp\'ere flow, which builds on continuous-time gradient flow arising from the Monge-Amp\'ere equation in optimal transport theory. The generative map from the latent space to the data space follows a dynamical system, where a learnable potential function guides a compressible fluid to flow towards the target density distribution. Training of the model amounts to solving an optimal control problem. The Monge-Amp\'ere flow has tractable likelihoods and supports efficient sampling and inference. One can easily impose symmetry constraints in the generative model by designing suitable scalar potential functions. We apply the approach to unsupervised density estimation of the MNIST dataset and variational calculation of the two-dimensional Ising model at the critical point. This approach brings insights and techniques from Monge-Amp\'ere equation, optimal transport, and fluid dynamics into reversible flow-based generative models.

SOLUTION: A gradient flow based dynamical system for invertible generative modeling

PROBLEM: We propose a new, multi-component energy function for energy-based Generative Adversarial Networks (GANs) based on methods from the image quality assessment literature. Our approach expands on the Boundary Equilibrium Generative Adversarial Network (BEGAN) by outlining some of the short-comings of the original energy and loss functions. We address these short-comings by incorporating an l1 score, the Gradient Magnitude Similarity score, and a chrominance score into the new energy function. We then provide a set of systematic experiments that explore its hyper-parameters. We show that each of the energy function's components is able to represent a slightly different set of features, which require their own evaluation criteria to assess whether they have been adequately learned. We show that models using the new energy function are able to produce better image representations than the BEGAN model in predicted ways.

SOLUTION: Image Quality Assessment Techniques Improve Training and Evaluation of Energy-Based Generative Adversarial Networks

PROBLEM: Time series forecasting plays a crucial role in marketing, finance and many other quantitative fields. A large amount of methodologies has been developed on this topic, including ARIMA, HoltWinters, etc. However, their performance is easily undermined by the existence of change points and anomaly points, two structures commonly observed in real data, but rarely considered in the aforementioned methods. In this paper, we propose a novel state space time series model, with the capability to capture the structure of change points and anomaly points, as well as trend and seasonality. To infer all the hidden variables, we develop a Bayesian framework, which is able to obtain distributions and forecasting intervals for time series forecasting, with provable theoretical properties. For implementation, an iterative algorithm with Markov chain Monte Carlo (MCMC), Kalman filter and Kalman smoothing is proposed. In both synthetic data and real data applications, our methodology yields a better performance in time series forecasting compared with existing methods, along with more accurate change point detection and anomaly detection.

SOLUTION:
We propose a novel state space time series model with the capability to capture the structure of change points and anomaly points, so that it has a better forecasting performance when there exist change points and anomalies in the time series.