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: Generative models that can model and predict sequences of future events can, in principle, learn to capture complex real-world phenomena, such as physical interactions. However, a central challenge in video prediction is that the future is highly uncertain: a sequence of past observations of events can imply many possible futures. Although a number of recent works have studied probabilistic models that can represent uncertain futures, such models are either extremely expensive computationally as in the case of pixel-level autoregressive models, or do not directly optimize the likelihood of the data. To our knowledge, our work is the first to propose multi-frame video prediction with normalizing flows, which allows for direct optimization of the data likelihood, and produces high-quality stochastic predictions. We describe an approach for modeling the latent space dynamics, and demonstrate that flow-based generative models offer a viable and competitive approach to generative modeling of video.

SOLUTION: We demonstrate that flow-based generative models offer a viable and competitive approach to generative modeling of video.

PROBLEM: We address the challenging problem of deep representation learning--the efficient adaption of a pre-trained deep network to different tasks. Specifically, we propose to explore gradient-based features. These features are gradients of the model parameters with respect to a task-specific loss given an input sample. Our key innovation is the design of a linear model that incorporates both gradient features and the activation of the network. We show that our model provides a local linear approximation to a underlying deep model, and discuss important theoretical insight. Moreover, we present an efficient algorithm for the training and inference of our model without computing the actual gradients. Our method is evaluated across a number of representation learning tasks on several datasets and using different network architectures. We demonstrate strong results in all settings. And our results are well-aligned with our theoretical insight.

SOLUTION: Given a pre-trained model, we explored the per-sample gradients of the model parameters relative to a task-specific loss, and constructed a linear model that combines gradients of model parameters and the activation of the model.

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, Holt–Winters, 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.