This paper focuses on the analysis of sequential image data, particularly
brain imaging data such as MRI, fMRI, CT, with the motivation of understanding
the brain aging process and neurodegenerative diseases. To achieve this goal,
we investigate image generation in a time series context. Specifically, we
formulate a min-max problem derived from the $f$-divergence between neighboring
pairs to learn a time series generator in a nonparametric manner. The generator
enables us to generate future images by transforming prior lag-k observations
and a random vector from a reference distribution. With a deep neural network
learned generator, we prove that the joint distribution of the generated
sequence converges to the latent truth under a Markov and a conditional
invariance condition. Furthermore, we extend our generation mechanism to a
panel data scenario to accommodate multiple samples. The effectiveness of our
mechanism is evaluated by generating real brain MRI sequences from the
Alzheimer's Disease Neuroimaging Initiative. These generated image sequences
can be used as data augmentation to enhance the performance of further
downstream tasks, such as Alzheimer's disease detection.

本研究聚焦于分析顺序图像数据，特别是脑成像数据如 MRI、fMRI、CT，目的是理解脑衰老过程和神经退行性疾病。通过在时间序列环境中进行图像生成，我们制定了一个最小 - 最大问题，从相邻对之间的 $f$- 散度中学习非参数化的时间序列生成器。生成器能够通过转换先前的 k 步观察和来自参考分布的随机向量生成未来图像。通过深度神经网络学习生成器，我们证明了生成序列的联合分布在马尔可夫和条件不变性条件下收敛于潜在真实分布。此外，我们将生成机制扩展到面板数据场景以适应多个样本。通过从阿尔茨海默病神经影像计划生成真实脑部 MRI 序列来评估我们的机制有效性，这些生成的图像序列可以用作数据增强，增强后续任务（如阿尔茨海默病检测）的性能。

时间序列生成学习在脑成像分析中的应用

Time Series Generative Learning with Application to Brain Imaging  Analysis

Real-world data can be multimodal distributed, e.g., data describing the
opinion divergence in a community, the interspike interval distribution of
neurons, and the oscillators natural frequencies. Generating multimodal
distributed real-world data has become a challenge to existing generative
adversarial networks (GANs). For example, neural stochastic differential
equations (Neural SDEs), treated as infinite-dimensional GANs, have
demonstrated successful performance mainly in generating unimodal time series
data. In this paper, we propose a novel time series generator, named directed
chain GANs (DC-GANs), which inserts a time series dataset (called a
neighborhood process of the directed chain or input) into the drift and
diffusion coefficients of the directed chain SDEs with distributional
constraints. DC-GANs can generate new time series of the same distribution as
the neighborhood process, and the neighborhood process will provide the key
step in learning and generating multimodal distributed time series. The
proposed DC-GANs are examined on four datasets, including two stochastic models
from social sciences and computational neuroscience, and two real-world
datasets on stock prices and energy consumption. To our best knowledge, DC-GANs
are the first work that can generate multimodal time series data and
consistently outperforms state-of-the-art benchmarks with respect to measures
of distribution, data similarity, and predictive ability.

本文提出了一种新的时间序列生成器 —— 指向连锁 GAN（DC-GANs），该生成器可以生成与邻域过程具有相同分布的新时间序列，并且可以在生成多模态时间序列方面显着优于现有最佳方法。