# Time Series Generative Learning with Application to Brain Imaging Analysis

arXiv: https://arxiv.org/abs/2407.14003 · HTML: https://mlsanity.com/paper/2407.14003/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 27 of its 51 references that are in the map.
- First posted on arXiv 19 Jul 2024.

## Builds on (most cited first, 27 of 27)

- [Denoising Diffusion Probabilistic Models](https://mlsanity.com/paper/2006.11239/) (2020)
- [Auto-Encoding Variational Bayes](https://mlsanity.com/paper/1312.6114/) (2013)
- [Improved Techniques for Training GANs](https://mlsanity.com/paper/1606.03498/) (2016)
- [Informer: Beyond Efficient Transformer for Long Sequence Time-Series Forecasting](https://mlsanity.com/paper/2012.07436/) (2020)
- [Modeling Long- and Short-Term Temporal Patterns with Deep Neural Networks](https://mlsanity.com/paper/1703.07015/) (2017)
- [Self-Attention Generative Adversarial Networks](https://mlsanity.com/paper/1805.08318/) (2018)
- [Enhancing the Locality and Breaking the Memory Bottleneck of Transformer on Time Series Forecasting](https://mlsanity.com/paper/1907.00235/) (2019)
- [Error bounds for approximations with deep ReLU networks](https://mlsanity.com/paper/1610.01145/) (2016)
- [f-GAN: Training Generative Neural Samplers using Variational Divergence Minimization](https://mlsanity.com/paper/1606.00709/) (2016)
- [Road Extraction by Deep Residual U-Net](https://mlsanity.com/paper/1711.10684/) (2017)
- [Deep Network Approximation for Smooth Functions](https://mlsanity.com/paper/2001.03040/) (2020)
- [Deep Network Approximation Characterized by Number of Neurons](https://mlsanity.com/paper/1906.05497/) (2019)
- [How to Construct Deep Recurrent Neural Networks](https://mlsanity.com/paper/1312.6026/) (2013)
- [SADM: Sequence-Aware Diffusion Model for Longitudinal Medical Image Generation](https://mlsanity.com/paper/2212.08228/) (2022)
- [Tucker Tensor Regression and Neuroimaging Analysis](https://mlsanity.com/paper/1304.5637/) (2013)
- [Degenerative Adversarial NeuroImage Nets: Generating Images that Mimic Disease Progression](https://mlsanity.com/paper/1907.02787/) (2019)
- [Autoregressive Models for Matrix-Valued Time Series](https://mlsanity.com/paper/1812.08916/) (2018)
- [Low-rank Tensor Estimation via Riemannian Gauss-Newton: Statistical Optimality and Second-Order Convergence](https://mlsanity.com/paper/2104.12031/) (2021)
- [Scalar-on-Image Regression via the Soft-Thresholded Gaussian Process](https://mlsanity.com/paper/1604.03192/) (2016)
- [Testing for the Markov Property in Time Series via Deep Conditional Generative Learning](https://mlsanity.com/paper/2305.19244/) (2023)
- [Inferential Wasserstein Generative Adversarial Networks](https://mlsanity.com/paper/2109.05652/) (2021)
- [Adversarial Counterfactual Augmentation: Application in Alzheimer's Disease Classification](https://mlsanity.com/paper/2203.07815/) (2022)
- [High Dimensional and Banded Vector Autoregressions](https://mlsanity.com/paper/1502.07831/) (2015)
- [Simultaneous Decorrelation of Matrix Time Series](https://mlsanity.com/paper/2103.09411/) (2021)
- [Modelling matrix time series via a tensor CP-decomposition](https://mlsanity.com/paper/2112.15423/) (2021)
- [Sparse Kronecker Product Decomposition: A General Framework of Signal Region Detection in Image Regression](https://mlsanity.com/paper/2210.09128/) (2022)
- [Deep Kronecker Network](https://mlsanity.com/paper/2210.13327/) (2022)

## Abstract (arXiv)

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.