# Variational Sampling of Temporal Trajectories

arXiv: https://arxiv.org/abs/2403.11418 · HTML: https://mlsanity.com/paper/2403.11418/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 21 of its 36 references that are in the map.
- First posted on arXiv 18 Mar 2024.

## Builds on (most cited first, 21 of 21)

- [BERT: Pre-training of Deep Bidirectional Transformers for Language Understanding](https://mlsanity.com/paper/1810.04805/) (2018)
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- [Learning Phrase Representations using RNN Encoder-Decoder for Statistical Machine Translation](https://mlsanity.com/paper/1406.1078/) (2014)
- [Neural Ordinary Differential Equations](https://mlsanity.com/paper/1806.07366/) (2018)
- [NTU RGB+D: A Large Scale Dataset for 3D Human Activity Analysis](https://mlsanity.com/paper/1604.02808/) (2016)
- [Improving Variational Inference with Inverse Autoregressive Flow](https://mlsanity.com/paper/1606.04934/) (2016)
- [NVAE: A Deep Hierarchical Variational Autoencoder](https://mlsanity.com/paper/2007.03898/) (2020)
- [Neural Controlled Differential Equations for Irregular Time Series](https://mlsanity.com/paper/2005.08926/) (2020)
- [Deep learning for universal linear embeddings of nonlinear dynamics](https://mlsanity.com/paper/1712.09707/) (2017)
- [Machine Learning for Fluid Mechanics](https://mlsanity.com/paper/1905.11075/) (2019)
- [A Recurrent Latent Variable Model for Sequential Data](https://mlsanity.com/paper/1506.02216/) (2015)
- [Variational Lossy Autoencoder](https://mlsanity.com/paper/1611.02731/) (2016)
- [Neural Stochastic Differential Equations: Deep Latent Gaussian Models in the Diffusion Limit](https://mlsanity.com/paper/1905.09883/) (2019)
- [Neural Rough Differential Equations for Long Time Series](https://mlsanity.com/paper/2009.08295/) (2020)
- [Bayesian Neural Networks: An Introduction and Survey](https://mlsanity.com/paper/2006.12024/) (2020)
- [Semantic Video Segmentation by Gated Recurrent Flow Propagation](https://mlsanity.com/paper/1612.08871/) (2016)
- [Efficient Variational Inference for Sparse Deep Learning with Theoretical Guarantee](https://mlsanity.com/paper/2011.07439/) (2020)
- [Improving Explorability in Variational Inference with Annealed Variational Objectives](https://mlsanity.com/paper/1809.01818/) (2018)
- [An Adaptive Empirical Bayesian Method for Sparse Deep Learning](https://mlsanity.com/paper/1910.10791/) (2019)
- [Bayesian inference for diffusion driven mixed-effects models](https://mlsanity.com/paper/1507.06807/) (2015)
- [Inferring Multidimensional Rates of Aging from Cross-Sectional Data](https://mlsanity.com/paper/1807.04709/) (2018)

## Abstract (arXiv)

A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition z0 ∈ Z and (b) transition function f: (Z, T) → Z often influenced by the control of the underlying dynamical system. Existing methods often model the transition function as a differential equation or as a recurrent neural network. Despite their effectiveness in predicting future measurements, few results have successfully established a method for sampling and statistical inference of trajectories using neural networks, partially due to constraints in the parameterization. In this work, we introduce a mechanism to learn the distribution of trajectories by parameterizing the transition function f explicitly as an element in a function space. Our framework allows efficient synthesis of novel trajectories, while also directly providing a convenient tool for inference, i.e., uncertainty estimation, likelihood evaluations and out of distribution detection for abnormal trajectories. These capabilities can have implications for various downstream tasks, e.g., simulation and evaluation for reinforcement learning.