Variational Sampling of Temporal Trajectories

TL;DR

This paper introduces a novel approach to learn and sample from the distribution of trajectories in temporal processes by explicitly parameterizing the transition function within a function space, enabling efficient trajectory synthesis and inference.

Contribution

It proposes a new method that parameterizes the transition function as a function space element, facilitating trajectory sampling and statistical inference in neural network models.

Findings

Enables efficient synthesis of novel trajectories.

Provides tools for uncertainty estimation and out-of-distribution detection.

Facilitates likelihood evaluation for temporal trajectories.

Abstract

A deterministic temporal process can be determined by its trajectory, an element in the product space of (a) initial condition $z_0 \in \mathcal{Z}$ and (b) transition function $f: (\mathcal{Z}, \mathcal{T}) \to \mathcal{Z}$ 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.