Meta-learning approach uncovers identifiable latent dynamics for better forecasting
Meta-iLaD: Identifiable Latent Dynamics via Meta-Learning of Dynamics Environments
Machine Learning
Summary
Understanding hidden patterns in complex sequences over time helps predict what might happen next. The authors present a method called Meta-iLaD that learns these hidden patterns across different environments without needing predefined labels. This approach can quickly adapt to new situations using only a few examples, making predictions more reliable even for unfamiliar settings. Their work also ensures that the hidden states and the rules governing their change can be uniquely determined, improving accuracy in forecasting beyond copying past observations.
What this means in practice
- •For time series modelers: Develop models that can quickly adapt to new but related temporal environments using few examples for improved prediction accuracy.
- •For robotics engineers: Improve robots’ ability to predict their environment’s changes by learning identifiable hidden states from limited interaction data.
Authors
Yubo Ye, Sweekar Piya, Xiajun Jiang, Linwei Wang
Abstract
Learning latent dynamics is central to assessing the current states and forecasting the future trajectories of high-dimensional time series. For locally-stationary latent dynamics $\mathcal{F}(\mathbf{z}_{<t}; \mathbf{c})$ with latent dynamics state $\mathbf{z}_t$ and environment variable $\mathbf{c}$, prior identifiability results have largely focused on $\mathbf{z}_t$ when conditioned on predefined label $u$ of dynamics environments. This leaves two limitations: reliance on predefined labels that hinder generalization to unseen environments, and a limited understanding of the identifiability of $\mathcal{F}$ and $\mathbf{c}$ which -- although offering important structural properties for the identifiability of $\mathbf{z}_t$ -- are learned jointly with $\mathbf{z}_t$. We address these limitations with Meta-iLaD, a novel identifiable latent dynamics framework attained by meta-learning across dynamics environments. Meta-iLaD introduces a novel conditional prior of $\mathbf{c}$, modeled as a feedforward meta-learner to rapidly extract $\mathbf{c}$ from few-shot examples. Meta-iLaD further establishes identifiability for $\mathbf{z}_t$, $\mathbf{c}$, and $\mathcal{F}$ simultaneously, for a general formulation of $\mathcal{F}(\mathbf{z}_{< t};\mathbf{c})$ without restricting the dimension of $\mathbf{c}$ or how it modulates $\mathcal{F}$. On synthetic and real data, we provide strong empirical evidence that 1) conditioning on few-shot examples enables generalization to out-of-distribution environments, and 2) identifiability for $\mathbf{c}$ and $\mathcal{F}$ is critical for accurate forecasting beyond reconstructing observed trajectories. Code is available at https://github.com/GoForIt-YYB/Meta-iLaD.