Meta-iLaD: Identifiable Latent Dynamics via Meta-Learning of Dynamics Environments

摘要

Learning *latent dynamics* is central to assessing current states and forecasting future trajectories for high-dimensional time series. For locally-stationary latent dynamics of the form $\mathcal{F}(\mathbf{z}_{<t}; \mathbf{c})$ with latent dynamics state $\mathbf{z}_t$ and environment variable $\mathbf{c}$, prior identifiability results largely focus on $\mathbf{z}_t$ when conditioned on pre-defined label $u$ of the dynamics environment. This leaves two limitations: reliance on pre-defined labels that hinder generalization to unseen environments, and limited understanding of the identifiability of $\mathcal{F}$ and $\mathbf{c}$ which---while offering important structural properties for the identifiabilty of $\mathbf{z}_t$---are learned jointly with $\mathbf{z}_t$. We address these challenges with Meta-iLaD, a novel latent dynamics framework to attain identifiability by meta-learning across dynamics environments. Meta-iLad replaces the conditioning of $\mathbf{c}$ on pre-defined labels with a novel condition prior, modeled as a feedforward meta-learner that rapidly extracts $\mathbf{c}$ from few-shot examples. We further establish simultaneous identifiability for $\mathbf{z}\_t$, $\mathbf{c}$ and $\mathcal{F}$, for a general formulation of $\mathcal{F}(\mathbf{z}\_{< t};\mathbf{c})$ without restricting the dimension of $\mathbf{c}$ or how it modulates $\mathcal{F}$. 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.