In scientific time series, observed variables typically have physical meaning, such as distances between residues in an RNA molecule or indices of climate phenomena. However, the latent factors driving these variables are often unknown, and discovering them is critical for understanding mechanisms. Existing methods either find latent factors without interpretation or interpret observed variables without identifiability guarantees. MOSAIC bridges this gap by transferring interpretability from observations to the latent space.
MOSAIC uses a two-stage training procedure. In the first stage, a variational autoencoder with a regime-conditioned temporal prior identifies latent factors. In the second stage, the dense decoder is replaced by an additive sparse decoder that, for each latent factor, recovers a small set of associated observed variables. Sparsity is achieved via entropy regularization on the normalized columns of the influence matrix. A parallel transition prior speeds up computations by more than 277 times.
MOSAIC outperforms all baseline methods on a synthetic benchmark: average Matthews correlation coefficient (MCC) of 0.912 and support recovery accuracy XZ@top3 of 0.978. On RNA molecular dynamics, the method localizes a regime-associated factor to the tetraloop, consistent with the known folding mechanism. In cross-domain experiments, MOSAIC correctly identifies expected variable groups in 12 out of 12 runs on solar wind, climate, chemical processes, and tokamak.
MOSAIC demonstrates that identifiable latent factors can be endowed with scientific interpretation through sparse connections to observed variables. This paves the way for automated discovery of mechanisms in complex systems where manual annotation is infeasible. Theoretical identifiability guarantees for the support of main effects hold even under non-additive mixing.
Future research could extend MOSAIC to multi-class regimes and joint analysis of multiple contrasts. Integrating the method with pairwise causal discovery tools to analyze connections within modules is also promising. Improving finite-sample guarantees for entropy regularization remains an open theoretical challenge.
MOSAIC can be applied in space weather, fusion diagnostics, climate monitoring, and chemical process safety.
Plans include adapting MOSAIC for multi-class regimes and integrating with causal discovery methods within modules.
In machine learning, the interpretability of latent representations remains an open problem. MOSAIC contributes by linking identifiable latent factors to observed variables through sparse additive models, partially addressing the issue of post-hoc interpretation.
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What the work does
The paper introduces MOSAIC, a method for extracting interpretable latent factors from multivariate time series. It combines identifiable causal representation learning with a sparse additive decoder, linking latent factors to small groups of observed variables. The method is validated on RNA molecular dynamics, solar wind, climate data, and industrial processes, where it recovers meaningful modules and outperforms baseline approaches.
Where its strength is
The strength of the work lies in shifting interpretability from observed variables to the latent space with guarantees on the identifiability of the support of main effects. This provides a rigorous foundation for automated discovery of mechanisms in complex systems.
Where it could go next
Worth trying
Nearby works in our archive
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The parallel transition prior accelerated training from 65 hours to 90 minutes on the synthetic benchmark.