gmtorch: Computing with Gaussian Mixture Uncertainty in PyTorch

Gaussian mixture models (GMMs) can represent multimodal, non-Gaussian
uncertainty while retaining analytical structure. Scientific workflows,
however, require more than fitting a mixture to observations: uncertain
quantities must remain available for subsequent transformations, arithmetic,
conditioning, and information combination. We present \textsc{gmtorch}, a
\textsc{PyTorch} framework for computing with GMM-represented uncertain scalar
and vector quantities. Mixtures may be constructed from parameters or
estimated from data; every mixture-valued result remains a complete distribution that can be
evaluated, sampled, summarized, conditioned, or used in a subsequent
calculation.
Marginalization, conditioning, affine maps, sums and differences under
independence, and normalized density products are evaluated analytically and
can be composed with assumptions made explicit by the selected operations and
with component counts tracked. When nonlinear maps leave the finite-GMM family, or exact operations
produce impractically many components, the framework provides explicit
sample--transform--refit propagation and mixture reduction. ... mehrFull-covariance
computations use Cholesky-based linear algebra and blocked pairwise kernels.
Reference checks compare exact operations with independently assembled
formulas, and a single-epoch localization example illustrates sequential
likelihood-based updating and the resulting growth in mixture components. The
contribution is a consistent software realization of
established GMM calculus, with exact and approximate steps made explicit.