Enforcing Latent Euclidean Geometry in VAEs for Statistical Manifold Interpolation
Keywords: scRNA-seq, Riemannian geometry, representation learning, trajectory inference, VAEs, statistical manifolds
TL;DR: We enforce a Euclidean latent manifold in scRNA-seq representations to improve trajectory inference.
Abstract: Latent linear interpolations are a powerful tool for navigating the representation space of deep generative models. This aspect is particularly relevant in applied settings, where meaningful latent traversals can be learnt to represent the evolution of a system's trajectory and mapped back to the often complex and high-dimensional data space. However, when data lies on a manifold with complex geometry, linear interpolations of the representation space do not directly correspond to geodesic paths along the manifold unless enforced. An example of such a setting is scRNA-seq, where high-dimensional and discrete cellular data is assumed to lie on a negative binomial statistical manifold modelled by the decoder of a variational autoencoder. We introduce FlatVI, a novel training framework enforcing Euclidean geometry in the latent space of discrete-likelihood variational autoencoders modelling count data. In our regularisation setting, straight lines in the latent domain correspond to geodesic interpolations in the decoded space, improving the combination of our model with methods assuming Euclidean latent geometry. Results on simulated data empirically support our claims, while experiments on temporally resolved biological datasets show improvements in the reconstruction of cellular trajectories and the learning of biologically meaningful velocity fields.
Primary Area: applications to physical sciences (physics, chemistry, biology, etc.)
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Submission Number: 7693
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