Finslerian latent-distance estimation

methods / Theoretical / Analytical / Geometric analysis / Finslerian latent-distance estimation

Techniqueadvanced

Replaces the expected (Riemannian) pullback metric on a stochastic generative model's latent space with a Finsler metric -- a norm on tangent vectors that need not be quadratic -- computed directly from the distribution of stochastic pullback metrics rather than from their expectation, correcting a systematic bias introduced whenever the common practice of approximating the stochastic metric by its mean is used.

Used in (1 observation)

A real trained GP-LVM's Riemannian and Finslerian latent geodesics converge on high-dimensional real datasets, but diverge in low-dimensional synthetic settingsmeasured

structure: Curvature profile of the representation manifold · models: GP-LVM (256-dim font-contour dataset, stochastic active-set inference), GP-LVM (48-dim qPCR single-cell gene-expression dataset) · paper: Identifying Latent Distances with Finslerian Geometry