The authors construct a Mortensen-type observer on the Wasserstein space P2(R^d), establish dynamic programming and viscosity solution properties for the associated HJB equation using two formulations, prove uniqueness via comparison, and introduce a convergent semi-Lagrangian scheme.
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Recasts covariance shrinkage as risk minimization over stochastic interpolants between distributions, recovering known estimators via scheduling, couplings, and early stopping, and proposing a neural estimator with quadratic risk bounds.
OTP-FM extends conditional flow matching by incorporating dynamic optimal transport potentials to enable efficient multimarginal transport learning with intermediate observed marginals.
Proposes a scale-calibrated median-of-means estimator for robust aggregation of distributed PCA estimates on the product of Euclidean space and Grassmann manifold.
An intrinsic effective sample size for manifold MCMC is defined via kernel discrepancy as the number of independent draws yielding equivalent expected squared discrepancy to the target.
A new type of PDE for selective density-constrained crowd motion is obtained as the stiff limit of conservation laws, with existence of solutions proven via uniform BV estimates and compactness.
The profile maximum likelihood estimator for the location in anisotropic hyperbolic wrapped normal models is strongly consistent, asymptotically normal, and attains the Hájek-Le Cam minimax lower bound under squared geodesic loss.
Introduces BRIDGE and SKFM algorithms that detect latent confounders via non-closing Lie brackets in interventional vector fields derived from density ratios.
An interior-point method is introduced to compute dynamical quantum optimal transport geodesics on density matrices, shown to approximate some quantum chemistry problems after parameter tuning.
Joint location-scale minimization for geometric medians on product manifolds degenerates to marginal medians, and three new scale-selection methods restore identifiability with asymptotic guarantees.
A latent-cluster quasi-Bayesian method with restarted updates yields sublinear cumulative Wasserstein-1 regret for online distributional prediction under drift and adversarial corruption.
A review reframing density estimation as 'density evolution' across scales, linking kernel smoothing to heat flow, mixtures to compression, and topology to level sets, while stating three structural results on modes, Gaussian semigroups, and log-concavity.
A tractable estimator for functional KL divergence provides a coherent way to compare trajectory inference methods and reveal discrepancies in inferred dynamics from snapshot data.
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An algorithm for dynamical quantum optimal transport with applications to quantum chemistry
An interior-point method is introduced to compute dynamical quantum optimal transport geodesics on density matrices, shown to approximate some quantum chemistry problems after parameter tuning.