Such embeddings induce the so-called maximum mean discrepancy (MMD; [Smola et al., 2007, Gretton et al., 2012]), which quantifies the discrepancy Many estimators for HSIC exist. The classical ones rely on U-statistics or V -statistics [Gretton et al., 2005, Quadrianto et al., 2009, Pfister et al., 2018] and are known to converge at a rate of Lower bounds for the related MMD are known [Tolstikhin et al., 2016], but the existing analysis considers radial kernels and relies on independent Gaussian distributions.

Existing VLN models are optimized through expert demonstrations by supervised behavioural cloning or incorporating manual reward engineering.

Heterogeneity, e.g., due to different types of layers or multiple sub-models, poses

Optimal transport (OT) barycenters are a mathematically grounded way of averaging probability distributions while capturing their geometric properties.

Typically, existing models are trained and tested on the same dataset, leading to poor generalizability across variations in device location, device mounting orientation, and human activity type.

However, these methods are not directly applicable to regression tasks.

We propose ManiPose, a manifold-constrained multi-hypothesis model for human-pose 2D-to-3D lifting.

Understanding how humans interact with each other is key to building realistic multi-human virtual reality systems. This area remains relatively unexplored due to the lack of large-scale datasets. Recent datasets focusing on this issue mainly consist of activities captured entirely in controlled indoor environments with choreographed actions, significantly affecting their diversity.