Robotic applications often involve working in environments that are uncertain, dynamic, and partially observable. Recently, diffusion models have been proposed for learning trajectory prediction models trained from expert demonstrations, which can be used for planning in robot tasks. Such models have demonstrated a strong ability to overcome challenges such as multi-modal action distributions, highdimensional output spaces, and training instability. It is crucial to quantify the uncertainty of these dynamics models when using them for planning. In this paper, we quantify the uncertainty of diffusion dynamics models using Conformal Prediction (CP).

Some of the most successful knowledge graph embedding (KGE) models for link prediction - CP, RESCAL, TUCKER, COMPLEX - can be interpreted as energy-based models. Under this perspective they are not amenable for exact maximum-likelihood estimation (MLE), sampling and struggle to integrate logical constraints. This work re-interprets the score functions of these KGEs as circuits - constrained computational graphs allowing efficient marginalisation. Then, we design two recipes to obtain efficient generative circuit models by either restricting their activations to be non-negative or squaring their outputs. Our interpretation comes with little or no loss of performance for link prediction, while the circuits framework unlocks exact learning by MLE, efficient sampling of new triples, and guarantee that logical constraints are satisfied by design.

Robust inference for non-linear regression models from the tsallis score:812 Application to coronavirus disease 2019 contagion in italy.