Motion forecasts of road users (i.e., agents) vary in complexity as a function of scene constraints and interactive behavior. We address this with a multi-task learning method for motion forecasting that includes a retrocausal flow of information. The corresponding tasks are to forecast (1) marginal trajectory distributions for all modeled agents and (2) joint trajectory distributions for interacting agents. Using a transformer model, we generate the joint distributions by re-encoding marginal distributions followed by pairwise modeling. This incorporates a retrocausal flow of information from later points in marginal trajectories to earlier points in joint trajectories. Per trajectory point, we model positional uncertainty using compressed exponential power distributions. Notably, our method achieves state-of-the-art results in the Waymo Interaction Prediction dataset and generalizes well to the Argoverse 2 dataset. Additionally, our method provides an interface for issuing instructions through trajectory modifications. Our experiments show that regular training of motion forecasting leads to the ability to follow goal-based instructions and to adapt basic directional instructions to the scene context. Code: https://github.com/kit-mrt/future-motion

While standard estimation assumes that all datapoints are from probability distribution of the same fixed parameters $\theta$, we will focus on maximum likelihood (ML) adaptive estimation for nonstationary time series: separately estimating parameters $\theta_T$ for each time $T$ based on the earlier values $(x_t)_{t

In this paper we propose a novel framework for the construction of sparsity-inducing priors. In particular, we define such priors as a mixture of exponential power distributions with a generalized inverse Gaussian density (EP-GIG). EP-GIG is a variant of generalized hyperbolic distributions, and the special cases include Gaussian scale mixtures and Laplace scale mixtures. Furthermore, Laplace scale mixtures can subserve a Bayesian framework for sparse learning with nonconvex penalization. The densities of EP-GIG can be explicitly expressed. Moreover, the corresponding posterior distribution also follows a generalized inverse Gaussian distribution. These properties lead us to EM algorithms for Bayesian sparse learning. We show that these algorithms bear an interesting resemblance to iteratively re-weighted $\ell_2$ or $\ell_1$ methods. In addition, we present two extensions for grouped variable selection and logistic regression.