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Title: Stochastic Prediction of Multi-Agent Interactions from Partial Observations

Paper content:
We present a method which learns to integrate temporal information, from a learned dynamics model, with ambiguous visual information, from a learned vision model, in the context of interacting agents.
Our method is based on a graph-structured variational recurrent neural network, which is trained end-to-end to infer the current state of the (partially observed) world, as well as to forecast future states.
We show that our method outperforms various baselines on two sports datasets, one based on real basketball trajectories, and one generated by a soccer game engine.
Imaging watching a soccer game on television.
At any given time, you can only see a subset of the players, and you may or may not be able to see the ball, yet you probably have some reasonable idea about where all the players currently are, even if they are not in the field of view.
(For example, the goal keeper is probably close to the goal.)
Similarly, you cannot see the future, but you may still be able to predict where the "agents" (players and ball) will be, at least approximately.
Crucially, these problems are intertwined: we are able to predict future states by using a state dynamics model, but we can also use the same dynamics model to infer the current state of the world by extrapolating from the last time we saw each agent.In this paper, we present a unified approach to state estimation and future forecasting for problems of this kind.
More precisely, we assume the observed data consists of a sequence of video frames, v 1:T , obtained from a stationary or moving camera.
The desired output is a (distribution over a) structured representation of the scene at each time step, p(s t |v 1:t ), as well as a forecast into the future, p(s t+∆ |v 1:t ), where s k t encodes the state (e.g., location) of the k'th agent and s t = {s DISPLAYFORM0 The classical approach to this problem (see, e.g., BID3 ) is to use state-space models, such as Kalman filters, for tracking and forecasting, combined with heuristics, such as nearest neighbor, to perform data association (i.e., inferring the mapping from observations to latent objects).
Such generative approaches require a dynamical model for the states, p(s t |s t−1 ), and a likelihood model for the pixels, p(v t |s t ).
These are then combined using Bayes' rule.
However, it is hard to learn good generative model of pixels, and inverting such models is even harder.
By contrast, our approach is discriminative, and learns an inference network to compute the posterior belief state p(s t |v 1:t ) directly.
In particular, our model combines ideas from graph networks, variational autoencoders, and RNNs in a novel way, to create what we call a graph-structured variational recurrent neural network (Graph-VRNN).We
have tested our approach on two datasets: real basketball trajectories, rendered as a series of (partially observed) bird's eye views of the court; and a simple simulated soccer game, rendered using a 3d graphics engine, and viewed from a simulated moving camera. We
show that our approach can infer the current state more accurately than other methods, and can also make more accurate future forecasts. We
also show that our method can vary its beliefs in a qualitatively sensible way. For
DISPLAYFORM1 Figure 1: Illustration of visual VRNN with a single agent. Dotted
edges are not used. Dashed
edges are non-standard edges that we add.example, it "knows" the location of the goalie even if it is not visible, since the goalie does not move much (in our simulation). Thus it
learns to "see beyond the pixels".In summary
, our main contribution is a unified way to do state estimation and future forecasting at the level of objects and relations directly from pixels using Graph-VRNN. We believe
our technique will have a variety of other applications beyond analysing sports videos, such as self-driving cars (where inferring and predicting the motion of pedestrians and vehicles is crucial), and human-robot interaction.
We have presented a method that learns to integrate temporal information with partially observed visual evidence, based on graph-structured VRNNs, and shown that it outperforms various baselines on two simple datasets.
In the future, we would like to consider more challenging datasets, such as real sports videos.
We would also like to reduce the dependence on labeled data, perhaps by using some form of self-supervised learning.A.1
SAMPLED SOCCER TRAJECTORIES Figure A1 : Sampled trajectories for Soccer World for 11 "home" players.
Figure A1 shows the sampled trajectories for Soccer World.
Unlike basketball, Soccer World has a moving camera with limited field of view.
We observe that the trajectories for the first few observed steps are quite shaky since only a few players have been observed.
We thus show the trajectories from t = 5.
From fig. A1 , we can see that the trajectories generated by RNN are very shaky.
Graph-VRNN generates much better trajectories, but some of the players are assigned incorrect identities, or incorrect locations.
We conjecture that this issue can be mitigated by providing longer visual inputs to the model, such that most of the players could be observed at some point of the videos.A.2
SAMPLED BASKETBALL TRAJECTORIES FIG1 and Figure

assistant: text: The authors propose Graph VRNN which models the interaction of multiple agents by deploying a VRNN for each agent