Understanding and modeling behavior of multi-agent systems is a central step for artificial intelligence. Here we present a deep generative model which captures behavior generating process of multi-agent systems, supports accurate predictions and inference, infers how agents interact in a complex system, as well as identifies agent groups and interaction types. Built upon advances in deep generative models and a novel attention mechanism, our model can learn interactions in highly heterogeneous systems with linear complexity in the number of agents. We apply this model to three multi-agent systems in different domains and evaluate performance on a diverse set of tasks including behavior prediction, interaction analysis and system identification. Experimental results demonstrate its ability to model multi-agent systems, yielding improved performance over competitive baselines. We also show the model can successfully identify agent groups and interaction types in these systems. Our model offers new opportunities to predict complex multi-agent behaviors and takes a step forward in understanding interactions in multi-agent systems.

Low-rank tensor regression, a new model class that learns high-order correlation from data, has recently received considerable attention. At the same time, Gaussian processes (GP) are well-studied machine learning models for structure learning. In this paper, we demonstrate interesting connections between the two, especially for multi-way data analysis. We show that low-rank tensor regression is essentially learning a multi-linear kernel in Gaussian processes, and the low-rank assumption translates to the constrained Bayesian inference problem. We prove the oracle inequality and derive the average case learning curve for the equivalent GP model. Our finding implies that low-rank tensor regression, though empirically successful, is highly dependent on the eigenvalues of covariance functions as well as variable correlations.

Multi-Rate Multivariate Time Series (MR-MTS) are the multivariate time series observations which come with various sampling rates and encode multiple temporal dependencies. State-space models such as Kalman filters and deep learning models such as deep Markov models are mainly designed for time series data with the same sampling rate and cannot capture all the dependencies present in the MR-MTS data. To address this challenge, we propose the Multi-Rate Hierarchical Deep Markov Model (MR-HDMM), a novel deep generative model which uses the latent hierarchical structure with a learnable switch mechanism to capture the temporal dependencies of MR-MTS. Experimental results on two real-world datasets demonstrate that our MR-HDMM model outperforms the existing state-of-the-art deep learning and state-space models on forecasting and interpolation tasks. In addition, the latent hierarchies in our model provide a way to show and interpret the multiple temporal dependencies.