Deep Policy Inference Q-Network (DPIQN)
We present DPIQN, a deep policy inference Q-network that targets multi-agent systems composed of controllable agents, collaborators, and opponents that interact with each other. We focus on one challenging issue in such systems—modeling agents with varying strategies—and propose to employ ‘policy features’ learned from raw observations (e.g., raw images) of collaborators and opponents by inferring their policies. DPIQN incorporates the learned policy features as a hidden vector into its own deep Q-network (DQN), such that it is able to predict better Q values for the controllable agents than the state-of-the-art deep reinforcement learning models. We further propose an enhanced version of DPIQN, called deep recurrent policy inference Q-network (DRPIQN), for handling partial observability. Both DPIQN and DRPIQN are trained by an adaptive training procedure, which adjusts the network’s attention to learn the policy features and its own Q-values at different phases of the training process. We present a comprehensive analysis of DPIQN and DRPIQN, and highlight their effectiveness and generalizability in various multi-agent settings. Our models are evaluated in a classic soccer game involving both competitive and collaborative scenarios. Experimental results performed on 1 vs. 1 and 2 vs. 2 games show that DPIQN and DRPIQN demonstrate superior performance to the baseline DQN and deep recurrent Q-network (DRQN) models. We also explore scenarios in which collaborators or opponents dynamically change their policies, and show that DPIQN and DRPIQN do lead to better overall performance in terms of stability and mean scores. …

Multiregression Dynamic Models (MDM)
Multiregression dynamic models are defined to preserve certain conditional independence structures over time across a multivariate time series. They are non-Gaussian and yet they can often be updated in closed form. The first two moments of their one-step-ahead forecast distribution can be easily calculated. Furthermore, they can be built to contain all the features of the univariate dynamic linear model and promise more efficient identification of causal structures in a time series than has been possible in the past …

Extremal Depth (ED)
We propose a new notion called `extremal depth’ (ED) for functional data, discuss its properties, and compare its performance with existing concepts. The proposed notion is based on a measure of extreme `outlyingness’. ED has several desirable properties that are not shared by other notions and is especially well suited for obtaining central regions of functional data and function spaces. In particular: a) the central region achieves the nominal (desired) simultaneous coverage probability; b) there is a correspondence between ED-based (simultaneous) central regions and appropriate point-wise central regions; and c) the method is resistant to certain classes of functional outliers. The paper examines the performance of ED and compares it with other depth notions. Its usefulness is demonstrated through applications to constructing central regions, functional boxplots, outlier detection, and simultaneous confidence bands in regression problems. …