  Humans make daily-routine decisions based on their internal states in
intricate interaction scenarios. This paper presents a probabilistically
reconstructive learning approach to identify the internal states of
multi-vehicle sequential interactions when merging at highway on-ramps. We
treated the merging task's sequential decision as a dynamic, stochastic process
and then integrated the internal states into an HMM-GMR model, a probabilistic
combination of an extended Gaussian mixture regression (GMR) and hidden Markov
models (HMM). We also developed a variant expectation-maximum (EM) algorithm to
estimate the model parameters and verified them based on a real-world data set.
Experimental results reveal that the interactive merge procedure at highway
on-ramps can be semantically described by three interpretable internal states.
This finding provides a basis for autonomous vehicles to develop a model-based
decision-making algorithm in a partially observable environment.
