We consider the problem of learning free-form symbolic expressions from raw data, such as that produced by an experiment in any scientific domain. Accurate and interpretable models of scientific phenomena are the cornerstone of scientific research. Simple yet interpretable models, such as linear or logistic regression and decision trees often lack predictive accuracy. Alternatively, accurate blackbox models such as deep neural networks provide high predictive accuracy, but do not readily admit human understanding in a way that would enrich the scientific theory of the phenomenon. Many great breakthroughs in science revolve around the development of parsimonious equational models with high predictive accuracy, such as Newton's laws, universal gravitation, and Maxwell's equations. Previous work on automating the search of equational models from data combine domain-specific heuristics as well as computationally expensive techniques, such as genetic programming and Monte-Carlo search. We develop a deep neural network (MACSYMA) to address the symbolic regression problem as an end-to-end supervised learning problem. MACSYMA can generate symbolic expressions that describe a dataset. The computational complexity of the task is reduced to the feedforward computation of a neural network. We train our neural network on a synthetic dataset consisting of data tables of varying length and varying levels of noise, for which the neural network must learn to produce the correct symbolic expression token by token. Finally, we validate our technique by running on a public dataset from behavioral science.

Prediction of pedestrian behavior is critical for fully autonomous vehicles to drive in busy city streets safely and efficiently. The future autonomous cars need to fit into mixed conditions with not only technical but also social capabilities. As more algorithms and datasets have been developed to predict pedestrian behaviors, these efforts lack the benchmark labels and the capability to estimate the temporal-dynamic intent changes of the pedestrians, provide explanations of the interaction scenes, and support algorithms with social intelligence. This paper proposes and shares another benchmark dataset called the IUPUI-CSRC Pedestrian Situated Intent (PSI) data with two innovative labels besides comprehensive computer vision labels. The first novel label is the dynamic intent changes for the pedestrians to cross in front of the ego-vehicle, achieved from 24 drivers with diverse backgrounds. The second one is the text-based explanations of the driver reasoning process when estimating pedestrian intents and predicting their behaviors during the interaction period. These innovative labels can enable several computer vision tasks, including pedestrian intent/behavior prediction, vehicle-pedestrian interaction segmentation, and video-to-language mapping for explainable algorithms. The released dataset can fundamentally improve the development of pedestrian behavior prediction models and develop socially intelligent autonomous cars to interact with pedestrians efficiently. The dataset has been evaluated with different tasks and is released to the public to access.