Peer grading systems aggregate noisy reports from multiple students to approximate a "true" grade as closely as possible. Most current systems either take the mean or median of reported grades; others aim to estimate students’ grading accuracy under a probabilistic model. This paper extends the state of the art in the latter approach in three key ways: (1) recognizing that students can behave strategically (e.g., reporting grades close to the class average without doing the work); (2) appropriately handling censored data that arises from discrete-valued grading rubrics; and (3) using mixed integer programming to improve the interpretability of the grades assigned to students. We demonstrate how to make Bayesian inference practical in this model and evaluate our approach on both synthetic and real-world data obtained by using our implemented system in four large classes. These extensive experiments show that grade aggregation using our model accurately estimates true grades, students' likelihood of submitting uninformative grades, and the variation in their inherent grading error; we also characterize our models' robustness.

In this work we perform symbolic discovery of differential operators in a situation where there is sparse experimental data. This small data regime in machine learning can be made tractable by providing our algorithms with prior information about the underlying dynamics. Physics Informed Neural Networks (PINNs) have been very successful in this regime (reconstructing entire ODE solutions using only a single point or entire PDE solutions with very few measurements of the initial condition). The Universal PINN approach (UPINN) adds a neural network that learns a representation of unknown hidden terms in the differential equation. The algorithm yields both a surrogate solution to the differential equation and a black-box representation of the hidden terms. These hidden term neural networks can then be converted into symbolic equations using symbolic regression techniques like AI Feynman. In order to achieve convergence of the neural networks, we provide our algorithms with (noisy) measurements of both the initial condition as well as (synthetic) experimental data obtained at later times. We demonstrate strong performance of UPINNs even when provided with very few measurements of noisy data in both the ODE and PDE regime.