Solving Probability and Statistics Problems by Program Synthesis

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Solving Probability and Statistics Problems by Program Synthesis Leonard Tang Harvard University MathematicsElizabeth Ke MIT MathematicsNikhil Singh MIT Media Lab Nakul Verma Columbia University Computer Science DepartmentIddo Drori MIT EECS Abstract We solve university level probability and statis- tics questions by program synthesis using OpenAI?s Codex, a Transformer trained on text and ?ne-tuned on code. We transform course problems from MIT?s 18.05 Introduc- tion to Probability and Statistics and Harvard?s STAT110 Probability into programming tasks. We then execute the generated code to get a solution. Since these course questions are grounded in probability, we often aim to have Codex generate probabilistic programs that simulate a large number of probabilistic depen- dencies to compute its solution. Our approach requires prompt engineering to transform the question from its original form to an explicit, tractable form that results in a correct program and solution. To estimat...

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• [1] https://arxiv.org/abs/2111.08267