Predicting price spikes in critical metals such as Cobalt, Copper, Magnesium, and Nickel is crucial for mitigating economic risks associated with global trends like the energy transition and reshoring of manufacturing. While traditional models have focused on regression-based approaches, our work introduces a neurosymbolic ensemble framework that integrates multiple neural models with symbolic error detection and correction rules. This framework is designed to enhance predictive accuracy by correcting individual model errors and offering interpretability through rule-based explanations. We show that our method provides up to 6.42% improvement in precision, 29.41% increase in recall at 13.24% increase in F1 over the best performing neural models. Further, our method, as it is based on logical rules, has the benefit of affording an explanation as to which combination of neural models directly contribute to a given prediction.

Machine learning models need to be continually updated or corrected to ensure that the prediction accuracy remains consistently high. In this study, we consider scenarios where developers should be careful to change the prediction results by the model correction, such as when the model is part of a complex system or software. In such scenarios, the developers want to control the specification of the corrections. To achieve this, the developers need to understand which subpopulations of the inputs get inaccurate predictions by the model. Therefore, we propose correction rule mining to acquire a comprehensive list of rules that describe inaccurate subpopulations and how to correct them. We also develop an efficient correction rule mining algorithm that is a combination of frequent itemset mining and a unique pruning technique for correction rules. We observed that the proposed algorithm found various rules which help to collect data insufficiently learned, directly correct model outputs, and analyze concept drift.

We present a new method for automatically providing feedback for introductory programming problems. In order to use this method, we need a reference implementation of the assignment, and an error model consisting of potential corrections to errors that students might make. Using this information, the system automatically derives minimal corrections to student's incorrect solutions, providing them with a quantifiable measure of exactly how incorrect a given solution was, as well as feedback about what they did wrong. We introduce a simple language for describing error models in terms of correction rules, and formally define a rule-directed translation strategy that reduces the problem of finding minimal corrections in an incorrect program to the problem of synthesizing a correct program from a sketch. We have evaluated our system on thousands of real student attempts obtained from 6.00 and 6.00x. Our results show that relatively simple error models can correct on average 65% of all incorrect submissions.