Sure, here is a 5-year research proposal to address the challenges related to human feedback, error, decisions, and trust in AI and machine learning:

Year 1: The Transparency Problem

- Develop a review of current research in interpretable models and explainable algorithms.

- Design and implement a set of experiments to evaluate the effectiveness of current approaches.

- Develop a new framework for enabling human-AI collaboration to improve transparency and trust.

Year 2: The Fairness Problem

- Conduct a comprehensive review of current research in detecting and mitigating bias in training data and algorithms.

- Develop novel algorithms that can mitigate bias and promote fairness in decision-making.

- Evaluate the effectiveness of these algorithms on large-scale datasets.

Year 3: The Human-Machine Interaction Problem

- Conduct a review of current research in human-machine interaction in various contexts.

- Develop a mathematical framework for optimizing human-machine interaction in HITL systems.

- Design and implement a set of experiments to evaluate the effectiveness of the new framework.

Year 4: Integration and Testing

- Integrate the frameworks developed for the Transparency Problem, the Fairness Problem, and the Human-Machine Interaction Problem.

- Develop a comprehensive testing plan to evaluate the effectiveness of the integrated framework.

- Conduct a set of experiments to evaluate the integrated framework on real-world datasets.

Year 5: Dissemination and Impact

- Prepare research papers and presentations for peer-reviewed conferences and journals.

- Develop educational materials and workshops to disseminate the research findings to the broader community.

- Engage in outreach activities to inform policymakers and industry leaders about the importance of these frameworks for ensuring the quality and trustworthiness of AI and machine learning systems.

Overall, this proposal aims to develop novel frameworks that can improve transparency, fairness, and human-machine interaction in AI and machine learning systems, and to evaluate their effectiveness in real-world scenarios. The ultimate goal is to improve the quality and trustworthiness of these systems, and to promote their responsible and equitable use in society.