[{"data":1,"prerenderedAt":-1},["ShallowReactive",2],{"doc-detail-118622-en":3,"doc-seo-118622-105":30,"detail-sidebar-cat-0-en-105":91},{"code":4,"msg":5,"data":6},0,"success",{"doc_id":7,"user_id":8,"nickname":9,"user_avatar":10,"doc_module":4,"category_id":11,"category_name":12,"doc_title":13,"doc_description":14,"doc_content":15,"file_id":16,"file_url":17,"file_type":18,"file_size":19,"view_count":4,"is_deleted":4,"is_public":20,"is_downloadable":20,"audit_status":20,"page_count":21,"language":22,"language_code":23,"site_id":24,"html_lang":23,"table_of_contents":25,"faqs":26,"seo_title":27,"seo_description":14,"update_tm":28,"read_time":29},118622,687197207919,"Theodora","https://ap-avatar.wpscdn.com/avatar/a000253d6f5f7c60be?x-image-process=image/resize,m_fixed,w_180,h_180&k=1779446848396160552",8,"Research & Report","Interpretable and Constrained Machine Learning via Combinatorial Optimization - Thesis","Recent advances in machine and deep learning enable recognition of complex patterns from large datasets, often without supervision, and have broadened the use of ML across domains such as healthcare and robotics. However, powerful models can produce internal representations that are hard for humans to understand and can be difficult to align with user-specified constraints. This interpretability gap, combined with limited constraint enforcement, reduces trust and slows adoption of ML systems. This dissertation develops methods for learning models that are both interpretable and compatible with formal constraints, using combinatorial optimization to train and integrate decision-tree-like structures and constraint-aware formulations.","Interpretable and Constrained Machine Learning via Combinatorial Optimization  \nby  \nPouya Shati  \nA thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy  \nDepartment of Computer Science University of Toronto  \n© Copyright 2025 by Pouya Shati  \nInterpretable and Constrained Machine Learning via Combinatorial Optimization  \nPouya Shati  \nDoctor of Philosophy  \nDepartment of Computer Science  \nUniversity of Toronto  \n2025  \nAbstract  \nRecent transformative advances in machine and deep learning have enabled the recognition of complex patterns from vast data, with or without human supervision. These advances have catalyzed the application of machine learning techniques to a diversity of problem settings, from healthcare to robotics. Unfortunately, sophisticated machine learning techniques can result in the construction of domain models that are challenging for humans to understand and in which it is difficult to enforce user-specified constraints. This lack of interpretability, as well as the inability to impose further constraints, has become a major obstacle to human trust in machine learning models and a challenge to the broad adoption of machine learning-based systems.  \nWhile one of the goals of artificial intelligence is, arguably, to extend its reasoning beyond the cognitive capabilities of humankind, such a pursuit should not disregard humancompatibility. Interpretable machine learning aims to develop human-understandable models and to explain so-called black-box models. Constrained machine learning addresses the problem by enforcing expert knowledge and formal requirements on solutions.  \nIn this dissertation we introduce methods to produce machine learning models/artifacts that are interpretable and amenable to human-specified constraints. We do so through the exploitation of techniques for solving combinatorial optimization problems.  \nIn particular, we propose novel formulations to learn inherently interpretable models such as decision trees. Our work includes encoding a variety of solution formats and objectives. We further propose frameworks and encodings for the integration of constraints during or after training. We show that our approaches successfully produce high-quality interpretable and constrained solutions in short runtimes, solving new problems and improving the state of the art in others. Our collective work shows that interpretability does not necessarily come at the expense of quality and, in fact, sometimes improves it. Utilizing constraints can  \nalso improve accuracy despite reducing the space of feasible solutions. Lastly, we discuss how the work presented in this dissertation can be extended in several interesting directions and inspire new approaches for using combinatorial optimization problems in machine learning.  \nTo My Family  \nAcknowledgements  \nI would like to start by expressing my deepest gratitude to my family, though I know words cannot do justice to all that they have done for me. We often pursue success by weighing all of the trade-offs along the way. However, we rarely consider the sacrifices that we impose on those who love us most. I want the unsung heroes of my life—my mother, father, and sister—to know that their support has shown me what it means to live truly. I feel unburdened by the arbitrary milestones we collectively and self-congratulatory came to perceive as goals. There is no higher goal to which I aspire than to embody their loving spirit in my life and be someone of whom they can be proud.  \nI would like to extend my heartfelt thanks to my supervisors—Professor Eldan Cohen and Professor Sheila McIlraith. My PhD had a troubled start which was further exacerbated by the restrictions imposed due to COVID-19 . Despite the difficult circumstances, Sheila and Eldan not only provided me with an academic home but also made my PhD Journey better than I could have ever wished for. Sheila has taught me so much and has never let me feel depriv","cbCaijYLLLPyEAru","https://ap.wps.com/l/cbCaijYLLLPyEAru","pdf",5013251,1,212,"English","en",105,"# Contents\n## 1 Introduction\n## 2 Background\n## 3 Optimal Decision Tree Classification\n## 4 Constrained Learning Frameworks\n## 5 Experiments and Results\n## 6 Discussion and Future Work","[{\"question\":\"What problem does this dissertation address in machine learning adoption?\",\"answer\":\"It targets the difficulty of building ML models that humans can understand and that also allow enforcement of user-specified constraints, which undermines trust and broad deployment.\"},{\"question\":\"How does the dissertation achieve interpretability and constraint compatibility?\",\"answer\":\"It introduces learning methods that produce interpretable models and artifacts while integrating constraints through techniques derived from combinatorial optimization.\"},{\"question\":\"What kinds of interpretable models and constraints are proposed?\",\"answer\":\"The work proposes novel formulations to learn inherently interpretable structures such as decision trees, and it includes encoding different solution formats, objectives, and frameworks for constraint integration during or after training.\"}]","Interpretable and Constrained Machine Learning via Combinatorial Optimization - 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