Algorithms for Learning Probabilistic and Causal Models with Possible Imperfect Advice
COM3 Level 1
SR12, COM3 01-21
Abstract:
Learning a useful representation of the world from data is a cornerstone of scientific discovery and the driving force behind successful modern machine learning methods. This process often involves learning probabilistic models for predictive tasks and causal models to understand interventional effects on systems, which is crucial for informed downstream decision-making. Meanwhile, real-world problems are frequently abstracted to be solved algorithmically before the solutions are mapped back to their real-world instances. However, this "abstract, solve, and map back" approach can overlook subtle but significant contextual information inherent in real-world instances. In this thesis, we address fundamental questions about learning probabilistic and causal models, offering new insights and results for these tasks. We further introduce innovative algorithmic ideas within the framework of learning-augmented algorithms that enhance performance by incorporating suitable contextual information as imperfect advice.