Exact Inference Optimization in Discrete Graphical Models

AI technologies are rapidly being adopted across sectors such as healthcare, finance, and manufacturing, delivering economic value through improved efficiency and automation. Much of this progress is driven by deep learning, now the dominant approach in modern machine learning. Yet deep learning methods face several challenges; they often require large datasets and offer limited interpretability, robustness, and uncertainty estimates. Exact inference in probabilistic graphical models offers a principled and more transparent way to handle uncertainty, addressing several of these drawbacks. Its main limitation, however, is computational cost, which has restricted its use in large-scale or time-critical settings. This dissertation investigates how to make exact inference more efficient and practical. It introduces four complementary advances: a metaprogramming framework that enables compile-time optimization of inference procedures; optimized numerical kernels for sum-product message computations; tensor-network-based formulations that unlock improved scalability; and memory-aware execution scheduling tailored to heterogeneous hardware. Together, these contributions demonstrate that substantial performance gains are possible without sacrificing exactness, expanding the range of real-world problems where probabilistic graphical models can be applied.

Eindhoven University of Technology