Neural Probabilistic Sentential Decision Diagrams

• Grant number: 25/01335-3
• Support Opportunities: Scholarships in Brazil - Master
• Start date: April 01, 2025
• End date: March 31, 2027
• Field of knowledge: Physical Sciences and Mathematics - Computer Science - Computing Methodologies and Techniques
• Principal Investigator: Denis Deratani Mauá
• Grantee: Anahí Coimbra Maciel
• Host Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
• Associated research grant: 22/02937-9 - Neural inductive logic programming, AP.PNGP.PI

Abstract

Probabilistic Sentential Decision Diagrams (PSDD) are discrete statistical models that allow the easy integration of probabilities and logic. In short, a PSDD is a logic circuit with a special syntax whose arcs (wires) are annotated with probabilities. The logic circuit e¿ciently specifies the distribution support as a logic constraint. This way, PSDDs can easily specify probability distributions over complex combinatorial objects such as rankings, routes, subsets, etc. Importantly, PSDDs are tractable models as they allow many inferences to be accomplished in time linear in the circuit size. They can also be learned purely from data, or, more interestingly, from a combination of data and expert knowledge (in the form of constraints. In this research, we shall investigate how to extend PSDDs to allow for tight integration with neural network, thus allowing PSDDs to be learned from raw, low-level data such as images, text, sound.