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Tractable Learning in Structured Probability Spaces

Simons Institute via YouTube

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Overview

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This course focuses on teaching representation learning in structured probability spaces. The learning outcomes include understanding structured probability spaces, Boolean constraints, and probabilistic decision diagrams. The course covers skills such as encoding rankings in logic, working with logical circuits, and learning preference distributions. The teaching method includes lectures, examples, and discussions. This course is intended for individuals interested in advanced topics in machine learning and probabilistic reasoning.

Syllabus

Intro
References
Running Example
Learning with Constraints
Example: Video
Example: Language
Example: Deep Learning
What are people doing now?
Structured Probability Spaces
Boolean Constraints
Combinatorial Objects: Rankings
Encoding Rankings in Logic
Structured Space for Paths
Logical Circuits
Property: Decomposability
Property: Determinism
Sentential Decision Diagram (SDD)
Tractable for Logical Inference
PSDD: Probabilistic SDD
Tractable for Probabilistic Inference
PSDDs are Arithmetic Circuits
Parameters are interpretable
Learning Algorithms
Learning Preference Distributions
What happens if you ignore constraints?
Structured Naïve Bayes Classifier
Structured Datasets
Learning from Incomplete Data
Structured Queries
Conclusions

Taught by

Simons Institute

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