Explore a 40-minute lecture on tractable learning in structured probability spaces presented by Adnan Darwiche from UCLA at the Simons Institute. Delve into topics such as representation learning, learning with constraints, and structured probability spaces. Examine examples from video, language, and deep learning domains. Investigate Boolean constraints, combinatorial objects like rankings, and their encoding in logic. Learn about structured spaces for paths, logical circuits, and properties like decomposability and determinism. Discover Sentential Decision Diagrams (SDD) and their probabilistic counterpart, PSDD. Understand how these structures enable tractable logical and probabilistic inference. Explore learning algorithms, preference distributions, and structured datasets. Gain insights into learning from incomplete data and structured queries. Enhance your understanding of advanced machine learning concepts and their applications in various domains.
Tractable Learning in Structured Probability Spaces
Overview
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
