Topics for Master Students.
Neural Network Verification
Neural networks have been applied in many areas. However, any method based on generalizations may fail and this is by design. The question is how to deal with such failures. To limit them, one can define rules that a neural network should follow and devise strategies to verify whether the rules are obeyed. The main tasks of this project are to study an algorithm for learning rules formulated in propositional Horn, implement the algorithm, and apply it to verify neural networks.
Queries and Concept Learning by Angluin (Machine Learning 1988)
Exact Learning: On the Boundary between Horn and CNF by Hermo and Ozaki (ACM TOCT 2020).
Extracting Automata from Recurrent Neural Networks Using Queries and Counterexamples by Weiss, Goldberg, Yahav (ICML 2018)
Knowledge Graph Embeddings
Knowledge graphs can be understood as labelled graphs whose nodes and edges are enriched with meta-knowledge, such as temporal validity, geographic coordinates, and provenance. Recent research in machine learning attempts to complete (or predict) facts in a knowledge graph by embedding entities and relations in low-dimensional vector spaces. The main tasks of this project are to study knowledge graph embeddings, study ways of integrating temporal validity in the geometrical model of a knowledge graph, implement and perform tests with an embedding that represents the temporal evolution of entities using their vector representations.
Translating Embeddings for Modeling Multi-relational Data by Bordes, Usunier, Garcia-Durán (NeurIPS 2013)
Temporally Attributed Description Logics by Ozaki, Krötzsch, Rudolph (Book chapter: Description Logic, Theory Combination, and All That 2019)
Attributed Description Logics: Reasoning on Knowledge Graphs by Krötzsch, Marx, Ozaki, Thost (ISWC 2017)
Decidability and Complexity of Learning
Gödel showed in 1931 that, essentially, there is no consistent and complete set of axioms that is capable of modelling traditional arithmetic operations. Recently, Ben-David et al. defined a general learning model and showed that learnability in this model may not be provable using the standard axioms of mathematics. The main tasks of this project are to study Gödel's incompleteness theorems, the connection between these theorems and the theory of machine learning, and to investigate learnability and complexity classes in the PAC and the exact learning models.
Learnability can be undecidable by Ben-David, Hrubeš, Moran, Shpilka, Yehudayoff (Nature 2019)
On the Complexity of Learning Description Logic Ontologies by Ozaki (RW 2020)
Learning Ontologies via Queries
In artificial intelligence, ontologies have been used to represent knowledge about a domain of interest in a machine-processable format. However, designing and maintaining ontologies is an expensive process that often requires the interaction between ontology engineers and domain experts. The main tasks of this project are to study an algorithm for learning ontologies formulated in the ELH description logic, implement the algorithm, and evaluate it using an artificial oracle developed in the literature that simulates the domain expert.
Learning Query Inseparable ELH ontologies by Ozaki, Persia, Mazzullo (AAAI 2020)ExactLearner: A Tool for Exact Learning of EL Ontologies by Duarte, Konev, Ozaki (KR 2018)
Exact Learning of Lightweight Description Logic Ontologies by Konev, Lutz, Ozaki, Wolter (JMLR 2018)
Mining Ontologies with Formal Concept Analysis
Formal Concept Analysis (FCA) is a method of data analysis that can be used to find implications that hold in a dataset (e.g., Chancellor -> Politician, meaning "a chancellor is a politician"). In FCA, a base for a dataset is a set of implications with minimal cardinality that characterize those implications that hold in the dataset. This notion can be adapted to the context of ontologies, where the base contains rules formulated in an ontology language instead of implications. The main tasks of this project are to study an algorithm for mining ontologies based on FCA, implement the algorithm, and evaluate it using portions of knowledge graphs such as Wikidata as datasets.
Mining of EL-GCIs by Borchmann and Distel (ICDMW 2011)
Learning Description Logic Ontologies. Five Approaches. Where Do They Stand? by Ozaki (KI 2020)
Own topic combining logic and learning
Contact: Ana Ozaki