Title: Analogy based regression: PAC-learnability results and performance guarantees 

We have recently revisited analogical inference from a foundational and unifying perspective: 

-F. Cunha, Y. Lepage, M. Couceiro, Z. Bouraoui. Generalizing Analogical Inference from Boolean to Continuous Domains.To appear in AAAI 2026.

In particular, we have explored a parameterized framework based on generalized means, allowing analogical inference to extend naturally to regression tasks. We characterized analogy-preserving functions in this setting and derived both worst-case and average-case guarantees based on functional distances. This framework bridges the gap between Boolean analogical classification and continuous regression, offering a general theory of analogical reasoning across domains. 

In this thesis, we want to go a step further and derive PAC-learnability results and performance guarantees, and explore extensions, e.g., to multidimensional representations (embeddings) as well as  to structured and probabilistic analogical forms.

Requisitos: Programing in Python, Machine learning and some data analysis.

Localização: Alameda ou Tagus

Co-supervisor: Pedro Alexandre Simões dos Santos

Further information please contact us:

Prof. Miguel Couceiro and Prof. Pedro A. Santos

IST, December 2025