4 citations · 6 across the 7 of their papers we have counts for
8 papers
Algebraic Machine Learning for Small-to-Medium Datasets Is Competitive against Strong Standard Baselines
David Mendez, Fernando Martin-Maroto, Gonzalo G. de Polavieja
Symbolic methods are generally not considered competitive with strong modern learners on realistic supervised tasks. We evaluate Algebraic Machine Learning (AML), a framework that…
Beyond ECE: Calibrated Size Ratio, Risk Assessment, and Confidence-Weighted Metrics
Fernando Martin-Maroto, Nabil Abderrahaman, Gonzalo G. de Polavieja
Confidence calibration has been dominated by the Expected Calibration Error (ECE), a linear metric that counts calibration offset equally regardless of the confidence level at whic…
The pairwise distributive law of semilattice congruences
Fernando Martin-Maroto, Antonio Ricciardo, Gonzalo G. de Polavieja
We show that the congruence lattice of a semilattice satsifies a form of distributivity relative to principal congruences of the form . Particularly, we establis…
Algebraic Machine Learning: Learning as computing an algebraic decomposition of a task
Fernando Martin-Maroto, Nabil Abderrahaman, David Mendez +1
Statistics and Optimization are foundational to modern Machine Learning. Here, we propose an alternative foundation based on Abstract Algebra, with mathematics that facilitates the…
Infinite Atomized Semilattices
Fernando Martin-Maroto, Antonio Ricciardo, David Mendez +1
We extend the theory of atomized semilattices to the infinite setting. We show that it is well-defined and that every semilattice is atomizable. We also study atom redundancy, focu…
Semantic Embeddings in Semilattices
Fernando Martin-Maroto, Gonzalo G. de Polavieja
To represent anything from mathematical concepts to real-world objects, we have to resort to an encoding. Encodings, such as written language, usually assume a decoder that underst…
Finite Atomized Semilattices
Fernando Martin-Maroto, Gonzalo G. de Polavieja
We show that every finite semilattice can be represented as an atomized semilattice, an algebraic structure with additional elements (atoms) that extend the semilattice's partial o…
Algebraic Machine Learning
Fernando Martin-Maroto, Gonzalo G. de Polavieja
Machine learning algorithms use error function minimization to fit a large set of parameters in a preexisting model. However, error minimization eventually leads to a memorization…