Published in Working paper, 2017
A set theory formalization in Agda.
Recommended citation: A. Calle-Saldarriaga. (2017). "A Set Theory Formalization." Tech. Report. Universidad EAFITs. https://acallesalda.github.io/files/settheoryagda.pdf
Published in Chemometrics and Intelligent Laboratory Systems, 2021
A DD-plot based test for funcional data.
Recommended citation: Calle-Saldarriaga, A.; Laniado, H.; Zuluaga, F.; Leiva, V. (2021). "Homogeneity tests for functional data based on depth-depth plots with chemical applications." Chemometrics and Intelligent Laboratory Systems. 219(104420). https://acallesalda.github.io/files/ddplot.pdf
Published:
Abstract: Automatic theorem provers need to recieve a reasonably small number of premises in order for them to be able to prove a given conjecture with limited processor time. In large theories this is not always possible, as many irrelevant clauses are added to the premises. In order to solve this problem, premise selection algorithms have emerged in the past few years, some using non-learning methods and others using learning ones. Our goal in this project is to implement a non-learning premise selection algorithm for Apia, in order to further link the interactive theorem prover Agda with Authomatic theorem provers. Slides
Published:
Abstract: Set theory has been is one of the most important fields for the foundations of mathematics, so having a formalization (i.e. a translation of its axiom and theorems into some proof assistant) is desirable. In this talk, we present a set theory formalization of the Z axioms and some theorems using Agda. Slides
Published:
A short introduction to Functional Data Analysis in the context of Big Data, given at EAFIT’s days of applied science.
Published:
Abstract: One of the classic concerns in statistics is determining if two samples come from the same population, i.e., homogeneity testing or two-sample testing. In this paper, we propose a homogeneity test in the context of Functional Data Analysis, adopting an idea from multivariate data analysis: the data depth plot (DD-plot). This DD-plot is a generalization of the univariate Q-Q plot (quantile-quantile plot). We propose some statistics based on these DD-plots, and we use bootstrapping techniques to estimate their distributions. We simulate our test’s finite-sample size and power, obtaining better results than other homogeneity tests proposed in the literature. Finally, we illustrate the procedure in samples of real heterogeneous data and get consistent results.
Continuous Education, Universidad EAFIT, Departmento de Ciencias Matemáticas, 2022
Led continuous education courses, mostly related to basic statistics or machine learning.
Undegrad, Universidad EAFIT, Departmento de Ciencias Matemáticas, 2022
A basic inference course for engineering undegrads. You can check some lecture notes here
Master, Universidad EAFIT, Departmento de Ciencias Matemáticas, 2022
Functional data analysis course for Master Students at EAFIT. Topics covered: exploratory fda, hilbert spaces, smoothing, fpca, functional linear model. Lecture notes here
Undergrad, Universidad EAFIT, Departmento de Ciencias Matemáticas, 2022
Undergrad discussion session, introductory probability.
TA, UW Madison, 2022
TA for Stats 301 (Fall 2022) (Introduction to statistics) (Prof. Gloria Rocío Bautista Mendoza)