An end-to-end analysis of continuous-time Markov chain (CTMC) convergence using uniformization. Covers generator matrix construction, Doeblin minorization, TV-distance mixing times across multiple initial distributions, expected reward convergence, and spectral gap analysis. Includes a structural comparison between dense and sparse transition matrices, with theoretical proofs for shared stationary distributions and Dobrushin's ergodicity theorem.

A regression analysis project modeling diamond prices using a 1,000-observation sample from a 54,000-record dataset. Covers simple and multiple linear regression, formal assumption diagnostics (linearity, constant variance, normality), log-transformation of the response variable, and model selection using adjusted R² and VIF. Includes confidence and prediction intervals for applied price forecasting.

A machine learning classification project predicting League of Legends match outcomes using interval snapshot data from 40,000 matches. Compares elastic net logistic regression, decision tree, random forest, and gradient boosted tree models via 5-fold cross-validation, achieving ROC AUC of 0.913. Includes cross-time analysis across 10–25 minute snapshots showing how prediction accuracy improves as the match progresses.

Histogram RG

Final Research April 17

Este proyecto desarrolla un pipeline de aprendizaje no supervisado para la segmentación de actividades humanas utilizando el algoritmo K-means sobre el dataset HAR de la UCI. Se abordan etapas clave como preprocesamiento, reducción de dimensionalidad y evaluación de clusters, con el objetivo de identificar patrones latentes en los datos y analizar la calidad de la segmentación obtenida.

Samuel Zamora

TALLER ESTADISTICA 2