"To think recursively means to address a problem by assuming that similar problems of a smaller nature have already been solved and figuring out how to put those solutions together to solve the larger problem".

This text is from the book, "Discrete Mathematics", by Susanna Epps. It's really less a book about math, per se, than an effort to get its readers to think about how to solve problems.

I recommend it highly [you can find it free online, I did] for anyone to improve their problem solving skills [my motivation]. Solving problems leads to confidence; what could be more useful than that?

10 Types of Data Analysis

(Mathematical and Statistical Methods) 1. Descriptive Analysis: It does what the name suggests - "Describe." It looks at data and analyzes past events for deciding how to approach the future.

2.  Regression Analysis: It allows modeling the relationship between a dependent variable and one or more independent variables.

3.  Dispersion Analysis: Dispersion is the spread to which a set of data is stretched. It is a technique of describing how extended a set of data is.

4.  Factor Analysis: Factor analysis is a regression based data analysis technique, used to find an underlying structure in a set of variables.

5.  Discriminant Analysis: The discriminant analysis utilizes variable measurements on different groups of items to underline points that distinguish the groups.

6.  Time Series: It is a process of modeling and explaining time-dependent series of data points. The goal is to draw meaningful information (rules, patterns) from the shape of data.  

(Methods Based on The Artificial Intelligence, Machine Learning and Heuristic Algorithms)

7.  Neural Networks: They present a brain metaphor for information processing. These models are biologically inspired computational models. They consist of an interconnected group of artificial neurons and process information using computation approach.

8.  Decision Trees: The decision tree is a tree-shaped diagram that represents classification or regression models. it divides a data set into smaller and smaller sub data sets while at the same time a related decision tree is continuously developed.

9.  Evolutionary Algorithms: A common concept that combines many different types of data analysis using evolutionary algorithms. Most popular of them are: genetic algorithms, genetic programming, and co-evolutionary algorithms.

Decision tree analysis was performed to examine nonlinear relationships among a set of explanatory variables and a binary categorical response variable. The following syntax was used to generate the classification tree for the variables under investigation.

Below is a picture of the results obtained including the classification tree.

Interpretation of the Results

Decision tree analysis was conducted to examine nonlinear relationships among a set of explanatory variables and a binary categorical response variable, life expectancy (classified as High vs. Low). All possible separations (for categorical variables) and cut points (for continuous variables) were evaluated. For the present analysis, a Gini impurity criterion was used to identify optimal splits, and a cost–complexity pruning algorithm was applied to reduce the full tree to a parsimonious final sub-tree. The explanatory variables included in the classification tree model were internet use rate, urban rate, and income per person.

Internet use rate emerged as the first and most influential variable separating the sample into two major subgroups. Countries with an internet use rate ≤ 26.6% were more likely to be classified as having Low Life Expectancy, whereas countries with higher internet penetration were more likely to exhibit High Life Expectancy. Among countries with low internet use (≤ 26.6%), a further subdivision was made based on urban rate. Countries with an urbanization level ≤ 53.8% were overwhelmingly classified as having Low Life Expectancy, with very low node impurity, indicating a high degree of homogeneity in this group. Within this subgroup, countries with very low urbanization (≤ 21.1%) showed an almost pure classification toward Low Life Expectancy.

For countries with higher internet use (> 26.6%), life expectancy outcomes were predominantly classified as High. A further split based on urban rate (≤ 59.8%) refined this classification, with higher urbanization consistently associated with higher life expectancy. At the terminal nodes, countries with urbanization levels exceeding 71.4% formed highly homogeneous groups classified as High Life Expectancy. The final pruned decision tree classified approximately 76% of cases correctly, with stronger performance in identifying countries with High Life Expectancy (higher sensitivity) than those with Low Life Expectancy (moderate specificity).

Su objetivo es predecir la proximidad al océano (ocean_proximity) de una vivienda, basándose en otras características de un archivo CSV llamado housing.csv.

Una vez preprocesados, los datos se dividen en dos conjuntos usando train_test_split: un 80% para entrenamiento y un 20% para prueba, garantizando resultados reproducibles con random_state=42. Posteriormente, se crea una instancia del DecisionTreeClassifier limitando su profundidad a 4 niveles (max_depth=4) para prevenir el sobreajuste y se entrena usando el criterio de entropy.

Tras el entrenamiento, el script evalúa el rendimiento del modelo sobre el conjunto de prueba, imprimiendo su precisión (accuracy_score) y un reporte de clasificación detallado.

Primeros pasos del código de árbol de decisión, lectura del archivo .csv con una base de datos de latitud, longitud, distancia al mar, étc.

Arbol de decisión creado en el entorno Python que surge de ejecutar el programa realizado.

📖 Decision Trees are among the most intuitive AI models — they mimic human decision-making by splitting data into branches and outcomes, helping both beginners and experts understand how predictions are made.

1️⃣ The Foundations

A tree-structured model used for both classification and regression tasks.

Data is split into branches based on features and conditions.

Each leaf node represents a final decision or prediction.

Common algorithms: ID3, C4.5, CART.

2️⃣ Where It’s Used

Finance: Loan approval and credit risk analysis.

Healthcare: Disease diagnosis and treatment suggestions.

Marketing: Customer segmentation and lead scoring.

Operations: Decision support and process optimization.

3️⃣ Strengths vs Limitations

Strengths

Easy to interpret and visualize.

Handles both categorical and numerical data.

Requires little data preparation.

Limitations

Prone to overfitting if not pruned.

Unstable with small data changes.

Biased toward features with more levels.

4️⃣ Pro Tips

Use pruning to simplify the tree and prevent overfitting.

Apply ensemble methods like Random Forest or XGBoost for better accuracy.

Visualize your tree to explain model decisions to non-technical teams.

💡 Final Note Decision Trees bridge the gap between human reasoning and machine learning. Their clarity and transparency make them essential for interpretable AI — especially in industries that demand explainability.

📌 Series Continuation This is Day 4 of the AI Models Explained series 🎉. Next up: Random Forest – Combining Multiple Trees for Smarter Predictions.