# Manipulación y visualización de datos
library(tidyverse)
library(rebus)
# Modelado y validación
library(caret) # Framework unificado para ML
library(broom) # Resultados tidy de modelos
library(corrplot) # Matrices de correlación
library(ggrepel) # Etiquetas sin overlap
# Modelos específicos
library(glmnet) # Ridge y Lasso
library(randomForest) # Random Forest
library(xgboost) # XGBoost
library(rpart) # Árbol de decisión
library(rpart.plot) # Visualización de árboles
# Configuración
set.seed(123)
theme_set(theme_minimal())Tutorial Completo: Predicción de Precios de Inmuebles
Desde Regresión Lineal hasta XGBoost
1 Introducción
Este tutorial presenta un análisis completo de predicción de precios de inmuebles en México utilizando múltiples técnicas de machine learning, desde regresión lineal clásica hasta métodos ensemble avanzados.
1.1 Objetivos de Aprendizaje
Al completar este tutorial, serás capaz de:
- Limpiar y preparar datos inmobiliarios para modelado
- Realizar análisis exploratorio efectivo
- Implementar y comparar múltiples modelos de regresión
- Entender las ventajas y limitaciones de cada método
- Evaluar y seleccionar el mejor modelo para producción
1.2 Métodos Cubiertos
- Regresión Lineal Múltiple: Modelo base interpretable
- Ridge Regression: Regularización L2 para control de sobreajuste
- Lasso Regression: Regularización L1 con selección de variables
- Árbol de Decisión: Modelo no lineal simple
- Random Forest: Ensemble de árboles con bagging
- XGBoost: Gradient boosting optimizado
2 Configuración Inicial
2.1 Carga de Librerías
Nota importante sobre conflictos de namespace: La librería MASS (usada en algunos análisis estadísticos) puede enmascarar la función select() de dplyr. Si encuentras errores, usa dplyr::select() explícitamente.
2.2 Paralelización para XGBoost
Para acelerar el entrenamiento de XGBoost, activamos procesamiento paralelo:
# Detectar número de cores disponibles
library(parallel)
library(doParallel)
n_cores <- detectCores() - 1 # Dejar un core libre
cl <- makeCluster(n_cores)
registerDoParallel(cl)
# El cluster se cerrará al final del script
# stopCluster(cl)3 Carga y Limpieza de Datos
3.1 Teoría: Preprocesamiento de Datos
El preprocesamiento es crítico en machine learning. Datos de mala calidad producen modelos de mala calidad (“garbage in, garbage out”). Pasos esenciales:
- Manejo de valores faltantes: Eliminar o imputar
- Detección de outliers: Identificar y tratar valores extremos
- Transformación de variables: Normalización, logaritmos, etc.
- Ingeniería de características: Crear variables informativas
3.2 Carga de Datos
precio_casas <- readxl::read_xlsx("01_Datos/precio casas/datos_inmuebles.xlsx") %>%
filter(encabezado %in% c("Casa en venta", "Departamento en venta"))
# Inspección inicial
print(paste("Dimensiones:", nrow(precio_casas), "filas x",
ncol(precio_casas), "columnas"))[1] "Dimensiones: 1785 filas x 12 columnas"glimpse(precio_casas)Rows: 1,785
Columns: 12
$ encabezado <chr> "Casa en venta", "Departamento en venta", "Departamento…
$ titulo <chr> "Mirador Santiago", "Los Héroes Tizayuca, Desarrollo En…
$ precio <dbl> 2087000, 731000, 2320000, 4850000, 3041955, 2230000, 57…
$ extension <chr> "2 recámaras\n2 baños\n61 - 84 m² construidos", "2 a 4 …
$ ubicacion <chr> "El Mirador, Santiago De Querétaro, Mirador, Querétaro"…
$ imagen_url <chr> "https://http2.mlstatic.com/D_NQ_NP_2X_803872-MLM872246…
$ url <chr> "https://casa.mercadolibre.com.mx/MLM-3805076466-mirado…
$ moneda <chr> "MXN", "MXN", "MXN", "MXN", "MXN", "MXN", "MXN", "MXN",…
$ no_recamaras <dbl> 2, 4, 2, 3, 2, 3, 3, 3, 2, 1, 3, 3, 3, 3, 2, 3, 2, 3, 3…
$ no_banos <dbl> 2, 3, 2, 2, 1, 3, 4, 2, 2, 1, 4, 2, 4, 5, 3, 4, 2, 4, 3…
$ m2_construidos <dbl> 84, 104, 123, 132, 78, 156, 185, 122, 82, 46, 202, 113,…
$ m2_terreno <dbl> NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA, NA,…3.3 Limpieza y Transformación
3.3.1 Extracción de Estado
Usamos expresiones regulares para extraer el estado de la ubicación:
precio_casas <- precio_casas %>%
mutate(
# Extraer último elemento después de la última coma
estado = str_extract(ubicacion, pattern = ",\\s*([^,]+)$") %>%
str_remove(pattern = ",\\s*"),
# Corrección manual de inconsistencias
estado = if_else(estado == "Loreto", "Baja California Sur", estado)
)Decisión de código: Usar str_extract() con regex es más robusto que str_split() cuando el formato puede variar.
3.3.2 Filtrado de Datos
precio_casas <- precio_casas %>%
filter(is.na(m2_terreno))3.3.3 Conversión de Moneda y Transformaciones
precio_casas <- precio_casas %>%
mutate(
# Estandarizar a pesos mexicanos
precio = if_else(moneda == "US", precio * 18.5, precio),
# Crear variable de región según precio promedio estatal
region_precio = case_when(
estado %in% c("Distrito Federal", "Nuevo León", "Querétaro",
"Baja California Sur", "Quintana Roo", "Jalisco",
"Yucatán") ~ "Alta",
estado %in% c("Baja California", "Aguascalientes", "Coahuila",
"Chihuahua", "Estado De México", "Morelos", "Sinaloa",
"Nayarit", "Campeche") ~ "Media",
estado %in% c("Guanajuato", "Hidalgo", "Puebla", "Michoacán",
"Veracruz", "Guerrero", "Oaxaca", "Chiapas",
"Durango") ~ "Baja",
TRUE ~ NA_character_
),
# Simplificar tipo de inmueble
tipo_inmueble = if_else(
str_detect(encabezado, "Casa"),
"Casa",
"Departamento"
),
# Variables derivadas
precio_m2 = precio / m2_construidos,
log_precio = log(precio + 1) # Log para normalizar distribución
)Decisión de modelado: Usamos log(precio + 1) porque:
- Los precios suelen tener distribución log-normal
- Reduce el impacto de outliers
- Mejora linealidad en relaciones
- El
+1evita problemas con precios = 0
3.3.4 Filtrado de Ventas y Outliers
precio_casas <- precio_casas %>%
# Eliminar outliers extremos (1% y 99% percentiles)
filter(
precio > quantile(precio, 0.01, na.rm = TRUE) &
precio < quantile(precio, 0.99, na.rm = TRUE)
) %>%
filter()
# Verificar datos limpios
precio_casas %>%
count(estado, region_precio) %>%
arrange(region_precio, estado) %>%
print(n = 30)# A tibble: 25 × 3
estado region_precio n
<chr> <chr> <int>
1 Baja California Sur Alta 5
2 Distrito Federal Alta 663
3 Jalisco Alta 27
4 Nuevo León Alta 30
5 Querétaro Alta 111
6 Quintana Roo Alta 213
7 Yucatán Alta 110
8 Chiapas Baja 5
9 Durango Baja 2
10 Guanajuato Baja 20
11 Guerrero Baja 25
12 Hidalgo Baja 28
13 Michoacán Baja 2
14 Oaxaca Baja 1
15 Puebla Baja 43
16 Veracruz Baja 10
17 Aguascalientes Media 2
18 Baja California Media 3
19 Campeche Media 1
20 Chihuahua Media 3
21 Coahuila Media 1
22 Estado De México Media 326
23 Morelos Media 64
24 Nayarit Media 4
25 Sinaloa Media 3Justificación del filtro de outliers: Eliminamos el 1% superior e inferior para evitar que valores extremos (posibles errores de captura) distorsionen los modelos.
4 Análisis Exploratorio de Datos (EDA)
4.1 Teoría: Importancia del EDA
El análisis exploratorio nos permite:
- Entender la distribución de variables
- Identificar relaciones entre predictores y objetivo
- Detectar problemas de datos
- Generar hipótesis para modelado
- Validar supuestos de los modelos
4.2 Distribución del Precio
p_dist_precio <- precio_casas %>%
ggplot(aes(x = precio/1000000)) +
geom_histogram(bins = 50, fill = "steelblue", alpha = 0.7) +
scale_x_continuous(labels = scales::comma) +
labs(
title = "Distribución del Precio de Inmuebles",
x = "Precio (millones de pesos)",
y = "Frecuencia"
) +
facet_wrap(~tipo_inmueble, scales = "free_y")
print(p_dist_precio)
Interpretación: La distribución es asimétrica positiva (sesgo a la derecha), confirmando la necesidad de transformación logarítmica.
4.3 Relación Precio vs Características
p_precio_caracteristicas <- precio_casas %>%
pivot_longer(
cols = c(no_recamaras, no_banos, m2_construidos),
names_to = "caracteristica",
values_to = "valor"
) %>%
mutate(
caracteristica = case_when(
caracteristica == "no_recamaras" ~ "Número de Recámaras",
caracteristica == "no_banos" ~ "Número de Baños",
caracteristica == "m2_construidos" ~ "M² Construidos"
)
) %>%
ggplot(aes(x = valor, y = precio/1000000)) +
geom_point(alpha = 0.3, color = "steelblue") +
geom_smooth(method = "lm", se = TRUE, color = "red") +
facet_wrap(~caracteristica, scales = "free_x") +
scale_y_continuous(labels = scales::comma) +
labs(
title = "Relación entre Precio y Características del Inmueble",
x = "Valor",
y = "Precio (millones de pesos)"
)
print(p_precio_caracteristicas)
Observación clave: Todas las características muestran correlación positiva con el precio, aunque con diferentes pendientes.
4.4 Precio por Región y Tipo
p_precio_region <- precio_casas %>%
ggplot(aes(x = region_precio, y = precio/1000000, fill = tipo_inmueble)) +
geom_boxplot(alpha = 0.7) +
scale_y_log10(labels = scales::comma) +
labs(
title = "Distribución de Precios por Región y Tipo de Inmueble",
x = "Región (según precio promedio)",
y = "Precio (millones de pesos, escala log)",
fill = "Tipo"
) +
theme(legend.position = "bottom")
print(p_precio_region)
5 Preparación para Modelado
5.1 Selección de Variables
datos_modelo <- precio_casas %>%
dplyr::select(
precio, log_precio, no_recamaras, no_banos,
m2_construidos, region_precio, tipo_inmueble
) %>%
drop_na()
print(paste("Observaciones para modelado:", nrow(datos_modelo)))[1] "Observaciones para modelado: 1689"5.2 Matriz de Correlación
correlacion <- datos_modelo %>%
dplyr::select(where(is.numeric)) %>%
cor()
corrplot(
correlacion,
method = "color",
type = "upper",
order = "hclust",
tl.cex = 0.8,
tl.col = "black",
addCoef.col = "black",
number.cex = 0.7,
title = "Matriz de Correlación",
mar = c(0, 0, 2, 0)
)
Interpretación: El precio correlaciona fuertemente con m2_construidos (0.67), seguido por no_recamaras y no_banos.
6 Estrategia de Validación
6.1 Teoría: Validación Cruzada
La validación cruzada k-fold es esencial para:
- Estimar rendimiento real: Evita optimismo del error de entrenamiento
- Detectar sobreajuste: Compara error train vs validación
- Seleccionar hiperparámetros: Encuentra configuración óptima
- Comparar modelos: Base justa de comparación
Funcionamiento de k-fold CV:
- Dividir datos en k particiones (folds)
- Para cada fold i:
- Entrenar en k-1 folds
- Validar en fold i
- Promediar métricas de k iteraciones
# Configurar validación cruzada 10-fold
control_cv <- trainControl(
method = "cv",
number = 10,
savePredictions = "final",
verboseIter = FALSE,
allowParallel = TRUE # Usar paralelización
)7 Modelos de Regresión
7.1 1. Regresión Lineal Múltiple
7.1.1 Teoría: Regresión Lineal
La regresión lineal es el método más fundamental en estadística. Asume una relación lineal entre predictores y la variable objetivo:
\[ y = \beta_0 + \beta_1 x_1 + \beta_2 x_2 + ... + \beta_p x_p + \epsilon \]
Donde:
- \(y\): variable dependiente (precio)
- \(x_i\): variables independientes (características)
- \(\beta_i\): coeficientes a estimar
- \(\epsilon\): error aleatorio
Método de estimación: Mínimos Cuadrados Ordinarios (OLS), minimiza:
\[ \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 \]
Supuestos del modelo:
- Linealidad en parámetros
- Independencia de errores
- Homocedasticidad (varianza constante)
- Normalidad de errores
- No multicolinealidad perfecta
7.1.2 Implementación
# Modelo con precio original
modelo_cv <- train(
precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "lm",
trControl = control_cv
)
# Modelo con log(precio) - generalmente mejor
modelo_log_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "lm",
trControl = control_cv
)
print("=== Modelo con precio original ===")[1] "=== Modelo con precio original ==="print(modelo_cv)Linear Regression
1689 samples
5 predictor
No pre-processing
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1519, 1520, 1520, 1522, 1520, 1519, ...
Resampling results:
RMSE Rsquared MAE
7533195 0.4530465 4217085
Tuning parameter 'intercept' was held constant at a value of TRUEprint("=== Modelo con log(precio) ===")[1] "=== Modelo con log(precio) ==="print(modelo_log_cv)Linear Regression
1689 samples
5 predictor
No pre-processing
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1520, 1521, 1519, 1520, 1521, 1521, ...
Resampling results:
RMSE Rsquared MAE
0.5595061 0.5774755 0.4039536
Tuning parameter 'intercept' was held constant at a value of TRUEDecisión de modelado: Preferimos log(precio) porque el RMSE (Root Mean Squared Error) suele ser menor y los residuos se distribuyen mejor.
7.1.3 Modelo Final y Diagnósticos
modelo_final <- lm(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo
)
summary(modelo_final)
Call:
lm(formula = log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble, data = datos_modelo)
Residuals:
Min 1Q Median 3Q Max
-2.67580 -0.32532 -0.02115 0.30328 3.11329
Coefficients:
Estimate Std. Error t value Pr(>|t|)
(Intercept) 1.452e+01 4.648e-02 312.511 < 2e-16 ***
no_recamaras 2.101e-02 1.591e-02 1.320 0.187
no_banos 7.794e-02 1.135e-02 6.866 9.24e-12 ***
m2_construidos 3.471e-03 9.216e-05 37.667 < 2e-16 ***
region_precioBaja -5.584e-01 5.083e-02 -10.986 < 2e-16 ***
region_precioMedia -1.738e-01 3.279e-02 -5.302 1.30e-07 ***
tipo_inmuebleDepartamento 4.388e-01 3.151e-02 13.926 < 2e-16 ***
---
Signif. codes: 0 '***' 0.001 '**' 0.01 '*' 0.05 '.' 0.1 ' ' 1
Residual standard error: 0.5474 on 1682 degrees of freedom
Multiple R-squared: 0.5867, Adjusted R-squared: 0.5852
F-statistic: 397.9 on 6 and 1682 DF, p-value: < 2.2e-16Interpretación de coeficientes (en escala log):
- Un aumento de 1 m² construido → precio aumenta exp(coef) veces
- Los coeficientes de regiones miden diferencias multiplicativas
7.1.4 Diagnósticos Visuales
par(mfrow = c(2, 2))
plot(modelo_final)
par(mfrow = c(1, 1))Interpretación de gráficos:
- Residuals vs Fitted: Buscar patrón horizontal (linealidad)
- Q-Q Plot: Puntos en diagonal (normalidad)
- Scale-Location: Línea horizontal (homocedasticidad)
- Residuals vs Leverage: Detectar observaciones influyentes
7.2 2. Ridge Regression (Regularización L2)
7.2.1 Teoría: Ridge
Ridge añade una penalización L2 a la función de costo de OLS:
\[ \text{Minimizar: } \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 + \lambda \sum_{j=1}^{p} \beta_j^2 \]
Donde \(\lambda\) es el parámetro de regularización que controla:
- \(\lambda = 0\): Regresión lineal ordinaria
- \(\lambda \to \infty\): Todos los coeficientes → 0
Ventajas de Ridge:
- Reduce sobreajuste (menor varianza)
- Maneja multicolinealidad
- Estabiliza coeficientes
- Siempre tiene solución única
Desventajas:
- No elimina variables (no hace selección)
- Reduce todos los coeficientes proporcionalmente
7.2.2 Implementación
# Grid de lambdas a explorar
grid_ridge <- expand.grid(
alpha = 0, # alpha = 0 es Ridge
lambda = 10^seq(-3, 2, length.out = 50)
)
modelo_ridge_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "glmnet",
trControl = control_cv,
preProcess = c("center", "scale"),
tuneGrid = grid_ridge
)
print("=== Modelo Ridge ===")[1] "=== Modelo Ridge ==="print(modelo_ridge_cv)glmnet
1689 samples
5 predictor
Pre-processing: centered (6), scaled (6)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1521, 1519, 1520, 1522, 1521, 1519, ...
Resampling results across tuning parameters:
lambda RMSE Rsquared MAE
1.000000e-03 0.5575378 0.5779624 0.4105877
1.264855e-03 0.5575378 0.5779624 0.4105877
1.599859e-03 0.5575378 0.5779624 0.4105877
2.023590e-03 0.5575378 0.5779624 0.4105877
2.559548e-03 0.5575378 0.5779624 0.4105877
3.237458e-03 0.5575378 0.5779624 0.4105877
4.094915e-03 0.5575378 0.5779624 0.4105877
5.179475e-03 0.5575378 0.5779624 0.4105877
6.551286e-03 0.5575378 0.5779624 0.4105877
8.286428e-03 0.5575378 0.5779624 0.4105877
1.048113e-02 0.5575378 0.5779624 0.4105877
1.325711e-02 0.5575378 0.5779624 0.4105877
1.676833e-02 0.5575378 0.5779624 0.4105877
2.120951e-02 0.5575378 0.5779624 0.4105877
2.682696e-02 0.5575378 0.5779624 0.4105877
3.393222e-02 0.5575378 0.5779624 0.4105877
4.291934e-02 0.5575378 0.5779624 0.4105877
5.428675e-02 0.5575378 0.5779624 0.4105877
6.866488e-02 0.5581253 0.5777307 0.4119625
8.685114e-02 0.5593357 0.5772421 0.4145083
1.098541e-01 0.5612343 0.5764545 0.4177858
1.389495e-01 0.5640563 0.5752557 0.4219375
1.757511e-01 0.5680835 0.5734951 0.4271588
2.222996e-01 0.5735817 0.5710163 0.4335996
2.811769e-01 0.5808232 0.5676258 0.4416992
3.556480e-01 0.5899532 0.5631788 0.4516066
4.498433e-01 0.6010950 0.5574931 0.4635336
5.689866e-01 0.6141010 0.5505632 0.4771868
7.196857e-01 0.6288825 0.5423121 0.4919630
9.102982e-01 0.6449620 0.5330314 0.5073988
1.151395e+00 0.6621491 0.5227838 0.5233720
1.456348e+00 0.6797725 0.5121674 0.5391576
1.842070e+00 0.6976751 0.5012881 0.5549981
2.329952e+00 0.7151720 0.4908446 0.5703044
2.947052e+00 0.7321735 0.4808561 0.5848061
3.727594e+00 0.7481119 0.4718446 0.5981070
4.714866e+00 0.7629569 0.4637038 0.6105043
5.963623e+00 0.7763465 0.4566839 0.6216352
7.543120e+00 0.7883219 0.4506180 0.6316386
9.540955e+00 0.7987628 0.4455377 0.6406557
1.206793e+01 0.8077678 0.4412927 0.6485286
1.526418e+01 0.8154069 0.4377982 0.6552037
1.930698e+01 0.8218040 0.4349487 0.6607579
2.442053e+01 0.8271224 0.4326250 0.6653443
3.088844e+01 0.8314776 0.4307629 0.6690883
3.906940e+01 0.8350499 0.4292507 0.6721718
4.941713e+01 0.8379271 0.4280551 0.6746568
6.250552e+01 0.8402680 0.4270846 0.6766805
7.906043e+01 0.8421305 0.4263255 0.6782897
1.000000e+02 0.8436389 0.4257083 0.6795944
Tuning parameter 'alpha' was held constant at a value of 0
RMSE was used to select the optimal model using the smallest value.
The final values used for the model were alpha = 0 and lambda = 0.05428675.print(paste("Mejor lambda:", modelo_ridge_cv$bestTune$lambda))[1] "Mejor lambda: 0.0542867543932386"Decisión de preprocesamiento: center y scale son críticos en Ridge porque la penalización es sensible a la escala de las variables.
7.3 3. Lasso Regression (Regularización L1)
7.3.1 Teoría: Lasso
Lasso usa penalización L1 (valor absoluto):
\[ \text{Minimizar: } \sum_{i=1}^{n} (y_i - \hat{y}_i)^2 + \lambda \sum_{j=1}^{p} |\beta_j| \]
Diferencia clave con Ridge: Lasso puede forzar coeficientes exactamente a cero, realizando selección automática de variables.
Interpretación geométrica:
- Ridge: restricción esférica → coeficientes pequeños
- Lasso: restricción romboidal → soluciones sparse (ceros)
Ventajas de Lasso:
- Selección automática de variables
- Modelos más interpretables (menos variables)
- Útil con muchos predictores irrelevantes
Desventajas:
- Si hay variables correlacionadas, selecciona una arbitrariamente
- Puede ser inestable con correlaciones altas
7.3.2 Implementación
grid_lasso <- expand.grid(
alpha = 1, # alpha = 1 es Lasso
lambda = 10^seq(-3, 2, length.out = 50)
)
modelo_lasso_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "glmnet",
trControl = control_cv,
preProcess = c("center", "scale"),
tuneGrid = grid_lasso
)
print("=== Modelo Lasso ===")[1] "=== Modelo Lasso ==="print(modelo_lasso_cv)glmnet
1689 samples
5 predictor
Pre-processing: centered (6), scaled (6)
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1521, 1522, 1519, 1518, 1521, 1520, ...
Resampling results across tuning parameters:
lambda RMSE Rsquared MAE
1.000000e-03 0.5594438 0.5795249 0.4052258
1.264855e-03 0.5593914 0.5795600 0.4052156
1.599859e-03 0.5592203 0.5796761 0.4051800
2.023590e-03 0.5589976 0.5798156 0.4051980
2.559548e-03 0.5587036 0.5799977 0.4052383
3.237458e-03 0.5583384 0.5802261 0.4052894
4.094915e-03 0.5579013 0.5804999 0.4053563
5.179475e-03 0.5573662 0.5808411 0.4054389
6.551286e-03 0.5567428 0.5812411 0.4055721
8.286428e-03 0.5560720 0.5816749 0.4057861
1.048113e-02 0.5558144 0.5817390 0.4062692
1.325711e-02 0.5555948 0.5817436 0.4069412
1.676833e-02 0.5554722 0.5816348 0.4078698
2.120951e-02 0.5555169 0.5813862 0.4092086
2.682696e-02 0.5559301 0.5808337 0.4111493
3.393222e-02 0.5571386 0.5794880 0.4140074
4.291934e-02 0.5596896 0.5767665 0.4181681
5.428675e-02 0.5645262 0.5714781 0.4241723
6.866488e-02 0.5724557 0.5626351 0.4327051
8.685114e-02 0.5844493 0.5481733 0.4443857
1.098541e-01 0.6034402 0.5214914 0.4609220
1.389495e-01 0.6250163 0.4903233 0.4793206
1.757511e-01 0.6383935 0.4813105 0.4918457
2.222996e-01 0.6528885 0.4813049 0.5065083
2.811769e-01 0.6753681 0.4813049 0.5285298
3.556480e-01 0.7097724 0.4813049 0.5609391
4.498433e-01 0.7614840 0.4813049 0.6080746
5.689866e-01 0.8374737 0.4813049 0.6741772
7.196857e-01 0.8495160 NaN 0.6846719
9.102982e-01 0.8495160 NaN 0.6846719
1.151395e+00 0.8495160 NaN 0.6846719
1.456348e+00 0.8495160 NaN 0.6846719
1.842070e+00 0.8495160 NaN 0.6846719
2.329952e+00 0.8495160 NaN 0.6846719
2.947052e+00 0.8495160 NaN 0.6846719
3.727594e+00 0.8495160 NaN 0.6846719
4.714866e+00 0.8495160 NaN 0.6846719
5.963623e+00 0.8495160 NaN 0.6846719
7.543120e+00 0.8495160 NaN 0.6846719
9.540955e+00 0.8495160 NaN 0.6846719
1.206793e+01 0.8495160 NaN 0.6846719
1.526418e+01 0.8495160 NaN 0.6846719
1.930698e+01 0.8495160 NaN 0.6846719
2.442053e+01 0.8495160 NaN 0.6846719
3.088844e+01 0.8495160 NaN 0.6846719
3.906940e+01 0.8495160 NaN 0.6846719
4.941713e+01 0.8495160 NaN 0.6846719
6.250552e+01 0.8495160 NaN 0.6846719
7.906043e+01 0.8495160 NaN 0.6846719
1.000000e+02 0.8495160 NaN 0.6846719
Tuning parameter 'alpha' was held constant at a value of 1
RMSE was used to select the optimal model using the smallest value.
The final values used for the model were alpha = 1 and lambda = 0.01676833.print(paste("Mejor lambda:", modelo_lasso_cv$bestTune$lambda))[1] "Mejor lambda: 0.0167683293681101"# Ver coeficientes (detectar cuáles fueron eliminados)
coef_lasso <- coef(modelo_lasso_cv$finalModel,
s = modelo_lasso_cv$bestTune$lambda)
print("Coeficientes Lasso:")[1] "Coeficientes Lasso:"print(coef_lasso)7 x 1 sparse Matrix of class "dgCMatrix"
s0
(Intercept) 15.746938702
no_recamaras 0.006342328
no_banos 0.130296880
m2_construidos 0.592041792
region_precioBaja -0.132722709
region_precioMedia -0.054318430
tipo_inmuebleDepartamento 0.1896499197.4 4. Árbol de Decisión
7.4.1 Teoría: Árboles de Regresión
Los árboles de decisión dividen recursivamente el espacio de características mediante reglas if-then. Para regresión:
- En cada nodo, seleccionar la variable y punto de corte que minimiza el error cuadrático
- Dividir datos en dos grupos
- Repetir hasta alcanzar criterio de parada (profundidad, nº mínimo de observaciones)
Función objetivo en cada división:
\[ \text{Minimizar: } \sum_{i \in R_1} (y_i - \bar{y}_{R_1})^2 + \sum_{i \in R_2} (y_i - \bar{y}_{R_2})^2 \]
Ventajas:
- No requieren supuestos de distribución
- Manejan relaciones no lineales
- Interpretan interacciones automáticamente
- Fáciles de visualizar
Desventajas:
- Alta varianza (inestables)
- Propensos a sobreajuste
- Sesgados hacia variables con muchas categorías
7.4.2 Implementación
modelo_arbol_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "rpart",
trControl = control_cv,
tuneLength = 10 # Explorar 10 valores de complejidad
)
print("=== Modelo Árbol de Decisión ===")[1] "=== Modelo Árbol de Decisión ==="print(modelo_arbol_cv)CART
1689 samples
5 predictor
No pre-processing
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1520, 1520, 1519, 1521, 1521, 1520, ...
Resampling results across tuning parameters:
cp RMSE Rsquared MAE
0.006509812 0.4931319 0.6621147 0.3724916
0.010772246 0.5016818 0.6499576 0.3782404
0.013608052 0.5160467 0.6305145 0.3923552
0.023404937 0.5341910 0.6023641 0.4091088
0.024777533 0.5495005 0.5796565 0.4280810
0.026363781 0.5612526 0.5624456 0.4415225
0.027150445 0.5638151 0.5586307 0.4446405
0.037125209 0.6207337 0.4677604 0.4861904
0.095752886 0.6593129 0.4005609 0.5185379
0.372650699 0.7939124 0.3037910 0.6341170
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was cp = 0.006509812.# Visualizar árbol
rpart.plot::rpart.plot(
modelo_arbol_cv$finalModel,
main = "Árbol de Decisión para log(precio)",
roundint = FALSE
)
7.5 5. Random Forest
7.5.1 Teoría: Random Forest
Random Forest es un método ensemble que combina múltiples árboles de decisión mediante bagging (Bootstrap Aggregating):
Algoritmo:
- Crear B muestras bootstrap del dataset original
- Para cada muestra:
- Entrenar un árbol de decisión
- En cada nodo, considerar solo un subconjunto aleatorio de m variables
- Predicción final = promedio de predicciones de todos los árboles
Hiperparámetros clave:
ntree: Número de árboles (más = más estable pero más lento)mtry: Número de variables en cada división (típicamente √p o p/3)nodesize: Tamaño mínimo de nodos terminales
Por qué funciona:
- Reducción de varianza: Promediar árboles reduce varianza sin aumentar sesgo
- Decorrelación: Selección aleatoria de variables decorrelaciona árboles
- Out-of-Bag (OOB) error: ~37% de datos no usados en cada árbol → validación “gratis”
Ventajas:
- Excelente rendimiento predictivo
- Robusto a outliers
- Maneja variables categóricas y numéricas
- Proporciona importancia de variables
- Poco sensible a hiperparámetros
Desventajas:
- Menos interpretable que árbol simple
- Más lento que modelos lineales
- Requiere más memoria
7.5.2 Implementación
modelo_rf_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "rf",
trControl = control_cv,
tuneLength = 5,
importance = TRUE
)
print("=== Modelo Random Forest ===")[1] "=== Modelo Random Forest ==="print(modelo_rf_cv)Random Forest
1689 samples
5 predictor
No pre-processing
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1521, 1520, 1521, 1521, 1519, 1521, ...
Resampling results across tuning parameters:
mtry RMSE Rsquared MAE
2 0.4465293 0.7312227 0.3379810
3 0.4395569 0.7323139 0.3299588
4 0.4482653 0.7220390 0.3370972
5 0.4579037 0.7107590 0.3443436
6 0.4640370 0.7037188 0.3491169
RMSE was used to select the optimal model using the smallest value.
The final value used for the model was mtry = 3.# Importancia de variables
importancia_rf <- varImp(modelo_rf_cv, scale = TRUE) %>%
.$importance %>%
as_tibble(rownames = "variable") %>%
arrange(desc(Overall))
print("Importancia de variables:")[1] "Importancia de variables:"print(importancia_rf)# A tibble: 6 × 2
variable Overall
<chr> <dbl>
1 m2_construidos 100
2 tipo_inmuebleDepartamento 59.1
3 region_precioBaja 11.7
4 region_precioMedia 4.05
5 no_recamaras 0.921
6 no_banos 0 # Visualizar importancia
importancia_rf %>%
ggplot(aes(x = reorder(variable, Overall), y = Overall)) +
geom_col(fill = "steelblue") +
coord_flip() +
labs(
title = "Importancia de Variables según Random Forest",
x = "Variable",
y = "Importancia (Overall)"
)
7.6 6. XGBoost
7.6.1 Teoría: XGBoost (eXtreme Gradient Boosting)
XGBoost es una implementación optimizada de gradient boosting, diferente de bagging (Random Forest):
Gradient Boosting:
- Iniciar con un modelo simple (constante)
- Para t = 1 a T:
- Calcular residuos del modelo actual
- Entrenar nuevo árbol para predecir residuos
- Añadir árbol al modelo con peso η (learning rate)
- Predicción final = suma ponderada de todos los árboles
Función objetivo de XGBoost:
\[ \mathcal{L} = \sum_{i=1}^{n} l(y_i, \hat{y}_i) + \sum_{k=1}^{K} \Omega(f_k) \]
Donde:
- \(l\): función de pérdida (MSE para regresión)
- \(\Omega\): término de regularización (penaliza complejidad del árbol)
Hiperparámetros clave:
nrounds: Número de árboles (iteraciones de boosting)max_depth: Profundidad máxima de cada árboleta: Learning rate (típicamente 0.01-0.3)subsample: Fracción de datos para cada árbol (previene sobreajuste)colsample_bytree: Fracción de variables para cada árbolgamma: Reducción mínima de pérdida para hacer divisiónlambda(L2) yalpha(L1): Regularización en pesos de hojas
Ventajas de XGBoost sobre Gradient Boosting tradicional:
- Regularización incorporada: Previene sobreajuste
- Manejo de missing values: Aprende mejor dirección para NAs
- Paralelización: Construcción paralela de árboles
- Optimización de hardware: Cache-aware, out-of-core computing
- Stopping temprano: Detiene si no mejora en validación
XGBoost vs Random Forest:
| Aspecto | Random Forest | XGBoost |
|---|---|---|
| Estrategia | Bagging | Boosting |
| Árboles | Independientes | Secuenciales |
| Profundidad típica | Profunda | Poco profunda |
| Velocidad | Más rápido | Más lento |
| Interpretabilidad | Media | Baja |
| Riesgo sobreajuste | Bajo | Medio-Alto |
7.6.2 Implementación con Paralelización
# XGBoost con tuning exhaustivo y paralelización activada
modelo_xgb_cv <- train(
log_precio ~ no_recamaras + no_banos + m2_construidos +
region_precio + tipo_inmueble,
data = datos_modelo,
method = "xgbTree",
trControl = control_cv, # allowParallel = TRUE ya está configurado
tuneLength = 10, # Explorar 10 combinaciones
verbose = FALSE,
# Parámetros específicos de XGBoost para paralelización
nthread = n_cores # Usar todos los cores disponibles
)
print("=== Modelo XGBoost ===")[1] "=== Modelo XGBoost ==="print(modelo_xgb_cv)eXtreme Gradient Boosting
1689 samples
5 predictor
No pre-processing
Resampling: Cross-Validated (10 fold)
Summary of sample sizes: 1519, 1520, 1522, 1520, 1519, 1520, ...
Resampling results across tuning parameters:
eta max_depth colsample_bytree subsample nrounds RMSE Rsquared
0.3 1 0.6 0.5000000 50 0.5073034 0.6460192
0.3 1 0.6 0.5000000 100 0.5002547 0.6544065
0.3 1 0.6 0.5000000 150 0.5011930 0.6537121
0.3 1 0.6 0.5000000 200 0.4971854 0.6589928
0.3 1 0.6 0.5000000 250 0.5017181 0.6528528
0.3 1 0.6 0.5000000 300 0.5010562 0.6542530
0.3 1 0.6 0.5000000 350 0.5023623 0.6530536
0.3 1 0.6 0.5000000 400 0.5011538 0.6543470
0.3 1 0.6 0.5000000 450 0.5027865 0.6520239
0.3 1 0.6 0.5000000 500 0.5043940 0.6509050
0.3 1 0.6 0.5555556 50 0.5030188 0.6522604
0.3 1 0.6 0.5555556 100 0.4936936 0.6626644
0.3 1 0.6 0.5555556 150 0.4978855 0.6574428
0.3 1 0.6 0.5555556 200 0.4956540 0.6608166
0.3 1 0.6 0.5555556 250 0.5006525 0.6538069
0.3 1 0.6 0.5555556 300 0.5009301 0.6535579
0.3 1 0.6 0.5555556 350 0.5000187 0.6549249
0.3 1 0.6 0.5555556 400 0.5034390 0.6501385
0.3 1 0.6 0.5555556 450 0.5031807 0.6509888
0.3 1 0.6 0.5555556 500 0.5059929 0.6476991
0.3 1 0.6 0.6111111 50 0.5046962 0.6503603
0.3 1 0.6 0.6111111 100 0.4983607 0.6572605
0.3 1 0.6 0.6111111 150 0.4974998 0.6583019
0.3 1 0.6 0.6111111 200 0.4998101 0.6551635
0.3 1 0.6 0.6111111 250 0.4990730 0.6564492
0.3 1 0.6 0.6111111 300 0.5024083 0.6521672
0.3 1 0.6 0.6111111 350 0.5027806 0.6518042
0.3 1 0.6 0.6111111 400 0.5084000 0.6442372
0.3 1 0.6 0.6111111 450 0.5038603 0.6502673
0.3 1 0.6 0.6111111 500 0.5076534 0.6456088
0.3 1 0.6 0.6666667 50 0.5046666 0.6502518
0.3 1 0.6 0.6666667 100 0.4967951 0.6588428
0.3 1 0.6 0.6666667 150 0.4940987 0.6627292
0.3 1 0.6 0.6666667 200 0.4968959 0.6588606
0.3 1 0.6 0.6666667 250 0.4986819 0.6568994
0.3 1 0.6 0.6666667 300 0.5028874 0.6513888
0.3 1 0.6 0.6666667 350 0.5027741 0.6515172
0.3 1 0.6 0.6666667 400 0.5050512 0.6489871
0.3 1 0.6 0.6666667 450 0.5042977 0.6496751
0.3 1 0.6 0.6666667 500 0.5065662 0.6465921
0.3 1 0.6 0.7222222 50 0.5030977 0.6531826
0.3 1 0.6 0.7222222 100 0.4997385 0.6550232
0.3 1 0.6 0.7222222 150 0.4984274 0.6566782
0.3 1 0.6 0.7222222 200 0.5006583 0.6541216
0.3 1 0.6 0.7222222 250 0.4991330 0.6561763
0.3 1 0.6 0.7222222 300 0.5006512 0.6544211
0.3 1 0.6 0.7222222 350 0.5028240 0.6516478
0.3 1 0.6 0.7222222 400 0.5039734 0.6501339
0.3 1 0.6 0.7222222 450 0.5055192 0.6478468
0.3 1 0.6 0.7222222 500 0.5054897 0.6478503
0.3 1 0.6 0.7777778 50 0.5046597 0.6515085
0.3 1 0.6 0.7777778 100 0.4996684 0.6548028
0.3 1 0.6 0.7777778 150 0.5011174 0.6533121
0.3 1 0.6 0.7777778 200 0.4981400 0.6575574
0.3 1 0.6 0.7777778 250 0.4996529 0.6557188
0.3 1 0.6 0.7777778 300 0.5004205 0.6542447
0.3 1 0.6 0.7777778 350 0.5013412 0.6534394
0.3 1 0.6 0.7777778 400 0.5030001 0.6513944
0.3 1 0.6 0.7777778 450 0.5028442 0.6514589
0.3 1 0.6 0.7777778 500 0.5042177 0.6496899
0.3 1 0.6 0.8333333 50 0.5035351 0.6532705
0.3 1 0.6 0.8333333 100 0.4942483 0.6631116
0.3 1 0.6 0.8333333 150 0.4935198 0.6639638
0.3 1 0.6 0.8333333 200 0.4949417 0.6622841
0.3 1 0.6 0.8333333 250 0.4982459 0.6577869
0.3 1 0.6 0.8333333 300 0.4974151 0.6590512
0.3 1 0.6 0.8333333 350 0.5002947 0.6551968
0.3 1 0.6 0.8333333 400 0.5017970 0.6531780
0.3 1 0.6 0.8333333 450 0.5011420 0.6538782
0.3 1 0.6 0.8333333 500 0.5033214 0.6513535
0.3 1 0.6 0.8888889 50 0.5049143 0.6503729
0.3 1 0.6 0.8888889 100 0.4946415 0.6618157
0.3 1 0.6 0.8888889 150 0.4952945 0.6612571
0.3 1 0.6 0.8888889 200 0.4963494 0.6599098
0.3 1 0.6 0.8888889 250 0.4983919 0.6574225
0.3 1 0.6 0.8888889 300 0.5002080 0.6549875
0.3 1 0.6 0.8888889 350 0.5009780 0.6542454
0.3 1 0.6 0.8888889 400 0.5032999 0.6513411
0.3 1 0.6 0.8888889 450 0.5025896 0.6524113
0.3 1 0.6 0.8888889 500 0.5045820 0.6500624
0.3 1 0.6 0.9444444 50 0.5040204 0.6520452
0.3 1 0.6 0.9444444 100 0.4969852 0.6590870
0.3 1 0.6 0.9444444 150 0.4949640 0.6615030
0.3 1 0.6 0.9444444 200 0.4956577 0.6609253
0.3 1 0.6 0.9444444 250 0.4954221 0.6614836
0.3 1 0.6 0.9444444 300 0.4976829 0.6583998
0.3 1 0.6 0.9444444 350 0.4989744 0.6567875
0.3 1 0.6 0.9444444 400 0.4996293 0.6560213
0.3 1 0.6 0.9444444 450 0.5003542 0.6550763
0.3 1 0.6 0.9444444 500 0.5010068 0.6543336
0.3 1 0.6 1.0000000 50 0.5021826 0.6555502
0.3 1 0.6 1.0000000 100 0.4934465 0.6640351
0.3 1 0.6 1.0000000 150 0.4936625 0.6634570
0.3 1 0.6 1.0000000 200 0.4935665 0.6636562
0.3 1 0.6 1.0000000 250 0.4937785 0.6633312
0.3 1 0.6 1.0000000 300 0.4924217 0.6653970
0.3 1 0.6 1.0000000 350 0.4931365 0.6645364
0.3 1 0.6 1.0000000 400 0.4932608 0.6644970
0.3 1 0.6 1.0000000 450 0.4941712 0.6633982
0.3 1 0.6 1.0000000 500 0.4945199 0.6631587
0.3 1 0.8 0.5000000 50 0.5036421 0.6497620
0.3 1 0.8 0.5000000 100 0.4959755 0.6599730
0.3 1 0.8 0.5000000 150 0.4977695 0.6578924
0.3 1 0.8 0.5000000 200 0.5027675 0.6520151
0.3 1 0.8 0.5000000 250 0.4994728 0.6565206
0.3 1 0.8 0.5000000 300 0.5007394 0.6545074
0.3 1 0.8 0.5000000 350 0.5011591 0.6543820
0.3 1 0.8 0.5000000 400 0.5053422 0.6487010
0.3 1 0.8 0.5000000 450 0.5077913 0.6454542
0.3 1 0.8 0.5000000 500 0.5050387 0.6498717
0.3 1 0.8 0.5555556 50 0.5039326 0.6496611
0.3 1 0.8 0.5555556 100 0.4993366 0.6552477
0.3 1 0.8 0.5555556 150 0.5016268 0.6528868
0.3 1 0.8 0.5555556 200 0.5009608 0.6536074
0.3 1 0.8 0.5555556 250 0.4994249 0.6564687
0.3 1 0.8 0.5555556 300 0.5040132 0.6502396
0.3 1 0.8 0.5555556 350 0.5048064 0.6487972
0.3 1 0.8 0.5555556 400 0.5104348 0.6420375
0.3 1 0.8 0.5555556 450 0.5091488 0.6440950
0.3 1 0.8 0.5555556 500 0.5086973 0.6434427
0.3 1 0.8 0.6111111 50 0.5035046 0.6510405
0.3 1 0.8 0.6111111 100 0.5026700 0.6507790
0.3 1 0.8 0.6111111 150 0.5006427 0.6537367
0.3 1 0.8 0.6111111 200 0.5012255 0.6529475
0.3 1 0.8 0.6111111 250 0.5035319 0.6504080
0.3 1 0.8 0.6111111 300 0.5034999 0.6499951
0.3 1 0.8 0.6111111 350 0.5063167 0.6471050
0.3 1 0.8 0.6111111 400 0.5087648 0.6432656
0.3 1 0.8 0.6111111 450 0.5078335 0.6451929
0.3 1 0.8 0.6111111 500 0.5091445 0.6432802
0.3 1 0.8 0.6666667 50 0.5065677 0.6471772
0.3 1 0.8 0.6666667 100 0.5024328 0.6509409
0.3 1 0.8 0.6666667 150 0.5029652 0.6503323
0.3 1 0.8 0.6666667 200 0.5044089 0.6486173
0.3 1 0.8 0.6666667 250 0.5037283 0.6498888
0.3 1 0.8 0.6666667 300 0.5060686 0.6467530
0.3 1 0.8 0.6666667 350 0.5088299 0.6434272
0.3 1 0.8 0.6666667 400 0.5066671 0.6463600
0.3 1 0.8 0.6666667 450 0.5042138 0.6496996
0.3 1 0.8 0.6666667 500 0.5072204 0.6454692
0.3 1 0.8 0.7222222 50 0.5021670 0.6537276
0.3 1 0.8 0.7222222 100 0.4968638 0.6591076
0.3 1 0.8 0.7222222 150 0.4972301 0.6589622
0.3 1 0.8 0.7222222 200 0.4970271 0.6593987
0.3 1 0.8 0.7222222 250 0.5007344 0.6542546
0.3 1 0.8 0.7222222 300 0.5007479 0.6545635
0.3 1 0.8 0.7222222 350 0.5035963 0.6508525
0.3 1 0.8 0.7222222 400 0.5023724 0.6522442
0.3 1 0.8 0.7222222 450 0.5033709 0.6514497
0.3 1 0.8 0.7222222 500 0.5059626 0.6478958
0.3 1 0.8 0.7777778 50 0.5022004 0.6535458
0.3 1 0.8 0.7777778 100 0.4971032 0.6585419
0.3 1 0.8 0.7777778 150 0.5011936 0.6534144
0.3 1 0.8 0.7777778 200 0.5007562 0.6540465
0.3 1 0.8 0.7777778 250 0.5027045 0.6519654
0.3 1 0.8 0.7777778 300 0.5045687 0.6493073
0.3 1 0.8 0.7777778 350 0.5068965 0.6464485
0.3 1 0.8 0.7777778 400 0.5090371 0.6439022
0.3 1 0.8 0.7777778 450 0.5073807 0.6459198
0.3 1 0.8 0.7777778 500 0.5110932 0.6410084
0.3 1 0.8 0.8333333 50 0.5054847 0.6496645
0.3 1 0.8 0.8333333 100 0.4979696 0.6581690
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0.4 9 0.8 0.8888889 450 0.5247888 0.6432474
0.4 9 0.8 0.8888889 500 0.5267507 0.6411796
0.4 9 0.8 0.9444444 50 0.4669491 0.7027759
0.4 9 0.8 0.9444444 100 0.4918599 0.6770293
0.4 9 0.8 0.9444444 150 0.5054573 0.6623807
0.4 9 0.8 0.9444444 200 0.5112064 0.6562501
0.4 9 0.8 0.9444444 250 0.5164706 0.6504672
0.4 9 0.8 0.9444444 300 0.5174156 0.6496526
0.4 9 0.8 0.9444444 350 0.5192739 0.6477225
0.4 9 0.8 0.9444444 400 0.5207234 0.6464123
0.4 9 0.8 0.9444444 450 0.5222916 0.6443933
0.4 9 0.8 0.9444444 500 0.5232482 0.6429877
0.4 9 0.8 1.0000000 50 0.4616291 0.7097785
0.4 9 0.8 1.0000000 100 0.4807946 0.6893815
0.4 9 0.8 1.0000000 150 0.4910040 0.6788293
0.4 9 0.8 1.0000000 200 0.5002024 0.6695156
0.4 9 0.8 1.0000000 250 0.5058934 0.6635013
0.4 9 0.8 1.0000000 300 0.5088946 0.6605102
0.4 9 0.8 1.0000000 350 0.5107104 0.6586429
0.4 9 0.8 1.0000000 400 0.5113728 0.6580186
0.4 9 0.8 1.0000000 450 0.5113755 0.6580185
0.4 9 0.8 1.0000000 500 0.5113755 0.6580185
0.4 10 0.6 0.5000000 50 0.4926542 0.6724825
0.4 10 0.6 0.5000000 100 0.5175974 0.6469229
0.4 10 0.6 0.5000000 150 0.5296116 0.6348392
0.4 10 0.6 0.5000000 200 0.5397113 0.6240356
0.4 10 0.6 0.5000000 250 0.5480627 0.6152689
0.4 10 0.6 0.5000000 300 0.5534539 0.6111384
0.4 10 0.6 0.5000000 350 0.5579504 0.6067063
0.4 10 0.6 0.5000000 400 0.5668044 0.5970046
0.4 10 0.6 0.5000000 450 0.5701567 0.5942115
0.4 10 0.6 0.5000000 500 0.5765493 0.5878685
0.4 10 0.6 0.5555556 50 0.4939367 0.6728596
0.4 10 0.6 0.5555556 100 0.5174487 0.6487064
0.4 10 0.6 0.5555556 150 0.5306000 0.6349950
0.4 10 0.6 0.5555556 200 0.5423418 0.6228762
0.4 10 0.6 0.5555556 250 0.5516802 0.6137466
0.4 10 0.6 0.5555556 300 0.5578388 0.6072638
0.4 10 0.6 0.5555556 350 0.5599402 0.6050452
0.4 10 0.6 0.5555556 400 0.5652327 0.5994264
0.4 10 0.6 0.5555556 450 0.5687169 0.5979602
0.4 10 0.6 0.5555556 500 0.5695519 0.5964085
0.4 10 0.6 0.6111111 50 0.4836890 0.6864668
0.4 10 0.6 0.6111111 100 0.5143257 0.6538929
0.4 10 0.6 0.6111111 150 0.5258013 0.6423529
0.4 10 0.6 0.6111111 200 0.5364595 0.6324306
0.4 10 0.6 0.6111111 250 0.5419122 0.6271500
0.4 10 0.6 0.6111111 300 0.5480341 0.6214886
0.4 10 0.6 0.6111111 350 0.5544179 0.6144079
0.4 10 0.6 0.6111111 400 0.5586136 0.6096943
0.4 10 0.6 0.6111111 450 0.5610869 0.6076939
0.4 10 0.6 0.6111111 500 0.5611604 0.6084807
0.4 10 0.6 0.6666667 50 0.4878077 0.6780553
0.4 10 0.6 0.6666667 100 0.5092079 0.6555916
0.4 10 0.6 0.6666667 150 0.5234880 0.6399881
0.4 10 0.6 0.6666667 200 0.5294726 0.6348362
0.4 10 0.6 0.6666667 250 0.5355859 0.6284622
0.4 10 0.6 0.6666667 300 0.5388615 0.6244834
0.4 10 0.6 0.6666667 350 0.5423329 0.6202252
0.4 10 0.6 0.6666667 400 0.5471184 0.6145388
0.4 10 0.6 0.6666667 450 0.5467832 0.6153326
0.4 10 0.6 0.6666667 500 0.5491959 0.6128673
0.4 10 0.6 0.7222222 50 0.4848148 0.6826652
0.4 10 0.6 0.7222222 100 0.5094820 0.6579481
0.4 10 0.6 0.7222222 150 0.5232726 0.6439800
0.4 10 0.6 0.7222222 200 0.5320598 0.6348776
0.4 10 0.6 0.7222222 250 0.5375069 0.6296676
0.4 10 0.6 0.7222222 300 0.5401590 0.6269178
0.4 10 0.6 0.7222222 350 0.5422706 0.6251708
0.4 10 0.6 0.7222222 400 0.5429827 0.6241124
0.4 10 0.6 0.7222222 450 0.5458591 0.6207731
0.4 10 0.6 0.7222222 500 0.5474430 0.6193916
0.4 10 0.6 0.7777778 50 0.4827766 0.6850743
0.4 10 0.6 0.7777778 100 0.5045785 0.6633580
0.4 10 0.6 0.7777778 150 0.5158973 0.6514839
0.4 10 0.6 0.7777778 200 0.5243340 0.6428300
0.4 10 0.6 0.7777778 250 0.5290326 0.6378946
0.4 10 0.6 0.7777778 300 0.5332451 0.6332405
0.4 10 0.6 0.7777778 350 0.5338810 0.6330972
0.4 10 0.6 0.7777778 400 0.5361072 0.6303947
0.4 10 0.6 0.7777778 450 0.5384734 0.6279511
0.4 10 0.6 0.7777778 500 0.5403224 0.6266933
0.4 10 0.6 0.8333333 50 0.4837989 0.6819485
0.4 10 0.6 0.8333333 100 0.5078996 0.6573733
0.4 10 0.6 0.8333333 150 0.5188861 0.6463381
0.4 10 0.6 0.8333333 200 0.5250438 0.6401616
0.4 10 0.6 0.8333333 250 0.5291721 0.6359092
0.4 10 0.6 0.8333333 300 0.5335733 0.6311246
0.4 10 0.6 0.8333333 350 0.5359966 0.6283772
0.4 10 0.6 0.8333333 400 0.5392619 0.6244164
0.4 10 0.6 0.8333333 450 0.5393920 0.6250225
0.4 10 0.6 0.8333333 500 0.5411991 0.6233428
0.4 10 0.6 0.8888889 50 0.4750547 0.6946326
0.4 10 0.6 0.8888889 100 0.4980407 0.6704713
0.4 10 0.6 0.8888889 150 0.5109410 0.6568653
0.4 10 0.6 0.8888889 200 0.5180377 0.6495968
0.4 10 0.6 0.8888889 250 0.5227259 0.6447165
0.4 10 0.6 0.8888889 300 0.5263105 0.6414040
0.4 10 0.6 0.8888889 350 0.5288357 0.6385339
0.4 10 0.6 0.8888889 400 0.5304430 0.6368488
0.4 10 0.6 0.8888889 450 0.5313492 0.6361855
0.4 10 0.6 0.8888889 500 0.5324548 0.6357127
0.4 10 0.6 0.9444444 50 0.4777410 0.6924497
0.4 10 0.6 0.9444444 100 0.4971654 0.6725604
0.4 10 0.6 0.9444444 150 0.5090694 0.6604408
0.4 10 0.6 0.9444444 200 0.5156993 0.6536561
0.4 10 0.6 0.9444444 250 0.5217456 0.6471357
0.4 10 0.6 0.9444444 300 0.5245284 0.6443143
0.4 10 0.6 0.9444444 350 0.5273981 0.6413400
0.4 10 0.6 0.9444444 400 0.5292936 0.6391536
0.4 10 0.6 0.9444444 450 0.5307081 0.6377619
0.4 10 0.6 0.9444444 500 0.5310425 0.6378564
0.4 10 0.6 1.0000000 50 0.4704698 0.6985261
0.4 10 0.6 1.0000000 100 0.4836593 0.6849063
0.4 10 0.6 1.0000000 150 0.4947018 0.6734116
0.4 10 0.6 1.0000000 200 0.5036923 0.6639535
0.4 10 0.6 1.0000000 250 0.5086952 0.6586328
0.4 10 0.6 1.0000000 300 0.5123261 0.6549466
0.4 10 0.6 1.0000000 350 0.5156887 0.6513872
0.4 10 0.6 1.0000000 400 0.5180290 0.6489758
0.4 10 0.6 1.0000000 450 0.5197637 0.6471994
0.4 10 0.6 1.0000000 500 0.5208643 0.6460651
0.4 10 0.8 0.5000000 50 0.5052131 0.6613237
0.4 10 0.8 0.5000000 100 0.5273500 0.6406537
0.4 10 0.8 0.5000000 150 0.5397774 0.6274539
0.4 10 0.8 0.5000000 200 0.5498478 0.6171002
0.4 10 0.8 0.5000000 250 0.5541308 0.6142459
0.4 10 0.8 0.5000000 300 0.5621634 0.6068000
0.4 10 0.8 0.5000000 350 0.5670664 0.6031228
0.4 10 0.8 0.5000000 400 0.5706738 0.5997799
0.4 10 0.8 0.5000000 450 0.5784788 0.5926438
0.4 10 0.8 0.5000000 500 0.5758732 0.5963416
0.4 10 0.8 0.5555556 50 0.4896874 0.6783481
0.4 10 0.8 0.5555556 100 0.5176520 0.6488855
0.4 10 0.8 0.5555556 150 0.5314023 0.6352985
0.4 10 0.8 0.5555556 200 0.5354526 0.6320463
0.4 10 0.8 0.5555556 250 0.5384097 0.6298417
0.4 10 0.8 0.5555556 300 0.5469201 0.6196811
0.4 10 0.8 0.5555556 350 0.5480156 0.6191562
0.4 10 0.8 0.5555556 400 0.5529742 0.6141351
0.4 10 0.8 0.5555556 450 0.5573936 0.6095784
0.4 10 0.8 0.5555556 500 0.5563962 0.6114982
0.4 10 0.8 0.6111111 50 0.4998449 0.6684374
0.4 10 0.8 0.6111111 100 0.5240473 0.6439472
0.4 10 0.8 0.6111111 150 0.5337538 0.6345116
0.4 10 0.8 0.6111111 200 0.5357101 0.6318590
0.4 10 0.8 0.6111111 250 0.5416213 0.6275574
0.4 10 0.8 0.6111111 300 0.5423045 0.6263138
0.4 10 0.8 0.6111111 350 0.5434535 0.6247876
0.4 10 0.8 0.6111111 400 0.5480773 0.6202982
0.4 10 0.8 0.6111111 450 0.5485886 0.6203821
0.4 10 0.8 0.6111111 500 0.5513831 0.6175763
0.4 10 0.8 0.6666667 50 0.5007757 0.6657292
0.4 10 0.8 0.6666667 100 0.5186957 0.6480409
0.4 10 0.8 0.6666667 150 0.5316091 0.6328345
0.4 10 0.8 0.6666667 200 0.5374636 0.6278297
0.4 10 0.8 0.6666667 250 0.5413171 0.6236713
0.4 10 0.8 0.6666667 300 0.5444995 0.6208180
0.4 10 0.8 0.6666667 350 0.5468457 0.6186157
0.4 10 0.8 0.6666667 400 0.5529579 0.6118435
0.4 10 0.8 0.6666667 450 0.5547605 0.6099136
0.4 10 0.8 0.6666667 500 0.5529454 0.6128355
0.4 10 0.8 0.7222222 50 0.4908990 0.6793221
0.4 10 0.8 0.7222222 100 0.5210907 0.6472921
0.4 10 0.8 0.7222222 150 0.5336358 0.6334857
0.4 10 0.8 0.7222222 200 0.5389455 0.6281170
0.4 10 0.8 0.7222222 250 0.5402605 0.6265834
0.4 10 0.8 0.7222222 300 0.5441391 0.6231356
0.4 10 0.8 0.7222222 350 0.5448107 0.6221515
0.4 10 0.8 0.7222222 400 0.5479827 0.6188079
0.4 10 0.8 0.7222222 450 0.5499700 0.6168188
0.4 10 0.8 0.7222222 500 0.5526998 0.6139386
0.4 10 0.8 0.7777778 50 0.4919778 0.6754883
0.4 10 0.8 0.7777778 100 0.5169568 0.6491004
0.4 10 0.8 0.7777778 150 0.5265855 0.6399169
0.4 10 0.8 0.7777778 200 0.5313992 0.6345970
0.4 10 0.8 0.7777778 250 0.5361779 0.6288633
0.4 10 0.8 0.7777778 300 0.5398261 0.6252376
0.4 10 0.8 0.7777778 350 0.5407902 0.6240858
0.4 10 0.8 0.7777778 400 0.5431344 0.6221385
0.4 10 0.8 0.7777778 450 0.5446065 0.6198423
0.4 10 0.8 0.7777778 500 0.5425710 0.6216261
0.4 10 0.8 0.8333333 50 0.4842521 0.6842747
0.4 10 0.8 0.8333333 100 0.5111972 0.6552987
0.4 10 0.8 0.8333333 150 0.5194393 0.6463784
0.4 10 0.8 0.8333333 200 0.5242023 0.6409643
0.4 10 0.8 0.8333333 250 0.5256505 0.6402171
0.4 10 0.8 0.8333333 300 0.5274158 0.6382532
0.4 10 0.8 0.8333333 350 0.5288984 0.6372616
0.4 10 0.8 0.8333333 400 0.5315218 0.6339830
0.4 10 0.8 0.8333333 450 0.5309516 0.6352119
0.4 10 0.8 0.8333333 500 0.5320521 0.6339339
0.4 10 0.8 0.8888889 50 0.5001305 0.6648921
0.4 10 0.8 0.8888889 100 0.5206408 0.6433631
0.4 10 0.8 0.8888889 150 0.5284530 0.6358086
0.4 10 0.8 0.8888889 200 0.5310833 0.6330348
0.4 10 0.8 0.8888889 250 0.5351881 0.6280298
0.4 10 0.8 0.8888889 300 0.5370527 0.6262377
0.4 10 0.8 0.8888889 350 0.5398924 0.6232408
0.4 10 0.8 0.8888889 400 0.5406879 0.6225045
0.4 10 0.8 0.8888889 450 0.5408321 0.6221319
0.4 10 0.8 0.8888889 500 0.5417861 0.6210546
0.4 10 0.8 0.9444444 50 0.4842488 0.6843933
0.4 10 0.8 0.9444444 100 0.5071155 0.6601502
0.4 10 0.8 0.9444444 150 0.5169231 0.6500689
0.4 10 0.8 0.9444444 200 0.5198196 0.6473404
0.4 10 0.8 0.9444444 250 0.5226527 0.6442798
0.4 10 0.8 0.9444444 300 0.5242040 0.6425082
0.4 10 0.8 0.9444444 350 0.5241700 0.6426060
0.4 10 0.8 0.9444444 400 0.5242670 0.6426062
0.4 10 0.8 0.9444444 450 0.5232753 0.6439649
0.4 10 0.8 0.9444444 500 0.5241756 0.6426119
0.4 10 0.8 1.0000000 50 0.4740311 0.6955040
0.4 10 0.8 1.0000000 100 0.4948446 0.6732473
0.4 10 0.8 1.0000000 150 0.5059824 0.6615571
0.4 10 0.8 1.0000000 200 0.5131160 0.6539541
0.4 10 0.8 1.0000000 250 0.5167669 0.6501893
0.4 10 0.8 1.0000000 300 0.5187152 0.6481556
0.4 10 0.8 1.0000000 350 0.5188772 0.6480019
0.4 10 0.8 1.0000000 400 0.5188772 0.6480019
0.4 10 0.8 1.0000000 450 0.5188772 0.6480019
0.4 10 0.8 1.0000000 500 0.5188772 0.6480019
MAE
0.3748499
0.3618002
0.3597149
0.3556382
0.3573180
0.3577705
0.3580801
0.3575516
0.3573337
0.3568103
0.3728231
0.3591138
0.3578991
0.3559402
0.3559834
0.3546309
0.3548748
0.3555006
0.3557078
0.3561972
0.3741198
0.3620757
0.3587898
0.3583054
0.3571470
0.3572287
0.3572137
0.3588510
0.3556919
0.3567748
0.3724748
0.3594783
0.3559880
0.3554242
0.3553539
0.3562067
0.3558164
0.3559837
0.3564085
0.3557369
0.3697377
0.3590928
0.3562699
0.3558981
0.3552313
0.3552074
0.3555128
0.3553448
0.3553452
0.3554864
0.3709492
0.3601545
0.3580992
0.3562326
0.3556455
0.3559001
0.3553966
0.3555831
0.3558391
0.3560832
0.3723567
0.3584964
0.3542583
0.3532207
0.3535706
0.3536788
0.3541636
0.3543575
0.3543614
0.3547241
0.3739429
0.3583063
0.3561615
0.3557101
0.3556226
0.3552281
0.3551925
0.3557310
0.3555842
0.3556842
0.3700454
0.3574132
0.3541704
0.3534632
0.3534698
0.3541433
0.3539878
0.3544051
0.3543685
0.3543262
0.3719074
0.3581906
0.3559977
0.3553263
0.3546412
0.3538479
0.3536513
0.3533371
0.3534140
0.3534008
0.3697818
0.3586159
0.3562511
0.3572355
0.3567152
0.3562095
0.3560462
0.3574684
0.3573380
0.3576541
0.3681015
0.3597617
0.3591206
0.3562693
0.3570426
0.3574766
0.3565379
0.3581669
0.3591840
0.3572682
0.3675890
0.3602506
0.3587458
0.3576136
0.3563613
0.3566645
0.3570410
0.3579930
0.3578183
0.3579681
0.3698671
0.3595420
0.3577939
0.3570937
0.3572788
0.3577173
0.3570695
0.3566936
0.3562576
0.3570043
0.3683262
0.3578357
0.3558991
0.3553668
0.3565562
0.3558138
0.3564660
0.3560049
0.3559238
0.3569567
0.3669180
0.3571696
0.3565906
0.3557227
0.3553214
0.3561100
0.3560236
0.3566195
0.3560512
0.3575111
0.3670158
0.3562627
0.3551972
0.3552072
0.3555521
0.3553955
0.3553336
0.3554175
0.3559671
0.3559912
0.3653111
0.3539131
0.3532896
0.3528564
0.3526106
0.3528199
0.3531222
0.3532282
0.3532169
0.3537421
0.3684143
0.3574243
0.3549372
0.3544613
0.3539607
0.3546859
0.3548183
0.3548309
0.3555901
0.3554771
0.3685864
0.3570305
0.3554103
0.3541638
0.3531419
0.3528145
0.3522771
0.3522404
0.3519973
0.3517702
0.3468709
0.3365692
0.3336163
0.3310216
0.3329310
0.3338715
0.3343165
0.3359030
0.3376727
0.3384523
0.3461808
0.3365686
0.3352099
0.3345282
0.3345529
0.3344617
0.3359361
0.3364597
0.3376217
0.3377569
0.3490740
0.3388324
0.3365861
0.3360041
0.3357145
0.3353578
0.3360502
0.3377615
0.3397717
0.3402066
0.3426065
0.3333367
0.3329538
0.3334849
0.3349250
0.3347770
0.3358054
0.3361612
0.3358035
0.3390204
0.3416800
0.3334561
0.3319370
0.3311731
0.3326230
0.3332353
0.3334038
0.3348427
0.3356196
0.3351724
0.3451052
0.3360712
0.3344969
0.3352012
0.3334208
0.3336916
0.3351141
0.3346164
0.3358784
0.3363264
0.3408655
0.3352889
0.3344334
0.3352876
0.3358395
0.3350858
0.3355938
0.3365413
0.3368502
0.3370988
0.3416655
0.3329054
0.3312647
0.3320219
0.3320812
0.3323466
0.3344725
0.3358185
0.3358235
0.3368115
0.3408218
0.3351343
0.3337542
0.3337293
0.3338189
0.3335944
0.3349607
0.3357706
0.3360439
0.3371555
0.3387559
0.3334490
0.3328903
0.3332215
0.3345196
0.3354256
0.3363587
0.3375567
0.3383685
0.3387913
0.3402021
0.3365807
0.3353726
0.3339489
0.3342242
0.3342498
0.3356331
0.3362399
0.3382470
0.3393500
0.3416645
0.3354306
0.3357827
0.3365510
0.3359461
0.3363542
0.3364432
0.3408796
0.3420717
0.3425582
0.3386108
0.3355081
0.3333672
0.3343499
0.3352920
0.3351872
0.3352205
0.3366824
0.3367596
0.3382918
0.3370519
0.3325398
0.3309935
0.3343784
0.3339327
0.3342988
0.3345514
0.3364647
0.3373563
0.3374109
0.3387452
0.3347695
0.3335568
0.3333992
0.3338984
0.3345860
0.3346711
0.3354167
0.3362344
0.3376371
0.3342305
0.3311367
0.3286191
0.3296419
0.3293588
0.3315501
0.3322302
0.3340921
0.3355027
0.3354703
0.3380110
0.3327998
0.3317549
0.3322630
0.3330536
0.3337393
0.3352236
0.3357522
0.3372191
0.3388473
0.3358781
0.3301667
0.3309321
0.3322783
0.3327339
0.3333481
0.3346430
0.3346830
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0.3986020
0.3496938
0.3594435
0.3690113
0.3771704
0.3816552
0.3844907
0.3871063
0.3888466
0.3901524
0.3909627
0.3826953
0.3981415
0.4080017
0.4144900
0.4154223
0.4227563
0.4255022
0.4274109
0.4353146
0.4333397
0.3741271
0.3933701
0.4026296
0.4042927
0.4063668
0.4142962
0.4153449
0.4179575
0.4210745
0.4205157
0.3746826
0.3937051
0.4009841
0.4021020
0.4060012
0.4052840
0.4071323
0.4090899
0.4117324
0.4138783
0.3778589
0.3931547
0.4009888
0.4068289
0.4089572
0.4119421
0.4141359
0.4187280
0.4194248
0.4183816
0.3670311
0.3903114
0.3991389
0.4038272
0.4057763
0.4091625
0.4103495
0.4123126
0.4145969
0.4162447
0.3714046
0.3913670
0.3976740
0.4013033
0.4038052
0.4067396
0.4072611
0.4089032
0.4092497
0.4094720
0.3623980
0.3855851
0.3920587
0.3955349
0.3964064
0.3978547
0.3977815
0.4005348
0.4005304
0.4005931
0.3713704
0.3882459
0.3937024
0.3958747
0.4000494
0.4019689
0.4031828
0.4038580
0.4037815
0.4049579
0.3649734
0.3822752
0.3907415
0.3924405
0.3950320
0.3953198
0.3953321
0.3954496
0.3946025
0.3949703
0.3569984
0.3714073
0.3812192
0.3865188
0.3892256
0.3906798
0.3907673
0.3907673
0.3907673
0.3907673
Tuning parameter 'gamma' was held constant at a value of 0
Tuning
parameter 'min_child_weight' was held constant at a value of 1
RMSE was used to select the optimal model using the smallest value.
The final values used for the model were nrounds = 50, max_depth = 4, eta
= 0.4, gamma = 0, colsample_bytree = 0.8, min_child_weight = 1 and subsample
= 0.8333333.# Mejores hiperparámetros
print("Mejores hiperparámetros:")[1] "Mejores hiperparámetros:"print(modelo_xgb_cv$bestTune) nrounds max_depth eta gamma colsample_bytree min_child_weight subsample
2761 50 4 0.4 0 0.8 1 0.8333333# Importancia de variables
importancia_xgb <- varImp(modelo_xgb_cv, scale = TRUE) %>%
.$importance %>%
as_tibble(rownames = "variable") %>%
arrange(desc(Overall))
print("Importancia de variables:")[1] "Importancia de variables:"print(importancia_xgb)# A tibble: 6 × 2
variable Overall
<chr> <dbl>
1 m2_construidos 100
2 no_banos 12.4
3 tipo_inmuebleDepartamento 6.12
4 no_recamaras 3.91
5 region_precioBaja 0.315
6 region_precioMedia 0 # Visualizar importancia
importancia_xgb %>%
ggplot(aes(x = reorder(variable, Overall), y = Overall)) +
geom_col(fill = "steelblue") +
coord_flip() +
labs(
title = "Importancia de Variables según XGBoost",
x = "Variable",
y = "Importancia (Overall)"
)
Nota sobre paralelización: El parámetro nthread controla cuántos cores usa XGBoost internamente. Combinado con allowParallel = TRUE en trainControl, obtenemos paralelización en dos niveles:
- Validación cruzada en paralelo (folds diferentes en cores diferentes)
- Construcción de árbol en paralelo (dentro de cada fold)
8 Comparación de Modelos
8.1 Métricas de Desempeño
# Extraer métricas de cada modelo
comparacion <- tibble(
Modelo = c("OLS (log)", "Ridge", "Lasso", "Árbol", "Random Forest", "XGBoost"),
RMSE = c(
modelo_log_cv$results$RMSE[1],
min(modelo_ridge_cv$results$RMSE),
min(modelo_lasso_cv$results$RMSE),
min(modelo_arbol_cv$results$RMSE),
min(modelo_rf_cv$results$RMSE),
min(modelo_xgb_cv$results$RMSE)
),
R2 = c(
modelo_log_cv$results$Rsquared[1],
max(modelo_ridge_cv$results$Rsquared),
max(modelo_lasso_cv$results$Rsquared),
max(modelo_arbol_cv$results$Rsquared),
max(modelo_rf_cv$results$Rsquared),
max(modelo_xgb_cv$results$Rsquared)
)
) %>%
arrange(RMSE)
print("=== Comparación de Desempeño ===")[1] "=== Comparación de Desempeño ==="print(comparacion)# A tibble: 6 × 3
Modelo RMSE R2
<chr> <dbl> <dbl>
1 XGBoost 0.431 0.743
2 Random Forest 0.440 0.732
3 Árbol 0.493 0.662
4 Lasso 0.555 NaN
5 Ridge 0.558 0.578
6 OLS (log) 0.560 0.5778.2 Visualización de Comparación
# RMSE
p_rmse <- comparacion %>%
ggplot(aes(x = reorder(Modelo, -RMSE), y = RMSE, fill = Modelo)) +
geom_col(alpha = 0.8) +
geom_text(aes(label = round(RMSE, 3)), vjust = -0.5, size = 3.5) +
labs(title = "Comparación de RMSE (menor es mejor)",
x = "Modelo", y = "RMSE") +
theme(axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
# R²
p_r2 <- comparacion %>%
ggplot(aes(x = reorder(Modelo, R2), y = R2, fill = Modelo)) +
geom_col(alpha = 0.8) +
geom_text(aes(label = round(R2, 3)), vjust = -0.5, size = 3.5) +
labs(title = "Comparación de R² (mayor es mejor)",
x = "Modelo", y = "R²") +
theme(axis.text.x = element_text(angle = 45, hjust = 1),
legend.position = "none")
gridExtra::grid.arrange(p_rmse, p_r2, ncol = 2)
8.3 Predicciones vs Valores Reales
# Generar predicciones para todos los modelos
pred_ols <- predict(modelo_final, newdata = datos_modelo)
pred_ridge <- predict(modelo_ridge_cv, newdata = datos_modelo)
pred_lasso <- predict(modelo_lasso_cv, newdata = datos_modelo)
pred_arbol <- predict(modelo_arbol_cv, newdata = datos_modelo)
pred_rf <- predict(modelo_rf_cv, newdata = datos_modelo)
pred_xgb <- predict(modelo_xgb_cv, newdata = datos_modelo)
# Consolidar en un dataframe
predicciones_consolidadas <- datos_modelo %>%
mutate(
precio_real = precio,
OLS = exp(pred_ols) - 1,
Ridge = exp(pred_ridge) - 1,
Lasso = exp(pred_lasso) - 1,
Árbol = exp(pred_arbol) - 1,
`Random Forest` = exp(pred_rf) - 1,
XGBoost = exp(pred_xgb) - 1
) %>%
transmute(
precio_real_millones = precio_real / 1e6,
OLS = OLS / 1e6,
Ridge = Ridge / 1e6,
Lasso = Lasso / 1e6,
Árbol = Árbol / 1e6,
`Random Forest` = `Random Forest` / 1e6,
XGBoost = XGBoost / 1e6
) %>%
pivot_longer(
cols = -precio_real_millones,
names_to = "modelo",
values_to = "precio_pred_millones"
)
# Gráfico de predicciones vs reales
predicciones_consolidadas %>%
filter(precio_pred_millones <= 50) %>% # Filtrar outliers para visualización
ggplot(aes(x = precio_real_millones, y = precio_pred_millones)) +
geom_point(alpha = 0.2, color = "steelblue") +
geom_abline(intercept = 0, slope = 1, linetype = "dashed", color = "red") +
facet_wrap(~modelo, ncol = 3) +
coord_equal() +
labs(
title = "Valores Observados vs Predichos por Modelo",
subtitle = "Línea roja = predicción perfecta",
x = "Precio Observado (millones de pesos)",
y = "Precio Predicho (millones de pesos)"
) +
theme_minimal()
9 Interpretación y Recomendaciones
9.1 Comparación de Coeficientes (OLS vs Ridge vs Lasso)
# Extraer coeficientes de cada modelo
coef_ols <- tidy(modelo_final) %>%
mutate(modelo = "OLS") %>%
dplyr::select(modelo, term, estimate)
coef_ridge <- coef(modelo_ridge_cv$finalModel,
s = modelo_ridge_cv$bestTune$lambda) %>%
as.matrix() %>%
as_tibble(rownames = "term") %>%
rename(estimate = s0) %>%
mutate(modelo = "Ridge")
coef_lasso <- coef(modelo_lasso_cv$finalModel,
s = modelo_lasso_cv$bestTune$lambda) %>%
as.matrix() %>%
as_tibble(rownames = "term") %>%
rename(estimate = s0) %>%
mutate(modelo = "Lasso")
# Consolidar
coef_comparacion <- bind_rows(coef_ols, coef_ridge, coef_lasso) %>%
filter(term != "(Intercept)")
# Visualizar
coef_comparacion %>%
ggplot(aes(x = term, y = estimate, color = modelo)) +
geom_point(size = 3, position = position_dodge(width = 0.6)) +
geom_hline(yintercept = 0, linetype = "dashed", color = "gray40") +
coord_flip() +
labs(
title = "Comparación de Coeficientes: OLS vs Ridge vs Lasso",
subtitle = "Variable dependiente: log(precio)",
x = "Variable explicativa",
y = "Coeficiente estimado",
color = "Modelo"
) +
theme_minimal() +
theme(legend.position = "top")
Interpretación:
- OLS: Coeficientes más grandes (sin regularización)
- Ridge: Todos los coeficientes reducidos proporcionalmente
- Lasso: Algunos coeficientes exactamente en cero (selección)
9.2 Conclusiones y Recomendaciones
9.2.1 Mejor Modelo
Basándonos en RMSE y R², el modelo XGBoost o Random Forest típicamente tendrán el mejor desempeño predictivo.
9.2.2 Trade-offs a Considerar
| Modelo | Interpretabilidad | Velocidad_Entrenamiento | Velocidad_Predicción | Rendimiento_Predictivo | Manejo_No_Linealidad |
|---|---|---|---|---|---|
| OLS | ★★★★★ | ★★★★★ | ★★★★★ | ★★☆☆☆ | ★☆☆☆☆ |
| Ridge/Lasso | ★★★★☆ | ★★★★☆ | ★★★★★ | ★★★☆☆ | ★☆☆☆☆ |
| Árbol | ★★★☆☆ | ★★★★☆ | ★★★★☆ | ★★★☆☆ | ★★★★★ |
| Random Forest | ★★☆☆☆ | ★★☆☆☆ | ★★★☆☆ | ★★★★☆ | ★★★★★ |
| XGBoost | ★☆☆☆☆ | ★☆☆☆☆ | ★★★☆☆ | ★★★★★ | ★★★★★ |
9.2.3 Recomendaciones por Caso de Uso
- Si necesitas interpretabilidad: Usa OLS o Lasso
- Puedes explicar el impacto de cada variable
- Apropiado para reportes a stakeholders no técnicos
- Si tienes multicolinealidad: Usa Ridge
- Estabiliza coeficientes correlacionados
- Si quieres selección automática de variables: Usa Lasso
- Identifica variables más importantes
- Reduce dimensionalidad
- Si rendimiento predictivo es prioritario: Usa XGBoost o Random Forest
- Mejor predicción pero menos interpretable
- Apropiado para producción
- Si tienes restricciones computacionales: Usa OLS o Lasso
- Más rápidos de entrenar y predecir
10 Ejemplo de Predicción
# Crear ejemplos para predicción
nuevos_datos <- tibble(
no_recamaras = c(2, 3, 4),
no_banos = c(1, 2, 3),
m2_construidos = c(80, 120, 200),
region_precio = c("Baja", "Media", "Alta"),
tipo_inmueble = c("Departamento", "Casa", "Casa")
)
# Predicciones con intervalo de confianza (OLS)
predicciones_conf <- predict(
modelo_final,
newdata = nuevos_datos,
interval = "confidence",
level = 0.95
) %>%
as_tibble() %>%
mutate(across(everything(), ~(exp(.) - 1) / 1e6)) %>%
bind_cols(nuevos_datos, .) %>%
rename(precio_estimado = fit, limite_inferior = lwr, limite_superior = upr)
print("=== Predicciones de Ejemplo (millones de pesos) ===")[1] "=== Predicciones de Ejemplo (millones de pesos) ==="print(predicciones_conf)# A tibble: 3 × 8
no_recamaras no_banos m2_construidos region_precio tipo_inmueble
<dbl> <dbl> <dbl> <chr> <chr>
1 2 1 80 Baja Departamento
2 3 2 120 Media Casa
3 4 3 200 Alta Casa
# ℹ 3 more variables: precio_estimado <dbl>, limite_inferior <dbl>,
# limite_superior <dbl>11 Limpieza Final
# Cerrar cluster de paralelización
stopCluster(cl)
registerDoSEQ() # Volver a modo secuencial12 Referencias y Recursos
12.1 Libros Recomendados
- “An Introduction to Statistical Learning” - James, Witten, Hastie, Tibshirani
- “The Elements of Statistical Learning” - Hastie, Tibshirani, Friedman
- “Applied Predictive Modeling” - Kuhn, Johnson
12.2 Documentación
12.3 Datasets
Fecha de creación: 2025-11-11
Curso: EC3002C.602 - Módulo 5: Inteligencia Artificial