Evidencia2
Mayela Caballero
10/18/2022
Descargar las librerías
library("stats")
library("psych")
library("MASS")
library("ISLR")
library("fRegression")
library("vcd")## Loading required package: grid##
## Attaching package: 'vcd'## The following object is masked from 'package:ISLR':
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## Hitterslibrary("dplyr")##
## Attaching package: 'dplyr'## The following object is masked from 'package:MASS':
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## select## The following objects are masked from 'package:stats':
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## filter, lag## The following objects are masked from 'package:base':
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## intersect, setdiff, setequal, unionlibrary("openxlsx")
library("mlbench")
library("magrittr")
library("neuralnet")##
## Attaching package: 'neuralnet'## The following object is masked from 'package:dplyr':
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## computelibrary("keras")
library("caret")## Loading required package: ggplot2##
## Attaching package: 'ggplot2'## The following objects are masked from 'package:psych':
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## %+%, alpha## Loading required package: latticelibrary("readxl")Primero se debe de leer la base de datos, en este caso tiene el nombre “BasedeDatos2”
data <- read_xlsx("BasedeDatos2.xlsx")
str(data)## tibble [1,492 × 6] (S3: tbl_df/tbl/data.frame)
## $ ID : num [1:1492] 1 1 1 1 1 1 2 2 2 2 ...
## $ Year : num [1:1492] 1999 2000 2001 2002 2003 ...
## $ Default: num [1:1492] 0 0 0 0 0 0 0 0 0 0 ...
## $ WC : num [1:1492] 0.501 0.548 0.451 0.307 0.447 ...
## $ RE : num [1:1492] 0.307 0.322 0.225 0.192 0.217 ...
## $ EBIT : num [1:1492] 0.0434 0.0518 0.0268 0.0301 0.0325 ...Asimismo es importante ver que no haya NAs en la base de datos, ya que en caso de que haya el modelo de Redes Neuronales no podrá ser ajustado
colSums(is.na(data)) ## ID Year Default WC RE EBIT
## 0 0 0 0 0 0Ajustar y Visualizar Redes Neuronales
Al momento de crear una red neuronal es importante mencionar las ‘capas ocultas’ de la red, en este caso crearemos una Red Neuronal dónde la primera capa oculta constará de 12 neuronas y la segunda capa consistirá de 7 neuronas.
set.seed(13)
train = createDataPartition(y = data$Default, p=0.8, list=FALSE, times = 1)
data_train = data[train,]
data_test = data[-train,]
RN <- neuralnet(Default ~ WC + RE + EBIT,
data = data_train,
hidden = c(12,7),
linear.output = T,
lifesign = 'full',
threshold = 0.05,
rep=1)## hidden: 12, 7 thresh: 0.05 rep: 1/1 steps: 1000 min thresh: 0.0515430915049259
## 1085 error: 1.62441 time: 1.81 secs?neuralnetPara poder realizar predicciones es importante estandarizar las variables, para esto debemos de guardar la información como matrices y separar la variable que deseamos predecir, que en este caso se encuenta en la columna 3.
#train/test split en matrices y separando variable a predecir
training <- as.matrix(data_train[,1:6])
trainingtarget <- as.matrix(data_train[,3])
test <- as.matrix(data_test[,1:6])
testtarget <- as.matrix(data_test[,3])
#Estandarización de variables
m <- colMeans(training) #Obtener medias por columna
s <- apply(training, 2, sd) #Calcular StandDev por columna (por ello el apply lleva el 2, si pusieran 1 sería por renglón)
training <- scale(training, center = m, scale = s)
test <- scale(test, center = m, scale = s)Es importante notar que tanto el data_train como el data_test se deben de estandarizar considerando las medias y desviaciones estándar obtenidas únicamente con los datos de entrenamiento.
Predicciones
A continuación se hace un reajuste del modelo con variables estanderizadas.
data_train_S <- as.data.frame(cbind(training,(trainingtarget - mean(trainingtarget))/sd(trainingtarget)))
colnames(data_train_S) <- colnames(data_train)
RNS <- neuralnet(Default ~ WC + RE + EBIT,
data = data_train_S,
hidden = c(12,7),
linear.output = T,
#linear.output se debe poner como T en modelos de regresion y como F en modelos de clasificación
lifesign = 'full',
rep=1,
# threshold=0.02,
stepmax=250000)## hidden: 12, 7 thresh: 0.01 rep: 1/1 steps: 1000 min thresh: 2.35350078657483
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## 170942 error: 0.03931 time: 4.1 minsVisualizar la Red Neuronal ajustada
plot(RNS,col.hidden = 'darkgreen',
col.hidden.synapse = 'darkgreen',
show.weights = T,
information = F,
fill = 'lightblue')Se realizan las predicciones
data_test_S <- as.data.frame(test)
colnames(data_test_S) <- colnames(data_test)[1:6]
RNSPredictions <- predict(RNS,data_test_S)
cor(RNSPredictions,(testtarget-mean(trainingtarget))/sd(trainingtarget))## Default
## [1,] 0.05575387Para calcular métricas de regresión es importante ‘desestandarizar’ las predicciones y eso es lo que se comparará contra los valores de testtarget
RNSPred <- RNSPredictions*sd(trainingtarget) + mean(trainingtarget)
plot(RNSPred,testtarget)
abline(a=0, b=1)
RSSnn <- (RNSPred - testtarget)^2
sum(RSSnn)/nrow(testtarget)## [1] 0.014065711 - sum(RSSnn)/sum((testtarget - mean(trainingtarget))^2)## [1] -0.05652631Este es un segundo intento con una Red Neuronal pero con una menor cantidad de neuronas.
data_train_S <- as.data.frame(cbind(training,(trainingtarget - mean(trainingtarget))/sd(trainingtarget)))
colnames(data_train_S) <- colnames(data_train)
RNS2 <- neuralnet(Default ~ WC + RE + EBIT,
data = data_train_S,
hidden = c(5,3),
linear.output = T,
lifesign = 'full',
rep=1,
# threshold=0.02,
stepmax=700000)## hidden: 5, 3 thresh: 0.01 rep: 1/1 steps: 1000 min thresh: 0.359444195307591
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## 447279 error: 82.29639 time: 4.31 minsPor medio de este código se puede visualizar la Red Neuronal Ajustada.
dev.set(dev.next())## pdf
## 3print(plot(RNS2,col.hidden = 'darkgreen',
col.hidden.synapse = 'darkgreen',
show.weights = T,
information = F,
fill = 'lightblue'))## NULLAquí se realiza la predicción.
data_test_S <- as.data.frame(test)
colnames(data_test_S) <- colnames(data_test)[1:6]
RNS2Predictions <- predict(RNS2,data_test_S)
cor(RNS2Predictions,(testtarget-mean(trainingtarget))/sd(trainingtarget))## Default
## [1,] -0.01186769Para calcular métricas de regresión es importante ‘desestandarizar’ las predicciones y eso es lo que se comparará contra los valores de testtarget.
RNS2Pred <- RNS2Predictions*sd(trainingtarget) + mean(trainingtarget)
plot(RNS2Pred,testtarget)
abline(a=0, b=1)
RSS2nn <- (RNS2Pred - testtarget)^2
sum(RSS2nn)/nrow(testtarget)## [1] 0.016703491 - sum(RSS2nn)/sum((testtarget - mean(trainingtarget))^2)## [1] -0.2546595A continuación hay 2 formas de comparar los moedlos de forma gráfica.
Primera forma, esta es mediante 2 gráficas diferentes.
par(mfrow=c(1,2))
plot(data_test$Default,RNS2Pred,col='red',main='Real vs predicted NN',pch=19,cex=1)
abline(0,1,lwd=2)
legend('bottomright',legend='NN',pch=18,col='red', bty='n')
plot(data_test$Default,RNSPred,col='blue',main='Real vs predicted LM',pch=15, cex=1)
abline(0,1,lwd=2)
legend('bottomright',legend='LM',pch=18,col='blue', bty='n', cex=.95)
En esta segunda forma se puede ver en una misma gráfica.
dev.set(dev.next())## pdf
## 3plot(data_test$Default,RNS2Pred,col='red',main='Real vs predicted NN',pch=19,cex=1)
points(data_test$Default,RNSPred,col='blue',pch=15,cex=1)
abline(0,1,lwd=2)
legend('bottomright',legend=c('NN','LM'),pch=c(19,15),col=c('red','blue'))#Conclusión
Una red neuronal, es un algoritmo que consiste en simular el comportamiento de un cerebro biológico mediante capas compuestas por nodos o neuronas que tienen una capa de entrada, una o más capas ocultas y una de salida y ada nodo se conecta a otro y tiene un peso asociado, así es como se forman miles de conexiones.
Estas redes sirven para problemas de clasificación como obtener alguna probabilidad o problemas de regresión, como predecir el número de algún dato, como lo es en esta evidencia en donde hacemos predicciones de la variable “Default”. Para lograr hacer predicciones utilizamos las variables WC,RE y EBIT.
En el área financiera las redes neuronales son muy importantes y cuentan con diversas aplicaciones. Entre ellas se pueden encontrar, en la administración de los portafolios de inversión, la evaluación de acciones y bonos, las estrategias de cobertura y arbitraje, el análisis de la volatilidad y correlación y la predicción de los precios de acciones, bonos, tasas de interés y de cambio, evolución de precios, valoración de créditos, identificación de falsificaciones entre otras.