带有 R 包 nnet 的神经网络：由于过度拟合导致的垃圾预测？

Question

试图弄清楚我是否有 R 问题或一般的神经网络问题。

假设我有这些数据：

set.seed(123)
n = 1e3
x = rnorm(n)
y = 1 + 3*sin(x/2) + 15*cos(pi*x) + rnorm(n = length(x))
df = data.frame(y,x)
df$train = sample(c(TRUE, FALSE), length(y), replace=TRUE, prob=c(0.7,0.3))
df_train = subset(df, train = TRUE)
df_test = subset(df, train = FALSE)

然后你训练神经网络，它看起来不错：

library(nnet)
nn = nnet(y~x, data = df_train, size = 60, linout=TRUE) 
yhat_nn = predict(nn, newdata = df_test)
plot(df_test$x,df_test$y)
points(df_test$x, yhat_nn, col = 'blue')

好的，所以我想，让我们生成新数据，然后使用训练好的网络进行预测。 但预测还差得很远：

x2 = rnorm(n)
y2 = 1 + 3*sin(x2/2) + 15*cos(pi*x2) + rnorm(n = length(x2))
df2 = data.frame(y2,x2)
plot(df2$x, df2$y)
points(df2$x, predict(nn, newdata = df2), col = 'blue')

这是因为我对训练集过度拟合了吗？ 我认为通过将原始数据拆分为测试训练可以避免过度拟合。

Answer 1

致命问题是您的新数据框df2没有正确的变量名称。 结果， predict.nnet找不到正确的值。

names(df)
#[1] "y"     "x"     "train"

names(df2)
#[1] "y2"     "x2"

为predict构建数据框时要小心。

## the right way
df2 <- data.frame(y = y2, x = x2)

## and it solves the mystery
plot(df2$x, df2$y)
points(df2$x, predict(nn, newdata = df2), col = 'blue')

---

另一个小问题是您subset的使用。 它应该是

## not train = TRUE or train = FALSE
df_train <- subset(df, train == TRUE) ## or simply subset(df, train)
df_test <- subset(df, train == FALSE) ## or simply subset(df, !train)

这有一个有趣的效果：

nrow(subset(df, train == TRUE))
#[1] 718

nrow(subset(df, train = TRUE))  ## oops!!
#[1] 1000

---

完整的 R 会话

set.seed(123)
n = 1e3
x = rnorm(n)
y = 1 + 3*sin(x/2) + 15*cos(pi*x) + rnorm(n = length(x))
df = data.frame(y,x)
df$train = sample(c(TRUE, FALSE), length(y), replace=TRUE, prob=c(0.7,0.3))
df_train = subset(df, train == TRUE)  ## fixed
df_test = subset(df, train == FALSE)  ## fixed

library(nnet)
nn = nnet(y~x, data = df_train, size = 60, linout=TRUE) 
yhat_nn = predict(nn, newdata = df_test)
plot(df_test$x,df_test$y)
points(df_test$x, yhat_nn, col = 'blue')

x2 = rnorm(n)
y2 = 1 + 3*sin(x2/2) + 15*cos(pi*x2) + rnorm(n = length(x2))
df2 = data.frame(y = y2, x = x2)  ## fixed
plot(df2$x, df2$y)
points(df2$x, predict(nn, newdata = df2), col = 'blue')