使用housing_renamed.csv中的数据构建两个不同的神经网络模型预测value_per_sq_ft：使用3折交叉验证来评价这两个不同的模型的好坏。用R语言解决并写出代码

好的，我可以帮你回答这个问题。

首先，我们需要导入housing_renamed.csv数据，加载所需的包和库：

library(tidyverse)
library(caret)

housing_data <- read.csv("housing_renamed.csv")

接下来，我们将数据分为训练集和测试集：

set.seed(123)
trainIndex <- createDataPartition(housing_data$value_per_sq_ft, p = .8, list = FALSE)
training <- housing_data[trainIndex, ]
testing <- housing_data[-trainIndex, ]

然后我们可以构建两个不同的神经网络模型。这里我们选择使用keras包来实现。第一个模型包含一个隐藏层，第二个模型包含两个隐藏层：

# 第一个模型
model_1 <- keras_model_sequential() %>% 
  layer_dense(units = 10, activation = "relu", input_shape = ncol(training) - 1) %>%
  layer_dense(units = 1)

# 第二个模型
model_2 <- keras_model_sequential() %>%
  layer_dense(units = 10, activation = "relu", input_shape = ncol(training) - 1) %>%
  layer_dense(units = 10, activation = "relu") %>%
  layer_dense(units = 1)

接下来，我们需要编译模型并指定损失函数、优化器和评价指标：

model_1 %>% compile(
  loss = "mean_squared_error",
  optimizer = "adam",
  metrics = "mean_absolute_error"
)

model_2 %>% compile(
  loss = "mean_squared_error",
  optimizer = "adam",
  metrics = "mean_absolute_error"
)

现在我们可以训练和评估模型。这里我们使用3折交叉验证：

# 3折交叉验证
set.seed(123)
num_folds <- 3
folds <- createFolds(training$value_per_sq_ft, k = num_folds, returnTrain = TRUE)

# 定义评价指标
rmse <- function(y_true, y_pred) sqrt(mean((y_pred - y_true)^2))
mae <- function(y_true, y_pred) mean(abs(y_pred - y_true))

# 训练和评估第一个模型
model_1_results <- list()
for (i in 1:num_folds) {
  cat("Training on fold", i, "\n")
  
  # 准备数据
  training_fold <- training[folds[[i]], ]
  validation_fold <- training[-folds[[i]], ]
  x_train <- as.matrix(training_fold[, -1])
  y_train <- training_fold[, 1]
  x_val <- as.matrix(validation_fold[, -1])
  y_val <- validation_fold[, 1]
  
  # 训练模型
  history <- model_1 %>% fit(
    x_train, y_train,
    epochs = 100,
    batch_size = 32,
    validation_data = list(x_val, y_val),
    verbose = 0
  )
  
  # 评估模型
  y_val_pred <- predict(model_1, x_val)
  fold_metrics <- c(
    rmse = rmse(y_val, y_val_pred),
    mae = mae(y_val, y_val_pred)
  )
  model_1_results[[i]] <- fold_metrics
}

# 训练和评估第二个模型
model_2_results <- list()
for (i in 1:num_folds) {
  cat("Training on fold", i, "\n")
  
  # 准备数据
  training_fold <- training[folds[[i]], ]
  validation_fold <- training[-folds[[i]], ]
  x_train <- as.matrix(training_fold[, -1])
  y_train <- training_fold[, 1]
  x_val <- as.matrix(validation_fold[, -1])
  y_val <- validation_fold[, 1]
  
  # 训练模型
  history <- model_2 %>% fit(
    x_train, y_train,
    epochs = 100,
    batch_size = 32,
    validation_data = list(x_val, y_val),
    verbose = 0
  )
  
  # 评估模型
  y_val_pred <- predict(model_2, x_val)
  fold_metrics <- c(
    rmse = rmse(y_val, y_val_pred),
    mae = mae(y_val, y_val_pred)
  )
  model_2_results[[i]] <- fold_metrics
}

最后，我们可以计算每个模型的平均性能指标：

# 计算平均性能指标
model_1_metrics <- do.call(rbind, model_1_results)
model_2_metrics <- do.call(rbind, model_2_results)
mean_metrics <- rbind(
  setNames(colMeans(model_1_metrics), paste0("model_1_", names(model_1_metrics))),
  setNames(colMeans(model_2_metrics), paste0("model_2_", names(model_2_metrics)))
)

这样我们就得到了两个不同的神经网络模型的平均性能指标。可以根据需要进行比较和评估。