tidymodels

lm_spec <- 
  linear_reg() %>% # Pick linear regression
  set_engine(engine = "lm") # set engine
lm_spec

## Linear Regression Model Specification (regression)
## 
## Computational engine: lm

lm_fit <- fit(lm_spec,
              mpg ~ horsepower,
              data = Auto)

Validation set approach

Auto_split <- initial_split(Auto, prop = 0.5)
Auto_split

## <Analysis/Assess/Total>
## <196/196/392>

• Extract the training and testing data

training(Auto_split)
testing(Auto_split)

Validation set approach

Auto_train <- training(Auto_split)

Auto_train

## # A tibble: 196 x 9
##      mpg cylinders displacement horsepower weight acceleration  year origin
##    <dbl>     <dbl>        <dbl>      <dbl>  <dbl>        <dbl> <dbl>  <dbl>
##  1    18         8          307        130   3504         12      70      1
##  2    18         8          318        150   3436         11      70      1
##  3    16         8          304        150   3433         12      70      1
##  4    17         8          302        140   3449         10.5    70      1
##  5    15         8          429        198   4341         10      70      1
##  6    15         8          390        190   3850          8.5    70      1
##  7    14         8          340        160   3609          8      70      1
##  8    15         8          400        150   3761          9.5    70      1
##  9    24         4          113         95   2372         15      70      3
## 10    22         6          198         95   2833         15.5    70      1
## # … with 186 more rows, and 1 more variable: name <fct>

A faster way!

• You can use last_fit() and specify the split
• This will automatically train the data on the train data from the split
• Instead of specifying which metric to calculate (with rmse as before) you can just use collect_metrics() and it will automatically calculate the metrics on the test data from the split

set.seed(100)
Auto_split <- initial_split(Auto, prop = 0.5)
lm_fit <- last_fit(lm_spec,
                   mpg ~ horsepower,
                   split = Auto_split)
lm_fit %>%
  collect_metrics()

## # A tibble: 2 x 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard       4.87 
## 2 rsq     standard       0.625

What about cross validation?

Auto_cv <- vfold_cv(Auto, v = 5)
Auto_cv

## #  5-fold cross-validation 
## # A tibble: 5 x 2
##   splits           id   
##   <list>           <chr>
## 1 <split [313/79]> Fold1
## 2 <split [313/79]> Fold2
## 3 <split [314/78]> Fold3
## 4 <split [314/78]> Fold4
## 5 <split [314/78]> Fold5

What if we wanted to do some preprocessing

• For the shrinkage methods we discussed it was important to scale the variables

What if we wanted to do some preprocessing

Auto_scaled <- Auto %>%
  mutate(horsepower = scale(horsepower))
sd(Auto_scaled$horsepower)

## [1] 1

Auto_cv_scaled <- vfold_cv(Auto_scaled, v = 5)
map_dbl(Auto_cv_scaled$splits,
        function(x) {
          dat <- as.data.frame(x)$horsepower
          sd(dat)
        })

## [1] 1.0115202 1.0025849 0.9834936 0.9733806 1.0293404

What if we wanted to do some preprocessing

• recipe()!
• Using the recipe() function along with step_*() functions, we can specify preprocessing steps and R will automagically apply them to each fold appropriately.

rec <- recipe(mpg ~ horsepower, data = Auto) %>%
  step_scale(horsepower)

• You can find all of the potential preprocessing steps here: https://tidymodels.github.io/recipes/reference/index.html

Where do we plug in this recipe?

• The recipe gets plugged into the fit_resamples() function

Auto_cv <- vfold_cv(Auto, v = 5)
rec <- recipe(mpg ~ horsepower, data = Auto) %>%
  step_scale(horsepower)
results <- fit_resamples(lm_spec,
                         preprocessor = rec,
                         resamples = Auto_cv)
results %>%
  collect_metrics()

## # A tibble: 2 x 5
##   .metric .estimator  mean     n std_err
##   <chr>   <chr>      <dbl> <int>   <dbl>
## 1 rmse    standard   4.88      5  0.317 
## 2 rsq     standard   0.613     5  0.0249

What if we want to predict mpg with more variables

• Now we still want to add a step to scale predictors
• We could either write out all predictors individually to scale them
• OR we could use the all_predictors() short hand.

rec <- recipe(mpg ~ horsepower + displacement + weight, data = Auto) %>%
  step_scale(all_predictors())

Putting it together

rec <- recipe(mpg ~ horsepower + displacement + weight, data = Auto) %>%
  step_scale(all_predictors())
results <- fit_resamples(lm_spec,
                         preprocessor = rec,
                         resamples = Auto_cv)
results %>%
  collect_metrics()

## # A tibble: 2 x 5
##   .metric .estimator  mean     n std_err
##   <chr>   <chr>      <dbl> <int>   <dbl>
## 1 rmse    standard   4.22      5  0.272 
## 2 rsq     standard   0.709     5  0.0153

Ridge, Lasso, and Elastic net

• When specifying your model, you can indicate whether you would like to use ridge, lasso, or elastic net. We can write a general equation to minimize:

$$RSS + \lambda\left((1-\alpha)\sum_{i=1}^p\beta_j^2+\alpha\sum_{i=1}^p|\beta_j|\right)$$

lm_spec <- linear_reg() %>%
  set_engine("glmnet")

• First specify the engine. We'll use glmnet
• The linear_reg() function has two additional parameters, penalty and mixture
• penalty is \(\lambda\) from our equation.
• mixture is a number between 0 and 1 representing \(\alpha\)

Ridge, Lasso, and Elastic net

$$RSS + \lambda\left((1-\alpha)\sum_{i=1}^p\beta_j^2+\alpha\sum_{i=1}^p|\beta_j|\right)$$

ridge_spec <- linear_reg(penalty = 100, mixture = 0) %>%
  set_engine("glmnet")

Ridge, Lasso, and Elastic net

$$RSS + \lambda\left((1-\alpha)\sum_{i=1}^p\beta_j^2+\alpha\sum_{i=1}^p|\beta_j|\right)$$

ridge_spec <- linear_reg(penalty = 100, mixture = 0) %>%
  set_engine("glmnet")

lasso_spec <- linear_reg(penalty = 5, mixture = 1) %>%
  set_engine("glmnet")

enet_spec <- linear_reg(penalty = 60, mixture = 0.7) %>%
  set_engine("glmnet")

Okay, but we wanted to look at 3 different models!

ridge_spec <- linear_reg(penalty = 100, mixture = 0) %>%
  set_engine("glmnet") 
results <- fit_resamples(ridge_spec,
                         preprocessor = rec,
                         resamples = Auto_cv)

lasso_spec <- linear_reg(penalty = 5, mixture = 1) %>%
  set_engine("glmnet") 
results <- fit_resamples(lasso_spec,
                         preprocessor = rec,
                         resamples = Auto_cv)

elastic_spec <- linear_reg(penalty = 60, mixture = 0.7) %>%
  set_engine("glmnet") 
results <- fit_resamples(elastic_spec,
                         preprocessor = rec,
                         resamples = Auto_cv)

• 😱 this looks like copy + pasting!

tune 🎶

penalty_spec <- linear_reg(penalty = tune(), mixture = tune()) %>%
  set_engine("glmnet")

• Notice the code above has tune() for the the penalty and the mixture. Those are the things we want to vary!

tune 🎶

• Now we need to create a grid of potential penalties ( \(\lambda\) ) and mixtures ( \(\alpha\) ) that we want to test
• Instead of fit_resamples() we are going to use tune_grid()

grid <- expand_grid(penalty = seq(0, 100, by = 10),
                    mixture = seq(0, 1, by = 0.2))
results <- tune_grid(penalty_spec,
                     preprocessor = rec,
                     grid = grid,
                     resamples = Auto_cv)

tune 🎶

results %>%
  collect_metrics()

## # A tibble: 132 x 7
##    penalty mixture .metric .estimator  mean     n std_err
##      <dbl>   <dbl> <chr>   <chr>      <dbl> <int>   <dbl>
##  1       0     0   rmse    standard   4.23      5  0.280 
##  2       0     0   rsq     standard   0.708     5  0.0166
##  3       0     0.2 rmse    standard   4.22      5  0.273 
##  4       0     0.2 rsq     standard   0.709     5  0.0154
##  5       0     0.4 rmse    standard   4.22      5  0.273 
##  6       0     0.4 rsq     standard   0.709     5  0.0154
##  7       0     0.6 rmse    standard   4.22      5  0.273 
##  8       0     0.6 rsq     standard   0.709     5  0.0154
##  9       0     0.8 rmse    standard   4.22      5  0.273 
## 10       0     0.8 rsq     standard   0.709     5  0.0153
## # … with 122 more rows

Subset results

results %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  arrange(mean)

## # A tibble: 66 x 7
##    penalty mixture .metric .estimator  mean     n std_err
##      <dbl>   <dbl> <chr>   <chr>      <dbl> <int>   <dbl>
##  1       0     0.2 rmse    standard    4.22     5   0.273
##  2       0     0.6 rmse    standard    4.22     5   0.273
##  3       0     0.4 rmse    standard    4.22     5   0.273
##  4       0     0.8 rmse    standard    4.22     5   0.273
##  5       0     1   rmse    standard    4.22     5   0.273
##  6       0     0   rmse    standard    4.23     5   0.280
##  7      10     0   rmse    standard    4.73     5   0.308
##  8      20     0   rmse    standard    5.29     5   0.313
##  9      10     0.2 rmse    standard    5.37     5   0.316
## 10      30     0   rmse    standard    5.70     5   0.314
## # … with 56 more rows

• Since this is a data frame, we can do things like filter and arrange!

results %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  ggplot(aes(penalty, mean, color = factor(mixture), group = factor(mixture))) +
  geom_line() +
  geom_point() + 
  labs(y = "RMSE")

Putting it all together

• Often we can use a combination of all of these tools together
• First split our data
• Do cross validation on just the training data to tune the parameters
• Use last_fit() with the selected parameters, specifying the split data so that it is evaluated on the left out test sample

Putting it all together

auto_split <- initial_split(Auto, prop = 0.5)
auto_train <- training(auto_split)
auto_cv <- vfold_cv(auto_train, v = 5)
rec <- recipe(mpg ~ horsepower + displacement + weight, data = auto_train) %>%
  step_scale(all_predictors())
tuning <- tune_grid(penalty_spec,
                     rec,
                     grid = grid,
                     resamples = auto_cv)
tuning %>%
  collect_metrics() %>%
  filter(.metric == "rmse") %>%
  arrange(mean)

## # A tibble: 66 x 7
##    penalty mixture .metric .estimator  mean     n std_err
##      <dbl>   <dbl> <chr>   <chr>      <dbl> <int>   <dbl>
##  1       0     0   rmse    standard    4.48     5   0.195
##  2       0     1   rmse    standard    4.49     5   0.223
##  3       0     0.8 rmse    standard    4.49     5   0.223
##  4       0     0.6 rmse    standard    4.49     5   0.223
##  5       0     0.4 rmse    standard    4.51     5   0.228
##  6       0     0.2 rmse    standard    4.51     5   0.228
##  7      10     0   rmse    standard    4.90     5   0.170
##  8      20     0   rmse    standard    5.44     5   0.203
##  9      10     0.2 rmse    standard    5.52     5   0.216
## 10      30     0   rmse    standard    5.84     5   0.228
## # … with 56 more rows

Putting it all together

final_spec <- linear_reg(penalty = 0, mixture = 0) %>%
  set_engine("glmnet")
fit <- last_fit(final_spec,
                rec,
                split = auto_split)
fit %>%
  collect_metrics()

## # A tibble: 2 x 3
##   .metric .estimator .estimate
##   <chr>   <chr>          <dbl>
## 1 rmse    standard       4.07 
## 2 rsq     standard       0.714