Let’s use drake to train and compare multiple models in a unified automated workflow.

Packages

First, we load our packages into a fresh R session.

library(drake)
library(keras)
library(tidyverse)
library(rsample)
library(recipes)
library(yardstick)

Functions

drake is R-focused and function-oriented. We create functions to preprocess the data,

prepare_recipe <- function(data) {
  data %>%
    training() %>%
    recipe(Churn ~ .) %>%
    step_rm(customerID) %>%
    step_naomit(all_outcomes(), all_predictors()) %>%
    step_discretize(tenure, options = list(cuts = 6)) %>%
    step_log(TotalCharges) %>%
    step_mutate(Churn = ifelse(Churn == "Yes", 1, 0)) %>%
    step_dummy(all_nominal(), -all_outcomes()) %>%
    step_center(all_predictors(), -all_outcomes()) %>%
    step_scale(all_predictors(), -all_outcomes()) %>%
    prep()
}

define a keras model,

define_model <- function(rec) {
  input_shape <- ncol(
    juice(rec, all_predictors(), composition = "matrix")
  )
  keras_model_sequential() %>%
    layer_dense(
      units = 16,
      kernel_initializer = "uniform",
      activation = "relu",
      input_shape = input_shape
    ) %>%
    layer_dropout(rate = 0.1) %>%
    layer_dense(
      units = 16,
      kernel_initializer = "uniform",
      activation = "relu"
    ) %>%
    layer_dropout(rate = 0.1) %>%
    layer_dense(
      units = 1,
      kernel_initializer = "uniform",
      activation = "sigmoid"
    )
}

train and serialize a model,

train_model <- function(data, rec, batch_size) {
  model <- define_model(rec)
  compile(
    model,
    optimizer = "adam",
    loss = "binary_crossentropy",
    metrics = c("accuracy")
  )
  x_train_tbl <- juice(
    rec,
    all_predictors(),
    composition = "matrix"
  )
  y_train_vec <- juice(rec, all_outcomes()) %>%
    pull()
  fit(
    object = model,
    x = x_train_tbl,
    y = y_train_vec,
    batch_size = batch_size,
    epochs = 35,
    validation_split = 0.30,
    verbose = 0
  )
  serialize_model(model)
}

compare the predictions of a serialized model against reality,

confusion_matrix <- function(data, rec, serialized_model) {
  model <- unserialize_model(serialized_model)
  testing_data <- bake(rec, testing(data))
  x_test_tbl <- testing_data %>%
    select(-Churn) %>%
    as.matrix()
  y_test_vec <- testing_data %>%
    select(Churn) %>%
    pull()
  yhat_keras_class_vec <- model %>%
    predict_classes(x_test_tbl) %>%
    as.factor() %>%
    fct_recode(yes = "1", no = "0")
  yhat_keras_prob_vec <-
    model %>%
    predict_proba(x_test_tbl) %>%
    as.vector()
  test_truth <- y_test_vec %>%
    as.factor() %>%
    fct_recode(yes = "1", no = "0")
  estimates_keras_tbl <- tibble(
    truth = test_truth,
    estimate = yhat_keras_class_vec,
    class_prob = yhat_keras_prob_vec
  )
  estimates_keras_tbl %>%
    conf_mat(truth, estimate)
}

and compare the performance of multiple models.

compare_models <- function(...) {
  batch_sizes <- match.call()[-1] %>%
    as.character() %>%
    gsub(pattern = "conf_", replacement = "")
  df <- map_df(list(...), summary) %>%
    filter(.metric %in% c("accuracy", "sens", "spec")) %>%
    mutate(
      batch_size = rep(batch_sizes, each = n() / length(batch_sizes))
    ) %>%
    rename(metric = .metric, estimate = .estimate)
  ggplot(df) +
    geom_line(
      aes(x = metric, y = estimate, color = batch_size, group = batch_size)
    ) +
    theme_gray(16)
}

Plan

Next, we define our workflow in a drake plan. We will prepare the data, train different models with different batch sizes, and compare the models in terms of performance.

batch_sizes <- c(16, 32)
plan <- drake_plan(
  data = read_csv(file_in("customer_churn.csv"), col_types = cols()) %>%
    initial_split(prop = 0.3),
  rec = prepare_recipe(data),
  model = target(
    train_model(data, rec, batch_size),
    transform = map(batch_size = !!batch_sizes)
  ),
  conf = target(
    confusion_matrix(data, rec, model),
    transform = map(model, .id = batch_size)
  ),
  comparison = target(
    compare_models(conf),
    transform = combine(conf)
  )
)

The plan is a data frame with the steps we are going to do.

plan

Dependency graph

The graph visualizes the dependency relationships among the steps of the workflow.

config <- drake_config(plan)
vis_drake_graph(config)

Run the models

Call make() to actually run the workflow.

make(plan)
target data
target rec
target model_16
target model_32
target conf_16
target conf_32
target comparison

Inspect the results

The two models performed about the same.

readd(comparison) # see also loadd()

Add models

Let’s try another batch size.

batch_sizes <- c(16, 32, 64)
plan <- drake_plan(
  data = read_csv(file_in("customer_churn.csv"), col_types = cols()) %>%
    initial_split(prop = 0.3),
  rec = prepare_recipe(data),
  model = target(
    train_model(data, rec, batch_size),
    transform = map(batch_size = !!batch_sizes)
  ),
  conf = target(
    confusion_matrix(data, rec, model),
    transform = map(model, .id = batch_size)
  ),
  comparison = target(
    compare_models(conf),
    transform = combine(conf)
  )
)

We already trained models with batch sizes 16 and 32, and their dependencies have not changed, so some of our work is already up to date.

config <- drake_config(plan)
vis_drake_graph(config) # see also outdated() and predict_runtime()

make() only trains the outdated or missing models and refreshes the post-processing. It skips the targets that are already up to date.

make(plan)
target model_64
target conf_64
target comparison

Inspect the results again

readd(comparison) # see also loadd()

Going forward, we can turn our attention to different tuning parameters and try to improve specificity.

Tips

---
title: "Automated workflow"
output: html_notebook
---

```{r setup, include = FALSE}
library(drake)
library(keras)
library(tidyverse)
library(rsample)
library(recipes)
library(yardstick)
options(
  drake_make_menu = FALSE,
  drake_clean_menu = FALSE,
  warnPartialMatchArgs = FALSE,
  crayon.enabled = FALSE,
  readr.show_progress = FALSE
)
clean(destroy = TRUE)
knitr::opts_chunk$set(
  collapse = TRUE,
  comment = "#>"
)
```

Let's use [`drake`](https://github.com/ropensci/drake) to train and compare multiple models in a unified automated workflow.

## Packages

First, we load our packages into a fresh R session.

```{r}
library(drake)
library(keras)
library(tidyverse)
library(rsample)
library(recipes)
library(yardstick)
```

## Functions

[`drake`](https://github.com/ropensci/drake) is R-focused and function-oriented. We create functions to [preprocess the data](https://github.com/tidymodels/recipes),

```{r}
prepare_recipe <- function(data) {
  data %>%
    training() %>%
    recipe(Churn ~ .) %>%
    step_rm(customerID) %>%
    step_naomit(all_outcomes(), all_predictors()) %>%
    step_discretize(tenure, options = list(cuts = 6)) %>%
    step_log(TotalCharges) %>%
    step_mutate(Churn = ifelse(Churn == "Yes", 1, 0)) %>%
    step_dummy(all_nominal(), -all_outcomes()) %>%
    step_center(all_predictors(), -all_outcomes()) %>%
    step_scale(all_predictors(), -all_outcomes()) %>%
    prep()
}
```

define a [`keras`](https://github.com/rstudio/keras) model,

```{r}
define_model <- function(rec) {
  input_shape <- ncol(
    juice(rec, all_predictors(), composition = "matrix")
  )
  keras_model_sequential() %>%
    layer_dense(
      units = 16,
      kernel_initializer = "uniform",
      activation = "relu",
      input_shape = input_shape
    ) %>%
    layer_dropout(rate = 0.1) %>%
    layer_dense(
      units = 16,
      kernel_initializer = "uniform",
      activation = "relu"
    ) %>%
    layer_dropout(rate = 0.1) %>%
    layer_dense(
      units = 1,
      kernel_initializer = "uniform",
      activation = "sigmoid"
    )
}
```

train and [serialize](https://tensorflow.rstudio.com/keras/reference/serialize_model.html) a model,


```{r}
train_model <- function(data, rec, batch_size) {
  model <- define_model(rec)
  compile(
    model,
    optimizer = "adam",
    loss = "binary_crossentropy",
    metrics = c("accuracy")
  )
  x_train_tbl <- juice(
    rec,
    all_predictors(),
    composition = "matrix"
  )
  y_train_vec <- juice(rec, all_outcomes()) %>%
    pull()
  fit(
    object = model,
    x = x_train_tbl,
    y = y_train_vec,
    batch_size = batch_size,
    epochs = 35,
    validation_split = 0.30,
    verbose = 0
  )
  serialize_model(model)
}
```

compare the predictions of a [serialized](https://tensorflow.rstudio.com/keras/reference/serialize_model.html) model against reality,

```{r}
confusion_matrix <- function(data, rec, serialized_model) {
  model <- unserialize_model(serialized_model)
  testing_data <- bake(rec, testing(data))
  x_test_tbl <- testing_data %>%
    select(-Churn) %>%
    as.matrix()
  y_test_vec <- testing_data %>%
    select(Churn) %>%
    pull()
  yhat_keras_class_vec <- model %>%
    predict_classes(x_test_tbl) %>%
    as.factor() %>%
    fct_recode(yes = "1", no = "0")
  yhat_keras_prob_vec <-
    model %>%
    predict_proba(x_test_tbl) %>%
    as.vector()
  test_truth <- y_test_vec %>%
    as.factor() %>%
    fct_recode(yes = "1", no = "0")
  estimates_keras_tbl <- tibble(
    truth = test_truth,
    estimate = yhat_keras_class_vec,
    class_prob = yhat_keras_prob_vec
  )
  estimates_keras_tbl %>%
    conf_mat(truth, estimate)
}
```

and compare the performance of multiple models. 

```{r}
compare_models <- function(...) {
  batch_sizes <- match.call()[-1] %>%
    as.character() %>%
    gsub(pattern = "conf_", replacement = "")
  df <- map_df(list(...), summary) %>%
    filter(.metric %in% c("accuracy", "sens", "spec")) %>%
    mutate(
      batch_size = rep(batch_sizes, each = n() / length(batch_sizes))
    ) %>%
    rename(metric = .metric, estimate = .estimate)
  ggplot(df) +
    geom_line(
      aes(x = metric, y = estimate, color = batch_size, group = batch_size)
    ) +
    theme_gray(16)
}
```

## Plan

Next, we define our workflow in a [`drake` plan](https://ropenscilabs.github.io/drake-manual/plans.html). We will prepare the data, train different models with different batch sizes, and compare the models in terms of performance. 

```{r}
batch_sizes <- c(16, 32)

plan <- drake_plan(
  data = read_csv(file_in("customer_churn.csv"), col_types = cols()) %>%
    initial_split(prop = 0.3),
  rec = prepare_recipe(data),
  model = target(
    train_model(data, rec, batch_size),
    transform = map(batch_size = !!batch_sizes)
  ),
  conf = target(
    confusion_matrix(data, rec, model),
    transform = map(model, .id = batch_size)
  ),
  comparison = target(
    compare_models(conf),
    transform = combine(conf)
  )
)
```

The plan is a data frame with the steps we are going to do.

```{r}
plan
```

## Dependency graph

The graph visualizes the dependency relationships among the steps of the workflow.

```{r}
config <- drake_config(plan)
vis_drake_graph(config)
```

## Run the models

Call [`make()`](https://ropensci.github.io/drake/reference/make.html) to actually run the workflow.

```{r}
make(plan)
```

## Inspect the results

The two models performed about the same.

```{r}
readd(comparison) # see also loadd()
```

## Add models

Let's try another batch size.

```{r}
batch_sizes <- c(16, 32, 64)

plan <- drake_plan(
  data = read_csv(file_in("customer_churn.csv"), col_types = cols()) %>%
    initial_split(prop = 0.3),
  rec = prepare_recipe(data),
  model = target(
    train_model(data, rec, batch_size),
    transform = map(batch_size = !!batch_sizes)
  ),
  conf = target(
    confusion_matrix(data, rec, model),
    transform = map(model, .id = batch_size)
  ),
  comparison = target(
    compare_models(conf),
    transform = combine(conf)
  )
)
```

We already trained models with batch sizes 16 and 32, and their dependencies have not changed, so some of our work is already up to date.

```{r}
config <- drake_config(plan)
vis_drake_graph(config) # see also outdated() and predict_runtime()
```

[`make()`](https://ropensci.github.io/drake/reference/make.html) only trains the outdated or missing models and refreshes the post-processing. It skips the targets that are already up to date.


```{r}
make(plan)
```

## Inspect the results again

```{r}
readd(comparison) # see also loadd()
```

Going forward, we can turn our attention to different tuning parameters and try to improve specificity.

## Tips

- To save this code in well-organized R scripts, see the [guidance on persistent `drake`-powered projects](https://ropenscilabs.github.io/drake-manual/projects.html).
- [`drake`](https://github.com/ropensci/drake) has [built-in distributed computing support](https://ropenscilabs.github.io/drake-manual/hpc.html) that lets you fit multiple models in parallel.

```{r, echo = FALSE}
clean(destroy = TRUE)
```
