4 - Iterative Search

Advanced tidymodels

Previously - Setup

library(tidymodels)
library(textrecipes)
library(bonsai)

# Max's usual settings: 
tidymodels_prefer()
theme_set(theme_bw())
options(
  pillar.advice = FALSE, 
  pillar.min_title_chars = Inf
)

data(hotel_rates)
set.seed(295)
hotel_rates <- 
  hotel_rates %>% 
  sample_n(5000) %>% 
  arrange(arrival_date) %>% 
  select(-arrival_date) %>%  
  mutate(
    company = factor(as.character(company)),
    country = factor(as.character(country)),
    agent = factor(as.character(agent))
  )

Previously - Data Usage

set.seed(4028)
hotel_split <- initial_split(hotel_rates, strata = avg_price_per_room)

hotel_train <- training(hotel_split)
hotel_test <- testing(hotel_split)

set.seed(472)
hotel_rs <- vfold_cv(hotel_train, strata = avg_price_per_room)

Previously - Boosting Model

hotel_rec <-
  recipe(avg_price_per_room ~ ., data = hotel_train) %>%
  step_YeoJohnson(lead_time) %>%
  step_dummy_hash(agent,   num_terms = tune("agent hash")) %>%
  step_dummy_hash(company, num_terms = tune("company hash")) %>%
  step_zv(all_predictors())

lgbm_spec <- 
  boost_tree(trees = tune(), learn_rate = tune(), min_n = tune()) %>% 
  set_mode("regression") %>% 
  set_engine("lightgbm", num_threads = 1)

lgbm_wflow <- workflow(hotel_rec, lgbm_spec)

lgbm_param <-
  lgbm_wflow %>%
  extract_parameter_set_dials() %>%
  update(`agent hash`   = num_hash(c(3, 8)),
         `company hash` = num_hash(c(3, 8)))

Iterative Search

Instead of pre-defining a grid of candidate points, we can model our current results to predict what the next candidate point should be.

Suppose that we are only tuning the learning rate in our boosted tree.

We could do something like:

mae_pred <- lm(mae ~ learn_rate, data = resample_results)

and use this to predict and rank new learning rate candidates.

Iterative Search

A linear model probably isn’t the best choice though (more in a minute).

To illustrate the process, we resampled a large grid of learning rate values for our data to show what the relationship is between MAE and learning rate.

Now suppose that we used a grid of three points in the parameter range for learning rate…

A Large Grid

A Three Point Grid

Gaussian Processes and Optimization

We can make a “meta-model” with a small set of historical performance results.

Gaussian Processes (GP) models are a good choice to model performance.

• It is a Bayesian model so we are using Bayesian Optimization (BO).
• For regression, we can assume that our data are multivariate normal.
• We also define a covariance function for the variance relationship between data points. A common one is:

\[\operatorname{cov}(\boldsymbol{x}_i, \boldsymbol{x}_j) = \exp\left(-\frac{1}{2}|\boldsymbol{x}_i - \boldsymbol{x}_j|^2\right) + \sigma^2_{ij}\]

GPs are good because

• they are flexible regression models (in the sense that splines are flexible).
• we need to get mean and variance predictions (and they are Bayesian)
• their variability is based on spatial distances.

Some people use random forests (with conformal variance estimates) or other methods but GPs are most popular.

Predicting Candidates

The GP model can take candidate tuning parameter combinations as inputs and make predictions for performance (e.g. MAE)

• The mean performance
• The variance of performance

The variance is mostly driven by spatial variability (the previous equation).

The predicted variance is zero at locations of actual data points and becomes very high when far away from any observed data.

Your turn

Your GP makes predictions on two new candidate tuning parameters.

We want to minimize MAE.

Which should we choose?

03:00

GP Fit (ribbon is mean +/- 1SD)

Choosing New Candidates

This isn’t a very good fit but we can still use it.

How can we use the outputs to choose the next point to measure?

Acquisition functions take the predicted mean and variance and use them to balance:

• exploration: new candidates should explore new areas.
• exploitation: new candidates must stay near existing values.

Exploration focuses on the variance, exploitation is about the mean.

Acquisition Functions

We’ll use an acquisition function to select a new candidate.

The most popular method appears to be expected improvement (EI) above the current best results.

• Zero at existing data points.
• The expected improvement is integrated over all possible improvement (“expected” in the probability sense).

We would probably pick the point with the largest EI as the next point.

(There are other functions beyond EI.)

Expected Improvement

Iteration

Once we pick the candidate point, we measure performance for it (e.g. resampling).

Another GP is fit, EI is recomputed, and so on.

We stop when we have completed the allowed number of iterations or if we don’t see any improvement after a pre-set number of attempts.

GP Fit with four points

Expected Improvement

GP Evolution

Expected Improvement Evolution

BO in tidymodels

We’ll use a function called tune_bayes() that has very similar syntax to tune_grid().

It has an additional initial argument for the initial set of performance estimates and parameter combinations for the GP model.

Initial grid points

initial can be the results of another tune_*() function or an integer (in which case tune_grid() is used under to hood to make such an initial set of results).

• We’ll run the optimization more than once, so let’s make an initial grid of results to serve as the substrate for the BO.

• I suggest at least the number of tuning parameters plus two as the initial grid for BO.

An Initial Grid

reg_metrics <- metric_set(mae, rsq)

set.seed(12)
init_res <-
  lgbm_wflow %>%
  tune_grid(
    resamples = hotel_rs,
    grid = nrow(lgbm_param) + 2,
    param_info = lgbm_param,
    metrics = reg_metrics
  )

show_best(init_res, metric = "mae")
#> # A tibble: 5 × 11
#>   trees min_n   learn_rate `agent hash` `company hash` .metric .estimator  mean     n std_err .config             
#>   <int> <int>        <dbl>        <int>          <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>               
#> 1   390    10 0.0139                 13             62 mae     standard    11.3    10   0.202 Preprocessor1_Model1
#> 2   718    31 0.00112                72             25 mae     standard    29.0    10   0.335 Preprocessor4_Model1
#> 3  1236    22 0.0000261              11             17 mae     standard    51.8    10   0.416 Preprocessor7_Model1
#> 4  1044    25 0.00000832             34             12 mae     standard    52.8    10   0.424 Preprocessor5_Model1
#> 5  1599     7 0.0000000402          254            179 mae     standard    53.2    10   0.427 Preprocessor6_Model1

BO using tidymodels

set.seed(15)
lgbm_bayes_res <-
  lgbm_wflow %>%
  tune_bayes(
    resamples = hotel_rs,
    initial = init_res,     # <- initial results
    iter = 20,
    param_info = lgbm_param,
    metrics = reg_metrics
  )

show_best(lgbm_bayes_res, metric = "mae")
#> # A tibble: 5 × 12
#>   trees min_n learn_rate `agent hash` `company hash` .metric .estimator  mean     n std_err .config .iter
#>   <int> <int>      <dbl>        <int>          <int> <chr>   <chr>      <dbl> <int>   <dbl> <chr>   <int>
#> 1  1769     2     0.0299          114            245 mae     standard    9.41    10   0.160 Iter13     13
#> 2  1969     3     0.0270          240             99 mae     standard    9.49    10   0.189 Iter11     11
#> 3  1780     5     0.0403           27             78 mae     standard    9.54    10   0.164 Iter17     17
#> 4  1454     3     0.0414          114             10 mae     standard    9.55    10   0.144 Iter10     10
#> 5  1253     2     0.0312          131            207 mae     standard    9.56    10   0.145 Iter19     19

Plotting BO Results

autoplot(lgbm_bayes_res, metric = "mae")

Plotting BO Results

autoplot(lgbm_bayes_res, metric = "mae", type = "parameters")

Plotting BO Results

autoplot(lgbm_bayes_res, metric = "mae", type = "performance")

ENHANCE

autoplot(lgbm_bayes_res, metric = "mae", type = "performance") +
  ylim(c(9, 14))

Your turn

Let’s try a different acquisition function: conf_bound(kappa).

We’ll use the objective argument to set it.

Choose your own kappa value:

• Larger values will explore the space more.
• “Large” values are usually less than one.

10:00

Notes

• Stopping tune_bayes() will return the current results.

• Parallel processing can still be used to more efficiently measure each candidate point.

• There are a lot of other iterative methods that you can use.

• The finetune package also has functions for simulated annealing search.

Finalizing the Model

Let’s say that we’ve tried a lot of different models and we like our lightgbm model the most.

What do we do now?

• Finalize the workflow by choosing the values for the tuning parameters.
• Fit the model on the entire training set.
• Verify performance using the test set.
• Document and publish the model(?)

Locking Down the Tuning Parameters

We can take the results of the Bayesian optimization and accept the best results:

best_param <- select_best(lgbm_bayes_res, metric = "mae")
final_wflow <- 
  lgbm_wflow %>% 
  finalize_workflow(best_param)
final_wflow
#> ══ Workflow ══════════════════════════════════════════════════════════
#> Preprocessor: Recipe
#> Model: boost_tree()
#> 
#> ── Preprocessor ──────────────────────────────────────────────────────
#> 4 Recipe Steps
#> 
#> • step_YeoJohnson()
#> • step_dummy_hash()
#> • step_dummy_hash()
#> • step_zv()
#> 
#> ── Model ─────────────────────────────────────────────────────────────
#> Boosted Tree Model Specification (regression)
#> 
#> Main Arguments:
#>   trees = 1769
#>   min_n = 2
#>   learn_rate = 0.0299391312149257
#> 
#> Engine-Specific Arguments:
#>   num_threads = 1
#> 
#> Computational engine: lightgbm

The Final Fit

We can use individual functions:

final_fit <- final_wflow %>% fit(data = hotel_train)

# then predict() or augment() 
# then compute metrics

Remember that there is also a convenience function to do all of this:

set.seed(3893)
final_res <- final_wflow %>% last_fit(hotel_split, metrics = reg_metrics)
final_res
#> # Resampling results
#> # Manual resampling 
#> # A tibble: 1 × 6
#>   splits              id               .metrics         .notes           .predictions         .workflow 
#>   <list>              <chr>            <list>           <list>           <list>               <list>    
#> 1 <split [3749/1251]> train/test split <tibble [2 × 4]> <tibble [0 × 3]> <tibble [1,251 × 4]> <workflow>

Test Set Results

final_res %>% 
  collect_predictions() %>% 
  cal_plot_regression(
    truth = avg_price_per_room, 
    estimate = .pred, 
    alpha = 1 / 4)

Test set performance:

final_res %>% collect_metrics()
#> # A tibble: 2 × 4
#>   .metric .estimator .estimate .config             
#>   <chr>   <chr>          <dbl> <chr>               
#> 1 mae     standard       9.63  Preprocessor1_Model1
#> 2 rsq     standard       0.948 Preprocessor1_Model1