Bayesian optimization of model parameters.

tune_bayes() uses models to generate new candidate tuning parameter combinations based on previous results.

Usage

tune_bayes(object, ...)

# S3 method for model_spec
tune_bayes(
  object,
  preprocessor,
  resamples,
  ...,
  iter = 10,
  param_info = NULL,
  metrics = NULL,
  eval_time = NULL,
  objective = exp_improve(),
  initial = 5,
  control = control_bayes()
)

# S3 method for workflow
tune_bayes(
  object,
  resamples,
  ...,
  iter = 10,
  param_info = NULL,
  metrics = NULL,
  eval_time = NULL,
  objective = exp_improve(),
  initial = 5,
  control = control_bayes()
)

Arguments

object: A parsnip model specification or an unfitted workflow(). No tuning parameters are allowed; if arguments have been marked with tune(), their values must be finalized.
...: Options to pass to GPfit::GP_fit() (mostly for the corr argument).
preprocessor: A traditional model formula or a recipe created using recipes::recipe().
resamples: An rset resampling object created from an rsample function, such as rsample::vfold_cv().
iter: The maximum number of search iterations.
param_info: A dials::parameters() object or NULL. If none is given, a parameters set is derived from other arguments. Passing this argument can be useful when parameter ranges need to be customized.
metrics: A yardstick::metric_set(), or NULL to compute a standard set of metrics. The first metric in metrics is the one that will be optimized.
eval_time: A numeric vector of time points where dynamic event time metrics should be computed (e.g. the time-dependent ROC curve, etc). The values must be non-negative and should probably be no greater than the largest event time in the training set (See Details below).
objective: A character string for what metric should be optimized or an acquisition function object.
initial: An initial set of results in a tidy format (as would result from tune_grid()) or a positive integer. It is suggested that the number of initial results be greater than the number of parameters being optimized.
control: A control object created by control_bayes().

Value

A tibble of results that mirror those generated by tune_grid(). However, these results contain an .iter column and replicate the rset

object multiple times over iterations (at limited additional memory costs).

Details

The optimization starts with a set of initial results, such as those generated by tune_grid(). If none exist, the function will create several combinations and obtain their performance estimates.

Using one of the performance estimates as the model outcome, a Gaussian process (GP) model is created where the previous tuning parameter combinations are used as the predictors.

A large grid of potential hyperparameter combinations is predicted using the model and scored using an acquisition function. These functions usually combine the predicted mean and variance of the GP to decide the best parameter combination to try next. For more information, see the documentation for exp_improve() and the corresponding package vignette.

The best combination is evaluated using resampling and the process continues.

Parallel Processing

tune supports parallel processing with the future package. To execute the resampling iterations in parallel, specify a plan with future first. The allow_par argument can be used to avoid parallelism.

For the most part, warnings generated during training are shown as they occur and are associated with a specific resample when control_bayes(verbose = TRUE). They are (usually) not aggregated until the end of processing.

For Bayesian optimization, parallel processing is used to estimate the resampled performance values once a new candidate set of values are estimated.

Initial Values

The results of tune_grid(), or a previous run of tune_bayes() can be used in the initial argument. initial can also be a positive integer. In this case, a space-filling design will be used to populate a preliminary set of results. For good results, the number of initial values should be more than the number of parameters being optimized.

Parameter Ranges and Values

In some cases, the tuning parameter values depend on the dimensions of the data (they are said to contain unknown values). For example, mtry in random forest models depends on the number of predictors. In such cases, the unknowns in the tuning parameter object must be determined beforehand and passed to the function via the param_info argument. dials::finalize() can be used to derive the data-dependent parameters. Otherwise, a parameter set can be created via dials::parameters(), and the dials update() function can be used to specify the ranges or values.

Performance Metrics

To use your own performance metrics, the yardstick::metric_set() function can be used to pick what should be measured for each model. If multiple metrics are desired, they can be bundled. For example, to estimate the area under the ROC curve as well as the sensitivity and specificity (under the typical probability cutoff of 0.50), the metrics argument could be given:


  metrics = metric_set(roc_auc, sens, spec)

Each metric is calculated for each candidate model.

If no metric set is provided, one is created:

For regression models, the root mean squared error and coefficient of determination are computed.
For classification, the area under the ROC curve and overall accuracy are computed.

Note that the metrics also determine what type of predictions are estimated during tuning. For example, in a classification problem, if metrics are used that are all associated with hard class predictions, the classification probabilities are not created.

The out-of-sample estimates of these metrics are contained in a list column called .metrics. This tibble contains a row for each metric and columns for the value, the estimator type, and so on.

collect_metrics() can be used for these objects to collapse the results over the resampled (to obtain the final resampling estimates per tuning parameter combination).

Obtaining Predictions

When control_bayes(save_pred = TRUE), the output tibble contains a list column called .predictions that has the out-of-sample predictions for each parameter combination in the grid and each fold (which can be very large).

The elements of the tibble are tibbles with columns for the tuning parameters, the row number from the original data object (.row), the outcome data (with the same name(s) of the original data), and any columns created by the predictions. For example, for simple regression problems, this function generates a column called .pred and so on. As noted above, the prediction columns that are returned are determined by the type of metric(s) requested.

This list column can be unnested using tidyr::unnest() or using the convenience function collect_predictions().

Case Weights

Some models can utilize case weights during training. tidymodels currently supports two types of case weights: importance weights (doubles) and frequency weights (integers). Frequency weights are used during model fitting and evaluation, whereas importance weights are only used during fitting.

To know if your model is capable of using case weights, create a model spec and test it using parsnip::case_weights_allowed().

To use them, you will need a numeric column in your data set that has been passed through either hardhat:: importance_weights() or hardhat::frequency_weights().

For functions such as fit_resamples() and the tune_*() functions, the model must be contained inside of a workflows::workflow(). To declare that case weights are used, invoke workflows::add_case_weights() with the corresponding (unquoted) column name.

From there, the packages will appropriately handle the weights during model fitting and (if appropriate) performance estimation.

Censored Regression Models

Three types of metrics can be used to assess the quality of censored regression models:

static: the prediction is independent of time.
dynamic: the prediction is a time-specific probability (e.g., survival probability) and is measured at one or more particular times.
integrated: same as the dynamic metric but returns the integral of the different metrics from each time point.

Which metrics are chosen by the user affects how many evaluation times should be specified. For example:

# Needs no `eval_time` value
metric_set(concordance_survival)

# Needs at least one `eval_time`
metric_set(brier_survival)
metric_set(brier_survival, concordance_survival)

# Needs at least two eval_time` values
metric_set(brier_survival_integrated, concordance_survival)
metric_set(brier_survival_integrated, concordance_survival)
metric_set(brier_survival_integrated, concordance_survival, brier_survival)

Values of eval_time should be less than the largest observed event time in the training data. For many non-parametric models, the results beyond the largest time corresponding to an event are constant (or NA).

Optimizing Censored Regression Models

With dynamic performance metrics (e.g. Brier or ROC curves), performance is calculated for every value of eval_time but the first evaluation time given by the user (e.g., eval_time[1]) is used to guide the optimization.

Extracting Information

The extract control option will result in an additional function to be returned called .extracts. This is a list column that has tibbles containing the results of the user's function for each tuning parameter combination. This can enable returning each model and/or recipe object that is created during resampling. Note that this could result in a large return object, depending on what is returned.

The control function contains an option (extract) that can be used to retain any model or recipe that was created within the resamples. This argument should be a function with a single argument. The value of the argument that is given to the function in each resample is a workflow object (see workflows::workflow() for more information). Several helper functions can be used to easily pull out the preprocessing and/or model information from the workflow, such as extract_preprocessor() and extract_fit_parsnip().

As an example, if there is interest in getting each parsnip model fit back, one could use:


  extract = function (x) extract_fit_parsnip(x)

Note that the function given to the extract argument is evaluated on every model that is fit (as opposed to every model that is evaluated). As noted above, in some cases, model predictions can be derived for sub-models so that, in these cases, not every row in the tuning parameter grid has a separate R object associated with it.

Examples

library(recipes)
library(rsample)
library(parsnip)

# define resamples and minimal recipe on mtcars
set.seed(6735)
folds <- vfold_cv(mtcars, v = 5)

car_rec <-
  recipe(mpg ~ ., data = mtcars) %>%
  step_normalize(all_predictors())

# define an svm with parameters to tune
svm_mod <-
  svm_rbf(cost = tune(), rbf_sigma = tune()) %>%
  set_engine("kernlab") %>%
  set_mode("regression")

# use a space-filling design with 6 points
set.seed(3254)
svm_grid <- tune_grid(svm_mod, car_rec, folds, grid = 6)

show_best(svm_grid, metric = "rmse")
#> # A tibble: 5 × 8
#>       cost    rbf_sigma .metric .estimator  mean     n std_err .config    
#>      <dbl>        <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>      
#> 1 25.3     0.248        rmse    standard    3.17     5   0.678 Preprocess…
#> 2  3.88    0.000510     rmse    standard    4.07     5   0.727 Preprocess…
#> 3  0.102   0.00000592   rmse    standard    5.96     5   0.970 Preprocess…
#> 4  0.00125 0.000138     rmse    standard    5.96     5   0.970 Preprocess…
#> 5  0.0192  0.0000000427 rmse    standard    5.96     5   0.970 Preprocess…

# use bayesian optimization to evaluate at 6 more points
set.seed(8241)
svm_bayes <- tune_bayes(svm_mod, car_rec, folds, initial = svm_grid, iter = 6)

# note that bayesian optimization evaluated parameterizations
# similar to those that previously decreased rmse in svm_grid
show_best(svm_bayes, metric = "rmse")
#> # A tibble: 5 × 9
#>    cost rbf_sigma .metric .estimator  mean     n std_err .config     .iter
#>   <dbl>     <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>       <int>
#> 1  31.5   0.00224 rmse    standard    2.59     5   0.219 Iter5           5
#> 2  31.6   0.00671 rmse    standard    2.61     5   0.208 Iter4           4
#> 3  32.0   0.00109 rmse    standard    2.62     5   0.253 Iter1           1
#> 4  31.6   0.00466 rmse    standard    2.63     5   0.182 Iter6           6
#> 5  25.3   0.248   rmse    standard    3.17     5   0.678 Preprocess…     0

# specifying `initial` as a numeric rather than previous tuning results
# will result in `tune_bayes` initially evaluating an space-filling
# grid using `tune_grid` with `grid = initial`
set.seed(0239)
svm_init <- tune_bayes(svm_mod, car_rec, folds, initial = 6, iter = 6)

show_best(svm_init, metric = "rmse")
#> # A tibble: 5 × 9
#>    cost rbf_sigma .metric .estimator  mean     n std_err .config .iter
#>   <dbl>     <dbl> <chr>   <chr>      <dbl> <int>   <dbl> <chr>   <int>
#> 1 12.6     0.109  rmse    standard    2.84     5   0.528 Iter4       4
#> 2 30.8     0.0423 rmse    standard    3.13     5   0.387 Iter5       5
#> 3 27.2     0.153  rmse    standard    3.23     5   0.748 Iter6       6
#> 4  8.33    0.455  rmse    standard    3.23     5   0.655 Iter3       3
#> 5 23.6     0.877  rmse    standard    3.37     5   0.693 Iter1       1