Exploring and Understanding Hyperparameter Tuning

Learners use hyperparameters to achieve better performance on particular datasets. When we use a machine learning package to choose the best hyperparmeters, the relationship between changing the hyperparameter and performance might not be obvious. mlr provides several new implementations to better understand what happens when we tune hyperparameters and to help us optimize our choice of hyperparameters.

Background

Let’s say you have a dataset, and you’re getting ready to flex your machine learning muscles. Maybe you want to do classification, or regression, or clustering. You get your dataset together and pick a few learners to evaluate.

The majority of learners that you might use for any of these tasks have hyperparameters that the user must tune. Hyperparameters may be able to take on a lot of possible values, so it’s typically left to the user to specify the values. If you’re using a popular machine learning library like sci-kit learn, the library will take care of this for you via cross-validation: auto-generating the optimal values for your hyperparameters. We’ll then take these best-performing hyperparameters and use those values for our learner. Essentially, we treat the optimization of hyperparameters as a black box.

In mlr, we want to open up that black box, so that you can make better decisions. Using the functionality built-in, we can answer questions like:

  • How does varying the value of a hyperparameter change the performance of the machine learning algorithm?
  • On a related note: where’s an ideal range to search for optimal hyperparameters?
  • How did the optimization algorithm (prematurely) converge?
  • What’s the relative importance of each hyperparameter?

Some of the users who might see benefit from “opening” the black box of hyperparameter optimization:

  • researchers that want to better understand learners in practice
  • engineers that want to maximize performance or minimize run time
  • teachers that want to demonstrate what happens when tuning hyperparameters

We’ll use Pima Indians dataset in this blog post, where we want to predict whether or not someone has diabetes, so we’ll perform classification, but the methods we discuss also work for regression and clustering.

Perhaps we decide we want to try kernlab’s svm for our classification task. Knowing that svm has several hyperparameters to tune, we can ask mlr to list the hyperparameters to refresh our memory:

library(mlr)
library(ggplot2)
# to make sure our results are replicable we set the seed
set.seed(7)
getParamSet("classif.ksvm")
##                        Type  len    Def
## scaled              logical    -   TRUE
## type               discrete    -  C-svc
## kernel             discrete    - rbfdot
## C                   numeric    -      1
## nu                  numeric    -    0.2
## epsilon             numeric    -    0.1
## sigma               numeric    -      -
## degree              integer    -      3
## scale               numeric    -      1
## offset              numeric    -      1
## order               integer    -      1
## tol                 numeric    -  0.001
## shrinking           logical    -   TRUE
## class.weights numericvector <NA>      -
## fit                 logical    -   TRUE
## cache               integer    -     40
##                                                 Constr Req Tunable
## scaled                                               -   -    TRUE
## type              C-svc,nu-svc,C-bsvc,spoc-svc,kbb-svc   -    TRUE
## kernel        vanilladot,polydot,rbfdot,tanhdot,lap...   -    TRUE
## C                                             0 to Inf   Y    TRUE
## nu                                            0 to Inf   Y    TRUE
## epsilon                                    -Inf to Inf   Y    TRUE
## sigma                                         0 to Inf   Y    TRUE
## degree                                        1 to Inf   Y    TRUE
## scale                                         0 to Inf   Y    TRUE
## offset                                     -Inf to Inf   Y    TRUE
## order                                      -Inf to Inf   Y    TRUE
## tol                                           0 to Inf   -    TRUE
## shrinking                                            -   -    TRUE
## class.weights                                 0 to Inf   -    TRUE
## fit                                                  -   -    TRUE
## cache                                         1 to Inf   -   FALSE
##               Trafo
## scaled            -
## type              -
## kernel            -
## C                 -
## nu                -
## epsilon           -
## sigma             -
## degree            -
## scale             -
## offset            -
## order             -
## tol               -
## shrinking         -
## class.weights     -
## fit               -
## cache             -

Noting that we have default values for each of the hyperparameters, we could simply accept the defaults for each of the hyperparameters and evaluate our mmce performance using 3-fold cross validation:

rdesc = makeResampleDesc("CV", iters = 3)
r = resample("classif.ksvm", pid.task, rdesc)
print(r)
## Resample Result
## Task: PimaIndiansDiabetes-example
## Learner: classif.ksvm
## mmce.aggr: 0.24
## mmce.mean: 0.24
## mmce.sd: 0.03
## Runtime: 0.0886385

While this result may seem decent, we have a nagging doubt: what if we chose hyperparameter values different from the defaults? Would we get better results?

Maybe we believe that the default of kernel = "rbfdot" will work well based on our prior knowledge of the dataset, but we want to try altering our regularization to get better performance. For kernlab’s svm, regularization is represented using the C hyperparameter. Calling getParamSet again to refresh our memory, we see that C defaults to 1.

getParamSet("classif.ksvm")
##                        Type  len    Def
## scaled              logical    -   TRUE
## type               discrete    -  C-svc
## kernel             discrete    - rbfdot
## C                   numeric    -      1
## nu                  numeric    -    0.2
## epsilon             numeric    -    0.1
## sigma               numeric    -      -
## degree              integer    -      3
## scale               numeric    -      1
## offset              numeric    -      1
## order               integer    -      1
## tol                 numeric    -  0.001
## shrinking           logical    -   TRUE
## class.weights numericvector <NA>      -
## fit                 logical    -   TRUE
## cache               integer    -     40
##                                                 Constr Req Tunable
## scaled                                               -   -    TRUE
## type              C-svc,nu-svc,C-bsvc,spoc-svc,kbb-svc   -    TRUE
## kernel        vanilladot,polydot,rbfdot,tanhdot,lap...   -    TRUE
## C                                             0 to Inf   Y    TRUE
## nu                                            0 to Inf   Y    TRUE
## epsilon                                    -Inf to Inf   Y    TRUE
## sigma                                         0 to Inf   Y    TRUE
## degree                                        1 to Inf   Y    TRUE
## scale                                         0 to Inf   Y    TRUE
## offset                                     -Inf to Inf   Y    TRUE
## order                                      -Inf to Inf   Y    TRUE
## tol                                           0 to Inf   -    TRUE
## shrinking                                            -   -    TRUE
## class.weights                                 0 to Inf   -    TRUE
## fit                                                  -   -    TRUE
## cache                                         1 to Inf   -   FALSE
##               Trafo
## scaled            -
## type              -
## kernel            -
## C                 -
## nu                -
## epsilon           -
## sigma             -
## degree            -
## scale             -
## offset            -
## order             -
## tol               -
## shrinking         -
## class.weights     -
## fit               -
## cache             -

Let’s tell mlr to randomly pick C values between 2^-5 and 2^5, evaluating mmce using 3-fold cross validation:

# create the C parameter in continuous space: 2^-5 : 2^5
ps = makeParamSet(
  makeNumericParam("C", lower = -5, upper = 5, trafo = function(x) 2^x)
)
# random search in the space with 100 iterations
ctrl = makeTuneControlRandom(maxit = 100L)
# 3-fold CV
rdesc = makeResampleDesc("CV", iters = 2L)
# run the hyperparameter tuning process
res = tuneParams("classif.ksvm", task = pid.task, control = ctrl, 
  resampling = rdesc, par.set = ps, show.info = FALSE)
print(res)
## Tune result:
## Op. pars: C=0.347
## mmce.test.mean=0.233

mlr gives us the best performing value for C, and we can see that we’ve improved our results vs. just accepting the default value for C. This functionality is available in other machine learning packages, like sci-kit learn’s random search, but this functionality is essentially treating our choice of C as a black box method: we give a search strategy and just accept the optimal value. What if we wanted to get a sense of the relationship between C and mmce? Maybe the relationship is linear in a certain range and we can exploit this to get better even performance! mlr provides 2 methods to help answer this question: generateHyperParsEffectData to generate the resulting data and plotHyperParsEffect providing many options built-in for the user to plot the data.

Let’s investigate the results from before where we tuned C:

data = generateHyperParsEffectData(res)
plotHyperParsEffect(data, x = "C", y = "mmce.test.mean")

plot of chunk first_chart

From the scatterplot, it appears our optimal performance is somewhere in the region between 2^-2.5 and 2^-1.75. This could provide us a region to further explore if we wanted to try to get even better performance!

We could also evaluate how “long” it takes us to find that optimal value:

plotHyperParsEffect(data, x = "iteration", y = "mmce.test.mean")

plot of chunk second_chart

By default, the plot only shows the global optimum, so we can see that we found the “best” performance in less than 25 iterations!

But wait, I hear you saying. I also want to tune sigma, the inverse kernel width of the radial basis kernel function. So now we have 2 hyperparameters that we want to simultaneously tune: C and sigma.

# create the C and sigma parameter in continuous space: 2^-5 : 2^5
ps = makeParamSet(
  makeNumericParam("C", lower = -5, upper = 5, trafo = function(x) 2^x),
  makeNumericParam("sigma", lower = -5, upper = 5, trafo = function(x) 2^x)
)
# random search in the space with 100 iterations
ctrl = makeTuneControlRandom(maxit = 100L)
# 3-fold CV
rdesc = makeResampleDesc("CV", iters = 2L)
# run the hyperparameter tuning process
res = tuneParams("classif.ksvm", task = pid.task, control = ctrl, 
  resampling = rdesc, par.set = ps, show.info = FALSE)
print(res)
## Tune result:
## Op. pars: C=0.233; sigma=0.0386
## mmce.test.mean=0.232
# collect the hyperparameter data
data = generateHyperParsEffectData(res)

We can use plotHyperParsEffect to easily create a heatmap with both hyperparameters. We get tons of functionality for free here. For example, mlr will automatically interpolate the grid to get an estimate for values we didn’t even test! All we need to do is pass a regression learner to the interpolate argument:

plotHyperParsEffect(data, x = "C", y = "sigma", z = "mmce.test.mean",
  plot.type = "heatmap", interpolate = "regr.earth")

plot of chunk third_chart

If we use the show.experiments argument, we can see which points were actually tested and which were interpolated:

plotHyperParsEffect(data, x = "C", y = "sigma", z = "mmce.test.mean",
  plot.type = "heatmap", interpolate = "regr.earth", show.experiments = TRUE)

plot of chunk fourth_chart

plotHyperParsEffect returns a ggplot2 object, so we can always customize it to better fit our needs downstream:

plt = plotHyperParsEffect(data, x = "C", y = "sigma", z = "mmce.test.mean",
  plot.type = "heatmap", interpolate = "regr.earth", show.experiments = TRUE)
min_plt = min(plt$data$mmce.test.mean, na.rm = TRUE)
max_plt = max(plt$data$mmce.test.mean, na.rm = TRUE)
mean_plt = mean(c(min_plt, max_plt))
plt + scale_fill_gradient2(breaks = seq(min_plt, max_plt, length.out = 4),
  low = "red", mid = "white", high = "blue", midpoint = mean_plt)

plot of chunk fifth_chart

Now we can get a good sense of where the separation happens for each of the hyperparameters: in this particular example, we want lower values for sigma and values around 1 for C.

This was just a taste of mlr’s hyperparameter tuning visualization capabilities. For the full tutorial, check out the mlr tutorial.

Some features coming soon:

  • “Prettier” plot defaults
  • Support for more than 2 hyperparameters
  • Direct support for hyperparameter “importance”

Thanks to the generous sponsorship from GSoC, and many thanks to my mentors Bernd Bischl and Lars Kotthoff!

Written on August 21, 2016 by Mason Gallo