sklearn: SVM classification¶
In this example we will use Optunity to optimize hyperparameters for a support vector machine classifier (SVC) in scikit-learn. We will learn a model to distinguish digits 8 and 9 in the MNIST data set in two settings
- tune SVM with RBF kernel
- tune SVM with RBF, polynomial or linear kernel, that is choose the kernel function and its hyperparameters at once
import optunity
import optunity.metrics
# comment this line if you are running the notebook
import sklearn.svm
import numpy as np
Create the data set: we use the MNIST data set and will build models to distinguish digits 8 and 9.
from sklearn.datasets import load_digits
digits = load_digits()
n = digits.data.shape[0]
positive_digit = 8
negative_digit = 9
positive_idx = [i for i in range(n) if digits.target[i] == positive_digit]
negative_idx = [i for i in range(n) if digits.target[i] == negative_digit]
# add some noise to the data to make it a little challenging
original_data = digits.data[positive_idx + negative_idx, ...]
data = original_data + 5 * np.random.randn(original_data.shape[0], original_data.shape[1])
labels = [True] * len(positive_idx) + [False] * len(negative_idx)
First, lets see the performance of an SVC with default hyperparameters.
# compute area under ROC curve of default parameters
@optunity.cross_validated(x=data, y=labels, num_folds=5)
def svm_default_auroc(x_train, y_train, x_test, y_test):
model = sklearn.svm.SVC().fit(x_train, y_train)
decision_values = model.decision_function(x_test)
auc = optunity.metrics.roc_auc(y_test, decision_values)
return auc
svm_default_auroc()
0.7328666183635757
Tune SVC with RBF kernel¶
In order to use Optunity to optimize hyperparameters, we start by defining the objective function. We will use 5-fold cross-validated area under the ROC curve. For now, lets restrict ourselves to the RBF kernel and optimize \(C\) and \(\gamma\).
We start by defining the objective function svm_rbf_tuned_auroc(),
which accepts \(C\) and \(\gamma\) as arguments.
#we will make the cross-validation decorator once, so we can reuse it later for the other tuning task
# by reusing the decorator, we get the same folds etc.
cv_decorator = optunity.cross_validated(x=data, y=labels, num_folds=5)
def svm_rbf_tuned_auroc(x_train, y_train, x_test, y_test, C, logGamma):
model = sklearn.svm.SVC(C=C, gamma=10 ** logGamma).fit(x_train, y_train)
decision_values = model.decision_function(x_test)
auc = optunity.metrics.roc_auc(y_test, decision_values)
return auc
svm_rbf_tuned_auroc = cv_decorator(svm_rbf_tuned_auroc)
# this is equivalent to the more common syntax below
# @optunity.cross_validated(x=data, y=labels, num_folds=5)
# def svm_rbf_tuned_auroc...
svm_rbf_tuned_auroc(C=1.0, logGamma=0.0)
0.5
Now we can use Optunity to find the hyperparameters that maximize AUROC.
optimal_rbf_pars, info, _ = optunity.maximize(svm_rbf_tuned_auroc, num_evals=150, C=[0, 10], logGamma=[-5, 0])
# when running this outside of IPython we can parallelize via optunity.pmap
# optimal_rbf_pars, _, _ = optunity.maximize(svm_rbf_tuned_auroc, 150, C=[0, 10], gamma=[0, 0.1], pmap=optunity.pmap)
print("Optimal parameters: " + str(optimal_rbf_pars))
print("AUROC of tuned SVM with RBF kernel: %1.3f" % info.optimum)
Optimal parameters: {'logGamma': -3.0716796875000005, 'C': 3.3025997497032007}
AUROC of tuned SVM with RBF kernel: 0.987
We can turn the call log into a pandas dataframe to efficiently inspect the solver trace.
import pandas
df = optunity.call_log2dataframe(info.call_log)
Lets look at the best 20 sets of hyperparameters to make sure the results are somewhat stable.
df.sort('value', ascending=False)[:10]
| C | logGamma | value | |
|---|---|---|---|
| 149 | 3.822811 | -3.074680 | 0.987413 |
| 92 | 3.302600 | -3.071680 | 0.987413 |
| 145 | 3.259690 | -3.033531 | 0.987252 |
| 14 | 3.542839 | -3.080013 | 0.987237 |
| 131 | 3.232732 | -3.080968 | 0.987237 |
| 53 | 7.328411 | -3.103471 | 0.987237 |
| 70 | 3.632562 | -3.088346 | 0.987237 |
| 146 | 3.067660 | -3.091143 | 0.987237 |
| 124 | 2.566381 | -3.114649 | 0.987237 |
| 100 | 3.340268 | -3.092535 | 0.987237 |
Tune SVC without deciding the kernel in advance¶
In the previous part we choose to use an RBF kernel. Even though the RBF kernel is known to work well for a large variety of problems (and yielded good accuracy here), our choice was somewhat arbitrary.
We will now use Optunity’s conditional hyperparameter optimization feature to optimize over all kernel functions and their associated hyperparameters at once. This requires us to define the search space.
space = {'kernel': {'linear': {'C': [0, 2]},
'rbf': {'logGamma': [-5, 0], 'C': [0, 10]},
'poly': {'degree': [2, 5], 'C': [0, 5], 'coef0': [0, 2]}
}
}
We will also have to modify the objective function to cope with
conditional hyperparameters. The reason we need to do this explicitly is
because scikit-learn doesn’t like dealing with None values for
irrelevant hyperparameters (e.g. degree when using an RBF kernel).
Optunity will set all irrelevant hyperparameters in a given set to
None.
def train_model(x_train, y_train, kernel, C, logGamma, degree, coef0):
"""A generic SVM training function, with arguments based on the chosen kernel."""
if kernel == 'linear':
model = sklearn.svm.SVC(kernel=kernel, C=C)
elif kernel == 'poly':
model = sklearn.svm.SVC(kernel=kernel, C=C, degree=degree, coef0=coef0)
elif kernel == 'rbf':
model = sklearn.svm.SVC(kernel=kernel, C=C, gamma=10 ** logGamma)
else:
raise ArgumentError("Unknown kernel function: %s" % kernel)
model.fit(x_train, y_train)
return model
def svm_tuned_auroc(x_train, y_train, x_test, y_test, kernel='linear', C=0, logGamma=0, degree=0, coef0=0):
model = train_model(x_train, y_train, kernel, C, logGamma, degree, coef0)
decision_values = model.decision_function(x_test)
return optunity.metrics.roc_auc(y_test, decision_values)
svm_tuned_auroc = cv_decorator(svm_tuned_auroc)
Now we are ready to go and optimize both kernel function and associated hyperparameters!
optimal_svm_pars, info, _ = optunity.maximize_structured(svm_tuned_auroc, space, num_evals=150)
print("Optimal parameters" + str(optimal_svm_pars))
print("AUROC of tuned SVM: %1.3f" % info.optimum)
Optimal parameters{'kernel': 'rbf', 'C': 3.634209495387873, 'coef0': None, 'degree': None, 'logGamma': -3.6018043228483627}
AUROC of tuned SVM: 0.990
Again, we can have a look at the best sets of hyperparameters based on the call log.
df = optunity.call_log2dataframe(info.call_log)
df.sort('value', ascending=False)
| C | coef0 | degree | kernel | logGamma | value | |
|---|---|---|---|---|---|---|
| 147 | 3.806445 | NaN | NaN | rbf | -3.594290 | 0.990134 |
| 124 | 3.634209 | NaN | NaN | rbf | -3.601804 | 0.990134 |
| 144 | 4.350397 | NaN | NaN | rbf | -3.539531 | 0.990128 |
| 82 | 5.998112 | NaN | NaN | rbf | -3.611495 | 0.989975 |
| 75 | 2.245622 | NaN | NaN | rbf | -3.392871 | 0.989965 |
| 139 | 4.462613 | NaN | NaN | rbf | -3.391728 | 0.989965 |
| 111 | 2.832370 | NaN | NaN | rbf | -3.384538 | 0.989965 |
| 92 | 5.531445 | NaN | NaN | rbf | -3.378162 | 0.989965 |
| 121 | 3.299037 | NaN | NaN | rbf | -3.617871 | 0.989818 |
| 99 | 2.812451 | NaN | NaN | rbf | -3.547038 | 0.989810 |
| 129 | 4.212451 | NaN | NaN | rbf | -3.518478 | 0.989809 |
| 135 | 3.921212 | NaN | NaN | rbf | -3.422389 | 0.989800 |
| 90 | 3.050174 | NaN | NaN | rbf | -3.431659 | 0.989800 |
| 103 | 3.181445 | NaN | NaN | rbf | -3.525796 | 0.989650 |
| 93 | 2.714779 | NaN | NaN | rbf | -3.292463 | 0.989641 |
| 89 | 2.345784 | NaN | NaN | rbf | -3.313704 | 0.989641 |
| 149 | 3.995946 | NaN | NaN | rbf | -3.303042 | 0.989641 |
| 100 | 3.516840 | NaN | NaN | rbf | -3.664992 | 0.989500 |
| 119 | 3.745784 | NaN | NaN | rbf | -3.678403 | 0.989500 |
| 125 | 4.387879 | NaN | NaN | rbf | -3.486348 | 0.989485 |
| 24 | 1.914779 | NaN | NaN | rbf | -3.476204 | 0.989484 |
| 136 | 5.865572 | NaN | NaN | rbf | -3.226204 | 0.989483 |
| 80 | 2.583507 | NaN | NaN | rbf | -3.198326 | 0.989482 |
| 146 | 5.398905 | NaN | NaN | rbf | -3.459538 | 0.989325 |
| 102 | 5.558878 | NaN | NaN | rbf | -3.467218 | 0.989325 |
| 108 | 2.721828 | NaN | NaN | rbf | -3.463704 | 0.989325 |
| 98 | 2.255162 | NaN | NaN | rbf | -3.230371 | 0.989324 |
| 64 | 1.686680 | NaN | NaN | rbf | -3.240209 | 0.989320 |
| 140 | 3.965939 | NaN | NaN | rbf | -3.241095 | 0.989320 |
| 34 | 2.381445 | NaN | NaN | rbf | -3.242871 | 0.989320 |
| ... | ... | ... | ... | ... | ... | ... |
| 68 | 1.608145 | NaN | NaN | rbf | -2.530371 | 0.979475 |
| 106 | 5.681445 | NaN | NaN | rbf | -2.526204 | 0.979156 |
| 50 | 1.477928 | NaN | NaN | rbf | -2.498326 | 0.977076 |
| 35 | 2.081445 | NaN | NaN | rbf | -2.459538 | 0.974526 |
| 15 | 3.014779 | NaN | NaN | rbf | -2.459538 | 0.974526 |
| 71 | 1.464779 | NaN | NaN | rbf | -2.451204 | 0.973405 |
| 49 | 2.239779 | NaN | NaN | rbf | -2.380371 | 0.969723 |
| 9 | 4.106445 | NaN | NaN | rbf | -2.380371 | 0.969723 |
| 53 | 3.648112 | NaN | NaN | rbf | -2.359129 | 0.968756 |
| 17 | 0.131419 | NaN | NaN | linear | NaN | 0.967925 |
| 6 | 1.913086 | NaN | NaN | linear | NaN | 0.967925 |
| 26 | 1.726419 | NaN | NaN | linear | NaN | 0.967925 |
| 7 | 0.038086 | NaN | NaN | linear | NaN | 0.967925 |
| 27 | 0.224753 | NaN | NaN | linear | NaN | 0.967925 |
| 16 | 1.819753 | NaN | NaN | linear | NaN | 0.967925 |
| 37 | 0.318086 | NaN | NaN | linear | NaN | 0.967925 |
| 58 | 2.074811 | NaN | NaN | rbf | -2.297038 | 0.964444 |
| 61 | 1.931445 | NaN | NaN | rbf | -2.217871 | 0.960290 |
| 19 | 3.639779 | NaN | NaN | rbf | -2.147038 | 0.958086 |
| 39 | 2.706445 | NaN | NaN | rbf | -2.147038 | 0.958086 |
| 43 | 4.114779 | NaN | NaN | rbf | -2.125796 | 0.957296 |
| 48 | 2.541478 | NaN | NaN | rbf | -2.063704 | 0.954737 |
| 51 | 2.398112 | NaN | NaN | rbf | -1.984538 | 0.951944 |
| 29 | 3.173112 | NaN | NaN | rbf | -1.913704 | 0.942719 |
| 41 | 2.864779 | NaN | NaN | rbf | -1.751204 | 0.634160 |
| 11 | 4.264779 | NaN | NaN | rbf | -1.051204 | 0.500000 |
| 31 | 3.331445 | NaN | NaN | rbf | -1.517871 | 0.500000 |
| 1 | 4.731445 | NaN | NaN | rbf | -0.817871 | 0.500000 |
| 8 | 1.606445 | NaN | NaN | rbf | -1.130371 | 0.500000 |
| 21 | 3.798112 | NaN | NaN | rbf | -1.284538 | 0.500000 |
150 rows × 6 columns