This page present some benchmarks of Nieme. For the moment it only concerns binary classification on moderate-size datasets.

Binary Classification - Moderate-size datasets

The experiment described below compares several learning machines from Nieme with a baseline linear SVM.

Datasets

The datasets are classical binary classification datasets that can be found in the libSVM datasets. When a train/test split was provided we kept it, otherwise we did a random split of 50% training and 50% of testing data. Datasets with binary sparse features are processed directly, whereas we use the scaled version (features in [-1,1]) for other datasets.

Baseline computation

The baseline is a linear SVM with the libSVM implementation. For each dataset, we tried the values 0.001, 0.01, 0.1, 1.0, 10.0 and 100.0 for the parameter C, and kept the best result.

Nieme machines

The experiment compares several learning machines in Nieme:

  • Online machines:
    • Losses: Perceptron, LargeMargin, LogBinomial
    • Learners: Stochastic Descent, MiniBatch Descent (mini batch sizes: 2, 5, 10, 20, 50, 100, 200, 500)
  • Batch machines:
    • Losses: LogBinomial, Exponential
    • Learners: OWLQN, LBFGS, RProp
    • Regularizers: None / Only L1 / Only L2 / Combined L1 and L2. For each regularizers we tried the weights 1e-8, 1e-7, 1e-6, 1e-5, 1e-4, 1e-3 and 0.01.

In all cases, the machines are based on a linear Architecture. These choices lead to a bit more than 400 differently parameterized learning machines.

Results

Each row of the table below corresponds to a dataset. We give the name of the dataset, the number of training and testing examples, the number of features, the best libSVM generalization accuracy with the corresponding parameter C, and the best Nieme's model generalization accuracy with its description.

Since we try much more models from Nieme than libSVM models, the former most-of-time outperforms the latter in accuracy. These results are only preliminary results and the aim is only to illustrate the variety of models that can be handled by Nieme.

More than 10.000 training examples

dataset train size test size features best libSVM acc best libSVM train time best libSVM C best Nieme acc best Nieme train time best Nieme machine
w8a 49749 14951 300 98.68 % 696.1 s 1 98.74 % 18.8 s RProp LogBinomial l1=1e-07
a9a 32561 16281 123 85.01 % 1753.7 s 0.1 85.22 % 10.1 s OWLQN LogBinomial l1=0.0001 l2=0.0001
w7a 24692 25057 300 98.71 % 427.9 s 10 98.71 % 8.0 s OWLQN LogBinomial l1=1e-07
w6a 17188 32561 300 98.68 % 183.4 s 10 98.70 % 6.8 s RProp LogBinomial l1=1e-07 l2=1e-07

More than 1.000 training examples

dataset train size test size features best libSVM acc best libSVM train time best libSVM C best Nieme acc best Nieme train time best Nieme machine
w5a 9888 39861 300 98.50 % 22.1 s 1 98.47 % 3.9 s RProp LogBinomial l1=1e-05
a5a 6414 26147 123 84.48 % 56.0 s 0.1 84.75 % 2.0 s OWLQN LogBinomial l1=1e-08 l2=1e-05
w3a 4912 44837 300 98.29 % 5.4 s 1 98.30 % 2.3 s RProp LogBinomial l1=1e-05 l2=1e-08
a4a 4781 27780 123 84.59 % 25.6 s 0.1 84.70 % 1.5 s LBFGS LogBinomial l1=0.0001 l2=0.0001
mushrooms 4062 4062 112 100.00 % 4.5 s 1 100.00 % 2.0 s RProp Exponential l1=0.0001 l2=1e-06
w2a 3470 46279 300 98.07 % 3.0 s 1 98.19 % 1.1 s RProp LogBinomial l1=0.0001 l2=1e-08
a3a 3185 29376 123 84.51 % 8.8 s 0.1 84.69 % 0.9 s RProp LogBinomial l1=1e-07 l2=0.001
w1a 2477 47272 300 97.74 % 1.6 s 1 97.91 % 1.0 s RProp LogBinomial l1=1e-07 l2=0.0001
a2a 2265 30296 123 84.61 % 4.6 s 0.1 84.70 % 0.7 s LBFGS LogBinomial l1=0.0001 l2=0.001
a1a 1605 30956 123 84.32 % 2.3 s 0.1 84.44 % 1.0 s OWLQN LogBinomial l1=0.0001 l2=1e-07

Small DataSets

dataset train size test size features best libSVM acc best libSVM train time best libSVM C best Nieme acc best Nieme train time best Nieme machine
german-number 500 500 24 75.40 % 1.8 s 10 77.40 % 0.1 s OWLQN LogBinomial l1=0.01 l2=1e-08
fourclass 431 431 2 77.03 % 0.1 s 0.1 78.89 % 0.4 s Online LargeMargin (per 5 examples)
diabetes 384 384 8 79.43 % 0.1 s 1 79.95 % 0.1 s OWLQN Exponential
australian 345 345 14 88.12 % 0.2 s 10 88.12 % 0.1 s OWLQN Exponential l1=0.01 l2=1e-05
breast-cancer 342 341 10 96.48 % 0.1 s 1 95.89 % 0.1 s RProp LogBinomial l1=1e-06 l2=0.0001
ionosphere 176 175 33 88.57 % 0.1 s 1 89.71 % 0.1 s LBFGS LogBinomial l1=0.001
liver-disorders 173 172 6 67.44 % 0.1 s 100 68.60 % 0.0 s LBFGS LogBinomial l1=0.0001 l2=0.001
heart 135 135 13 85.93 % 0.0 s 0.1 86.67 % 0.1 s Online LargeMargin (per 50 examples)
sonar 104 104 60 69.23 % 0.1 s 10 78.85 % 0.0 s LBFGS Exponential l1=1e-05 l2=0.0001
leu 38 34 7129 82.35 % 1.9 s 0.001 100.00 % 2.7 s OWLQN LogBinomial l1=1e-05 l2=1e-06
duke 38 48 7129 95.83 % 2.1 s 0.001 100.00 % 1.1 s LBFGS LogBinomial l1=1e-06 l2=1e-05
colon-cancer 31 31 2000 96.77 % 0.2 s 0.001 93.55 % 0.5 s OWLQN LogBinomial l1=0.001 l2=1e-06