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I'm using SMO, Logistic Regression, Bayesian Network and Simple CART algorithms for classification. Results form WEKA:

Algorithm               Sensitivity (%)       Specificity (%)         Overall accuracy (%)
Bayesian Network            57.49                 76.09                    65.24
Logistic Regression         64.73                 69.86                    66.87
SMO                         54.32                 79.20                    64.69
Simple CART                 71.88                 61.51                    67.56

SMO gives the best result for my classification problem, since it correctly classify the 79.20% of the class which is important for me. I want to increase this accuracy by stacking. I tried to combine some of them. In most of the cases I couldn't increase the accuracy but stacking SMO with Logistic Regression made a little increment in accuracy.

How can I explain why stacking SMO with Logistic Regression is better than others?

Is there any generalization such as combining tree classifiers gives good result in stacking? What should I care about while stacking?

EDIT:

                                Bayesian Network    Logistic Reg.   SMO         CART 
Kappa statistic                   0.3196             0.3367         0.3158      0.3335 
Mean absolute error               0.3517             0.4164         0.3531      0.4107 
Root mean squared error           0.5488             0.4548         0.5942      0.4547 
Relative absolute error (%)      72.3389              85.65        72.6299      84.477 
Root relative squared error (%) 111.3076            92.2452       120.5239     92.2318 
Weighted Avg. of F-Measure        0.653               0.671          0.676     92.2318 
ROC Area                          0.725               0.727          0.668       0.721

Total number of instance is 25106. 14641 of them is class a, and 10465 of them belong to class b.

=== Confusion Matrix of Simple CART ===
     a     b   <-- classified as
 10524  4117 |     a = 0
  4028  6437 |     b = 1

=== Confusion Matrix of SMO ===

    a    b   <-- classified as
 7953 6688 |    a = 0
 2177 8288 |    b = 1

=== Confusion Matrix of Logistic Regression ===

    a    b   <-- classified as
 9477 5164 |    a = 0
 3154 7311 |    b = 1

Since SMO is successful at class b and CART is successful at class a, I tried to ensemble these two algorithms. But I couldn't increase the accuracy. Then I tried to combine SMO with Logistic Regression, the accuracy is increased a little bit. Why ensembling SMO with Logistic Regression is better than ensebling SMO with CART, is there any explanation?

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  • $\begingroup$ In addition to answer of @lollercoaster. I found the paper of LUDMILA I. KUNCHEVA and CHRISTOPHER J. WHITAKE which title is "Measures of Diversity in Classifier Ensembles and Their Relationship with the Ensemble Accuracy". I found it very explanatory about diversity. $\endgroup$ – ahmet Jul 26 '15 at 15:37
  • $\begingroup$ what does SMO mean? $\endgroup$ – develarist Apr 15 at 21:13
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To directly answer your question about stacking: you should care about minimizing 1) bias, and 2) variance. This is obvious, but in practice this often comes down to simply having models which are "diverse". (I apologize that link is behind a paywall, but there are a few others like it and you may well find it other ways)

You don't want ensembles of like-minded models - they will make the same mistakes and reinforce each other.

In the case of stacking, what is happening? You are letting the outputs of the probabilistic classifiers on the actual feature input become the new features. A diverse set of classifiers which can in any way give signals about edge cases is desirable. If classifier 1 is terrible at classes A, B, and C but fantastic at class D, or a certain edge case, it is still a good contribution to the ensemble.

This is why neural nets are so good at what they do in image recognition - deep nets are in fact recursive logistic regression stacking ensembles! Nowadays people don't always use the sigmoid activation and there are many layer architectures, but it's the same general idea.

What I would recommend is trying to maximize the diversity of your ensemble by using some of the similarity metrics on the classifiers' prediction output vectors (ie, Diettrich's Kappa statistic) in training. Here is another good reference.

Hope that helps.

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  • $\begingroup$ Thanks for your attention. I will try what you suggested and will get back to you. $\endgroup$ – ahmet Jul 10 '15 at 6:11
  • $\begingroup$ Great. If you think that has answered your question, please mark at as such. In any case, best of luck. $\endgroup$ – lollercoaster Jul 10 '15 at 15:09
  • $\begingroup$ I think, I should ensemble SMO with CART according to your suggestion. I edited my question. $\endgroup$ – ahmet Jul 10 '15 at 19:48
  • $\begingroup$ Few things: 1) Why not try each combination of three algorithms you have?, 2) for that matter, why aren't you adding other algorithms? Random Forest, KNN come to mind as strong for difficult problems, 3) At some point stacking will not help - you'll need more examples, better features, and hyperparameter tuning. That's going beyond scope of this post and more than someone can answer in a comment. Stacking, unfortunately, is not an solution in itself - merely an augmentation to the basics. $\endgroup$ – lollercoaster Jul 10 '15 at 22:29
  • $\begingroup$ Actually these are the algorithms which I had the best results and I tried each combination of them. I didn't want to just say I tried the everything and these are the best results. I wanted to add some logical explanations, like I select Logistic Regression because it have ... properties, which SMO doesn't have, to improve SMO. Thanks for your answer. $\endgroup$ – ahmet Jul 10 '15 at 22:42
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Read the following by MLWave: http://mlwave.com/kaggle-ensembling-guide/

This is very good starting point to stacking / ensembles.

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  • $\begingroup$ SE discourages link-only answers -- summarize the content that is relevant to the answer? $\endgroup$ – Sean Owen Jul 7 '15 at 8:23

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