I am conducting research on credit risk prediction using neural networks and K-Nearest Neighbour models (K=10) in Matlab. The dataset has 490 samples with 19 features, from which I want to predict 1 binary output variable (the credit risk of companies, Bankrupt/Non-Bankrupt). Data is split into 75% training and 30% validation and testing.

Now I want to combine both models so get one accuracy rate, as I guess it will be higher than using only one of the NN or KNN models. My question therefore is: how to combine both to give me one accuracy rate in Matlab? I know stacking and bagging techniques exist - how to use/implement them in Matlab (and test them for their real performance)?

Simple example of the neural network setup:

  1. input layer: 19 input variables (X1---X19), accounting ratios (liquidity profitability ... ratios), for 420 sample (companies across different years).

  2. hidden layer: 2 hidden layers with 10 neurons each, sigmoid function, training based on percentage training and validation. Backpropagation algorithm for learning and adjusting the weights.

  3. output layer: Y (the company status: $<0.5$ indicates bankrupt, $>0.5$ indicates non bankrupt).

Simple example of the KNN setup:

I use the KNNclassify function with K=5 and Euclidean distance. Input and output are the same as with the ANN exmaple.

I see that can use as you said Bagging or stacking, I may try do both since Matlab has already a ready-to-use function for both. My main problem is that I cannot find a guide to combine both models to give me ONE prediction and its accuracy so my ensemble model want to do in Matlab is as follows:

  1. NN --> output
  2. KNN --> output
  3. Stacking or bagging
  4. get final output

How to achieve this?

  • $\begingroup$ I tried to clarify the question, feel free to rollback in case I misunderstood something. And please review the "training ratio 75% and 30% validation and testing ratio" part - those don't add up to 100% percent. Do I understand that you have 19 samples that you use to train and evaluate both your KNN and ANN model? $\endgroup$ Jul 4, 2016 at 12:32
  • $\begingroup$ @geekoverdose thanks for keeping up I edited the question, I hope you can just give me an example for ensembling both models or Neural network and anyother model in matlab, my data is 19 input variable for 490 cases with one output ( 0/1) $\endgroup$
    – Koa
    Jul 4, 2016 at 22:05
  • $\begingroup$ I've updated my answer - I hope that its details will now help you to simply implement/use those methods without any predefined API yourself - they are so simple that you don't necessarily need to rely on what certain packages give you. For example, model averaging as 1 line of code: $output_{final} = \frac{output_1+output_2}{2}$. For bagging you additionally need to a) train multiple KNN and ANN models + randomly subset the training samples for each. But this is easy to do too. $\endgroup$ Jul 4, 2016 at 22:37
  • $\begingroup$ @geekoverdose thanks for reply and keeping with me, but that not what i want, but I will try model averaging since it is easy, but I want to implement the other bagging and stacking techniques isnot there a equations to use so it includes (the esnembled models (NN and KNN), the algorithm for ensembling ( BAgging stacking, averaging) )? like that mathworks.com/help/stats/ensemble-methods.html but it only get for weaker learner $\endgroup$
    – Koa
    Jul 5, 2016 at 10:25
  • $\begingroup$ @geekoverdose can you help me how to implement stacking, I trained the two models ( base learner ) based on my inputs and output training, so I will train the decision tree as the stacking model learner, but with what inputs? $\endgroup$
    – Koa
    Jul 8, 2016 at 15:29

1 Answer 1


Independently of the exact setup you have (model types, amount of samples and features), you could use a number of ensemble techniques. Note that you don't necessarily need to use the provided APIs in your ML tool/language for this - e.g. model avearging, bagging, and stacking can usually be implemented with a few extra lines of code.

  • Model averaging: you train $N$ models with training data, then use all $N$ trained models on new samples to obtain $N$ predictions per sample. Per sample, the $N$ predictions are usually averaged to obtain the scalar ensemble prediction (therefore the name "model averaging"). For classification, class probability metrics could also be derived from the amount of votes for each class (e.g. 4 votes / 10 models = 0.4). You can easily do model averaging yourself: it does not need an modified training procedure, so you can use any amount and type of ready trained models you already have - just average the output as mentioned above.

  • Bagging: is nearly the same as model averaging, but requires a slightly modified training procedure, as it uses a subset of samples to train each model$^1$. You will therefore want to use more than 1 KNN and 1 ANN model therefore. Like with averaging, prediction outputs over all $N$ models are averaged to obtain a scalar ensemble output. Like model averaging, you could easily implement this yourself: select a subset of samples, train one model, and repeat the process $N$ times until you have the desired amount of models to average predictions from afterwards.

  • Stacking: also requires a slightly modified training procedure. You train $N$ models to predict the output for a new sample. You then use the $N$ predicted outputs for all training samples as input for another model that is "stacked" upon the other models (so it becomes a layered chain of models). This final models predicts the actual output for new samples. Again, you can easily implement this yourself: use your $N$ models to generate $N$ predictions for training samples, then train another final model using the $N$ outputs as inputs. Note that you will likely need more than 2 models to base the final model on to notice a significant boost in results.

There would also be Boosting, but this is a bit more complex and probably not what you are aiming for right now.

$^1$ Note that bagging can also be applied on features ("random subspace").

  • $\begingroup$ great for the information you provided and illustration, but I want to know how to do that in matlab? do I create Neural Network model and KNN model in the workspace then use them in the equation for ensembling?so would you provide simple quick example about how to ensemble both? that step what I am missing actually. $\endgroup$
    – Koa
    Jul 4, 2016 at 15:14
  • $\begingroup$ @EssamA Please add a minimal example/snippet in your question, that shows how you currently predict the output of a new sample with both models, otherwise the snipped I could provide will be pretty much "into the blue". $\endgroup$ Jul 4, 2016 at 15:19

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