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This repository contains StackNet Meta modelling methodology (and software) which is part of my work as a PhD Student in the computer science department at UCL. My PhD was sponsored by dunnhumby.

StackNet is empowered by H2O's agorithms

(NEW) There is a Python implementation of StackNet

StackNet and other topics can now be discussed on FaceBook too :

Contents

Alt text

What is StackNet

StackNet is a computational, scalable and analytical framework implemented with a software implementation in Java that resembles a feedforward neural network and uses Wolpert's stacked generalization [1] in multiple levels to improve accuracy in machine learning problems. In contrast to feedforward neural networks, rather than being trained through back propagation, the network is built iteratively one layer at a time (using stacked generalization), each of which uses the final target as its target.

The Sofware is made available under MIT licence.

[1] Wolpert, D. H. (1992). Stacked generalization. Neural networks, 5(2), 241-259.

How does it work

Given some input data, a neural network normally applies a perceptron along with a transformation function like relu, sigmoid, tanh or others.

The StackNet model assumes that this function can take the form of any supervised machine learning algorithm

Logically the outputs of each neuron, can be fed onto next layers.

The algorithms can be classifiers or regressors or any estimator that produces an output..

For classification problems, to create an output prediction score for any number of unique categories of the response variable, all selected algorithms in the last layer need to have outputs dimensionality equal to the number those unique classes. In case where there are many such classifiers, the results is the scaled average of all these output predictions and can be written as:

The Modes

The stacking element of the StackNet model could be run with two different modes.

Normal stacking mode

The first mode (e.g. the default) is the one already mentioned and assumes that in each layer uses the predictions (or output scores) of the direct previous one similar with a typical feedforward neural network or equivalently:

Restacking mode

The second mode (also called restacking) assumes that each layer uses previous neurons activations as well as all previous layers neurons (including the input layer). Therefore the previous formula can be re-written as:

The intuition behind this mode is derived from the fact that the higher level algorithm has extracted information from the input data, but rescanning the input space may yield new information not obvious from the first passes. This is also driven from the forward training methodology discussed below and assumes that convergence needs to happen within one model iteration.

The modes may also be viewed bellow:

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K-fold Training

The typical neural networks are most commonly trained with a form of backpropagation, however, stacked generalization requires a forward training methodology that splits the data into two parts – one of which is used for training and the other for predictions. The reason this split is necessary is to avoid overfitting .

However splitting the data into just two parts would mean that in each new layer the second part needs to be further dichotomized increasing the bias as each algorithm will have to be trained and validated on increasingly fewer data. To overcome this drawback, the algorithm utilises a k-fold cross validation (where k is a hyperparameter) so that all the original training data is scored in different k batches thereby outputting n shape training predictions where n is the size of the samples in the training data. Therefore the training process consists of two parts:

  1. Split the data k times and run k models to output predictions for each k part and then bring the k parts back together to the original order so that the output predictions can be used in later stages of the model.

  2. Rerun the algorithm on the whole training data to be used later on for scoring the external test data. There is no reason to limit the ability of the model to learn using 100% of the training data since the output scoring is already unbiased (given that it is always scored as a holdout set).

The K-fold train/predict process is illustrated below:

Alt text

It should be noted that (1) is only applied during training to create unbiased predictions for the second layers model to fit one. During the scoring time (and after model training is complete) only (2) is in effect.

All models must be run sequentially based on the layers, but the order of the models within the layer does not matter. In other words, all models of layer one need to be trained to proceed to layer two but all models within the layer can be run asynchronously and in parallel to save time. The k-fold may also be viewed as a form of regularization where a smaller number of folds (but higher than 1) ensure that the validation data is big enough to demonstrate how well a single model could generalize. On the other hand higher k means that the models come closer to running with 100% of the training and may yield more unexplained information. The best values could be found through cross-validation. Another possible way to implement this could be to save all the k models and use the average of their predicting to score the unobserved test data, but this has all the models never trained with 100% of the training data and may be suboptimal.

Some Notes about StackNet

StackNet is (commonly) better than the best single model it contains in each first layer however, its ability to perform well still relies on a mix of strong and diverse single models in order to get the best out of this Meta modelling methodology.

StackNet (methodology - not the software) was also used to win the Truly Native data modelling competition hosted by the popular data science platform Kaggle in 2015

StackNet in simple terms is also explained in kaggle's blog

Network's example:

Alt text

StackNet is made available now with a handful of classifiers and regressors. The implementations are based on the original papers and software. However, most have some personal tweaks in them.

Algorithms contained

Native

Native - Not fully developed

Wrappers

H2O

Python

Sklearn(New)

Keras

Generic for user defined scripts (New)

Algorithm's Tuning parameters

For the common models, have a look at:

parameters

Run StackNet

You can do so directly from the jar file, using Java higher than 1.6. You need to add Java as an environmental variable (e.g., add it to PATH).

The basic format is:

Java –jar stacknet.jar [train or predict] [task=regression or classification]  [parameter = value]

Installations

This sections explains how to install the different external tools StackNet uses in its ensemble.

Install Xgboost

Awesome xgboost can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64), mac and linux.

verify that the 'lib' folder os in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd xg/
chmod +x xgboost

You can test that it works with : ./xgboost

It should print :

Usage: <config>

In windows and mac the behaviour should be similar. After executing xgboost from inside the lib/your_operation_system/xg/ you should see the:

Usage: <config>

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/xg/ .

You may find the follwing sources usefull:

Small Note: The user would need to delete the '.mod' files from inside the model/ folder when no longer need them. StackNet does not do that automatically as it is not possible to determine when they are not needed anymore.

IMPORTANT NOTE: This implementation does not include all Xgboost's features and the user is advised to use it directly from source to exploit its full potential. Also the version included is 6.0 and it is not certain whether it will be updated in the future as it required manual work to find all libraries and files required that need to be included for it to run. The performance and memory consumption will also be worse than running it directly from source. Additionally the descritpion of the parameters may not match the one in the offcial website, hence it is advised to use xgboost's online parameter thread in github for more information about them.

Install lightGBM

lightGBM can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64), mac and linux.

Verify that the 'lib' folder is in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd lightgbm/
chmod +x lightgbm

You can test that it works with : ./lightgbm

It should print something in the form of:

[LightGBM] [Info] Finished loading parameters
[LightGBM] [Fatal] No training/prediction data, application quit
Met Exceptions:
No training/prediction data, application quit

In windows and mac the behaviour should be similar. After executing lightgbm from inside the lib/your_operation_system/lightgbm/ you should see the:

[LightGBM] [Info] Finished loading parameters...

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/lightgbm/ .

You may find the follwing sources usefull:

Install LightGBM

Small Note: The user would need to delete the '.mod' files from inside the model/ folder when no longer need them. StackNet does not do that automatically as it is not possible to determine when they are not needed anymore.

IMPORTANT NOTE: This implementation does not include all LightGBM's features and the user is advised to use it directly from source to exploit its full potential. it is not certain whether it will be updated in the future as it required manual work to find all libraries and files required that need to be included for it to run. The performance and memory consumption will also be worse than running it directly from source. Additionally the descritpion of the parameters may not match the one in the offcial website, hence it is advised to use LightGBM's online parameter thread in github for more information about them.

Install H2O Algorithms

All the required jars are already packaged within the StackNet jar, however the user may find them inside the repo too.

No special installation is required , but experimentally system protection might be blocking it , therefore make certain that the StackNet.jar is in the exceptions (firewall).

Additionally the first time StackNet uses an H2o Algorithm within the ensemble it takes more time (in comparison to every other time) because it sets up a cluster .

Install Fast_rgf

fast_rgf can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64), mac and linux.

Verify that the 'lib' folder is in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd frgf/
chmod +x forest_train
chmod +x forest_predict

You can test that it works with : ./forest_train

It should print something in the form of:

using up to x threads

In windows and mac the behaviour should be similar. After executing forest_train from inside the lib/your_operation_system/frgf/ you should see the:

using up to x threads...

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/frgf/ .

If you need to make the compilling manually for windows, you may find useful to download cmake fom :

Install cmake

and use mingw32-make.exe as a compiler.

Small Note: The user would need to delete the '.mod' files from inside the model/ folder when no longer need them. StackNet does not do that automatically as it is not possible to determine when they are not needed anymore.

IMPORTANT NOTE: This implementation does not include all fast_rgf's features and the user is advised to use it directly from source to exploit its full potential. it is not certain whether it will be updated in the future as it required manual work to find all libraries and files required that need to be included for it to run. The performance and memory consumption will also be worse than running it directly from source. Additionally the descritpion of the parameters may not match the one in the offcial website, hence it is advised to use fast_rgf's online parameter thread in github for more information about them.

Install Sklearn Algorithms

To install Sklearn in StackNet you need python higher-equal-to 2.7. Python needs to be found in PATH as StackNet makes subprocesses in the command line. This would require privileges to save and change files where the .jar is executed.

verify that the 'lib' folder is in the same directory where the StackNet.jar file is

Once Python is installed and can be found on PATH, the user needs to isnstall sklearn version 0.18.2 .

The following should do the trick in linux and mac.

pip install scipy
pip install sklearn

For an easier installation in windows, the user could download Anaconda and make certain to check the Add Anaconda's python to PATH when it shows up during the installation.

All sklearn python scripts executed by StackNet are put in lib/python/

Install Python Generic Algorithms

This a new feature that allows the user to run his/her own models as long as all libraries required can be found in his/her system when calling python. Assuming python is installed as explained in sklearn version above, the user may have a look inside lib/python/.

The scripts PythonGenericRegressor0.py and PythonGenericClassifier0.py are sample scripts that show how to format these models. The '0' is the main hyper parameter (called index) of the model PythonGenericRegressor (or PythonGenericClassifier). The data gets loaded in sparse format, but after this the user could add whetver he/she wants.

One could make many scritps and name them PythonGenericRegressor1,PythonGenericRegressor2...PythonGenericRegressorN and call them as:

PythonGenericRegressor index:1 seed:1 verbose:False 
PythonGenericRegressor index:2 seed:1 verbose:False 
PythonGenericRegressor index:N seed:1 verbose:False

Once again Verify that the 'lib' folder in the same directory where the StackNet.jar file is.

Install original libfm

libFM can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64), mac and linux. Note for windows libfm is compiled with cygwin

Verify that the 'lib' folder is in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd libfm/
chmod +x libfm

You can test that it works with : ./libfm

It should print something in the form of:

libFM
  Version: 1.4.2
   ...
   ...

In windows and mac the behaviour should be similar. After executing libfm from inside the lib/your_operation_system/libfm/ you should see the same.

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/libfm/.

You may find the follwing sources usefull:

libfm manual

IMPORTANT NOTE: This implementation may not include all libFM features plus it actually uses a version of it that had a bug on purpose. You can find more information about why this was chosen in the following python wrapper for libFM. It basically had this bug that was allowing you to get the parameters of the trained models for all training methods. These parameters are now extracted once a model has been trained and the scoring uses only these parameters (e.g. not the libFM executable).

Also, multiclass problems are formed as binary 1-vs-all.

Bear in mind the licence of libfm. If you find it useful, cite the following paper : Rendle, S. (2012). Factorization machines with libfm. ACM Transactions on Intelligent Systems and Technology (TIST), 3(3), 57.Chicago . Link

Install vowpal wabbit

vowpal wabbit can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64) and linux.

Mac was more difficult than expected and generally there is a lack of expertise working with Mac. If someone could help here, please email me at kazanovassoftware@gmail.com.

For mac, you have to install vowpal wabbit from source and drop the executable in lib/mac/vw/. Consider the following link. brew install vowpal-wabbit will most probably do the trick. If that does not work, you may execute thelib/mac/vw/script.sh. This is not advised though as it will override some files you may have already installed - use it as a last resort.

Verify that the 'lib' folder is in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd vw/
chmod +x vw

You can test that it works with : ./vw

It should print something in the form of:

	Num weight bits = 18
	learning rate = 0.5
	initial_t = 0
    ...

In windows and mac the behaviour should be similar. After executing vw from inside the lib/your_operation_system/vw/ you should see the same.

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/vw/.

You may find the follwing sources usefull:

Download suggestions

IMPORTANT NOTE: This implementation may not include all Vowpal Wabbit features and the user is advised to use it directly from the source. Also the version may not be the final and it is not certain whether it will be updated in the future as it required manual work to find all libraries and files required that need to be included for it to run. The performance and memory consumption will also be worse than running directly. Additionally the descritpion of the parameters may not match the one in the website, hence it is advised to use VW's online parameter thread in github for more information about them.

Install libffm

libffm can be used as a subprocess now in StackNet. This would require privileges to save and change files where the .jar is executed.

It is already pre-compiled for windows(64), mac and linux.

Verify that the 'lib' folder is in the same directory where the StackNet.jar file is. By default it should be there when you do git clone

for linux and mac you most probably need to change privileges for the executable :

cd lib/
cd linux/
cd libffm/
chmod +x ffm-train
chmod +x ffm-predict

You can test that it works with : ./ffm-train

It should print something in the form of:

usage: ffm-train [options] training_set_file [model_file]

options:
-l <lambda>: set regularization parameter (default 0.00002)
-k <factor>: set number of latent factors (default 4)
-t <iteration>: set number of iterations (default 15)

You should also test that it works with : ./ffm-predict

It should print:

usage: ffm-predict test_file model_file output_file

In windows and mac the behaviour should be similar. After executing ffm-train or ffm-predict from inside the lib/your_operation_system/libffm/ you should see the same results.

If you don't see this, then you need to compile it manually and drop the executables inside lib/your_operation_system/libffm/ .

You may find the follwing sources usefull:

Install libffm . Search for Installation ... and OpenMP and SSE ...

Small Note: The user would need to delete the '.mod' files from inside the model/ folder when no longer need them. StackNet does not do that automatically as it is not possible to determine when they are not needed anymore.

IMPORTANT NOTE: This implementation may not include all libffm features and the user is advised to use it directly from the source. Also the version may not be the final and it is not certain whether it will be updated in the future as it required manual work to find all libraries and files required that need to be included for it to run. The performance and memory consumption will also be worse than running directly . Additionally the descritpion of the parameters may not match the one in the website, hence it is advised to use libffm online parameter thread in github for more information about them. Also, multiclass problems are formed as binary 1-vs-all.

Command Line Parameters

CommandExplanation
taskcould be either regression or classification.</li>
sparseTrue if the data to be imported are in sparse format (libsvm) or dense (false)
has_headTrue if train_file and test_file have headers else false
modelName of the output model file.
pred_fileName of the output prediction file.
train_fileName of the training file.
test_fileName of the test file.
output_namePrefix of the models to be printed per iteration. This is to allow the Meta features of each iteration to be printed. Defaults to nothing.
data_prefixprefix to be used when the user supplies own pairs of [X_train,X_cv] datasets for each fold as well as an X file for the whole training data. This is particularly useful for when likelihood features are needed or generally features than must be computed within cv. Each train/valid pair is identified by prefix_train[fold_index_starting_from_zero].txt/prefix_cv[fold_index_starting_from_zero].txt and prefix_train.txt for the final set. For example if prefix=mystack and folds=2 then stacknet is expecting 2 pairs of train/cv files. e.g [[mystack_train0.txt,mystack_cv0.txt],[mystack_train1.txt,mystack_cv1.txt]]. It also expects a [mystack_train.txt] for the final train set. These files can be either dense or sparse ( when 'sparse=True') and need to have the target variable in the beginning. If you use output_name to extract the predictions, these will be stacked vertically in the same order as the cv files.
indices_nameA prefix. When given any value it prints a .csv file for each fold with the corresponding train(0) and valiation(1) indices stacked vertically .The format is “row_index,[0 if train else 1 for validation]”. First it prints the train indices and then the validation indices in exactly the same order as they appear when modelling inside StackNet.
input_index (New)Name of file to load in order to form the train and cv indices during kfold cross validation. This overrides the internal process for generating kfolds and ignores the given folds. Each row needs to contain an integer in that file. Row size of the file needs to be the same as the train_file. It should not contain headers. one line=one integer - the indice of the validation fold the case belongs to.There is an example
include_target (New)True to enable printing the target column in the output file for train holdout predictions (when output_name is not empty).
test_targetTrue if the test file has a target variable in the beginning (left) else false (only predictors in the file).
paramsParameter file where each line is a model. empty lines correspond to the creation of new levels
verboseTrue if we need StackNet to output its progress else false
threadsNumber of models to run in parallel. This is independent of any extra threads allocated from the selected algorithms. e.g. it is possible to run 4 models in parallel where one is a randomforest that runs on 10 threads (it selected).
metricMetric to output in cross validation for each model-neuron. can be logloss, accuracy or auc (for binary only) for classification and rmse ,rsquared or mae for regerssion .defaults to 'logloss' for classification and 'rmse' for regression.
stackdataTrue for restacking else false
seedInteger for randomised procedures
binsA parameter that allows classifiers to be used in regression problems. It first bins (digitises) the target variable and then runs classifiers on the transformed variable. Defaults to 2</li>.
foldsNumber of folds for re-usable kfold

Parameters' File

In The parameter file, each line is a model. When there is an empty line then any new algorithm is used in the next level. This is a sample format. Note this file accepts comments (#). Anything on the right of the # symbol is ignored.(New)

LogisticRegression C:1 Type:Liblinear maxim_Iteration:100 scale:true verbose:false
RandomForestClassifier bootsrap:false estimators:100 threads:5 logit.offset:0.00001 verbose:false cut_off_subsample:1.0 feature_subselection:1.0 gamma:0.00001 max_depth:8 max_features:0.25 max_tree_size:-1 min_leaf:2.0 min_split:5.0 Objective:ENTROPY row_subsample:0.95 seed:1
GradientBoostingForestClassifier estimators:100 threads: offset:0.00001 verbose:false trees:1 rounding:2 shrinkage:0.05 cut_off_subsample:1.0 feature_subselection:0.8 gamma:0.00001 max_depth:8 max_features:1.0 max_tree_size:-1 min_leaf:2.0 min_split:5.0 Objective:RMSE row_subsample:0.9 seed:1
Vanilla2hnnclassifier UseConstant:true usescale:true seed:1 Type:SGD maxim_Iteration:50 C:0.000001 learn_rate:0.009 smooth:0.02 h1:30 h2:20 connection_nonlinearity:Relu init_values:0.02
LSVC Type:Liblinear threads:1 C:1.0 maxim_Iteration:100 seed:1
LibFmClassifier lfeatures:3 init_values:0.035 smooth:0.05 learn_rate:0.1 threads:1 C:0.00001 maxim_Iteration:15 seed:1
NaiveBayesClassifier usescale:true threads:1 Shrinkage:0.1 seed:1 verbose:false
XgboostRegressor booster:gbtree objective:reg:linear num_round:100 eta:0.015 threads:1 gamma:2.0 max_depth:4 subsample:0.8 colsample_bytree:0.4 seed:1 verbose:false
XgboostRegressor booster:gblinear objective:reg:gamma num_round:500 eta:0.5 threads:1 lambda:1 alpha:1 seed:1 verbose:false

RandomForestClassifier estimators=1000 rounding:3 threads:4 max_depth:6 max_features:0.6 min_leaf:2.0 Objective:ENTROPY gamma:0.000001 row_subsample:1.0 verbose:false copy=false

Tip: To tune a single model, one may choose an algorithm for the first layer and a dummy one for the second layer. StackNet expects at least two algorithms, so with this format the user can visualize the performance of single algorithm inside the K-fold. For example, if I wanted to tune a Random Forest Classifier, I would put it in the first line (layer) and also put any model (lets say Logistic Regression) in the second layer and could break the process immediately after the first layer kfold is done:

RandomForestClassifier bootsrap:false estimators:100 threads:5 logit.offset:0.00001 verbose:false cut_off_subsample:1.0 feature_subselection:1.0 gamma:0.00001 max_depth:8 max_features:0.25 max_tree_size:-1 min_leaf:2.0 min_split:5.0 Objective:ENTROPY row_subsample:0.95 seed:1

LogisticRegression verbose:false

Data Format

For dense input data, the file needs to start with the target variable followed by a comma, separated variables like:

1,0,0,2,3,2.4

0,1,1,0,0,12

For sparse format , it is the same as libsvm (same example as above) :

1 2:2 3:3 4:2.4

0 0:1 1:1 4:12

warning: Some algorithms (mostly tree-based) may not be very fast with this format)

If test_target is false, then the test data may not have a target and start directly from the variables.

A train method needs at least a train_file and a params_file. It also needs at least two algorithms, and the and last layer must not contain a regressor unless the metric is auc and the problem is binary.

A predict method needs at least a test_file and a model_file.

Commandline Train Statement

Java –jar stacknet.jar train task=classification sparse=false has_head=true model=model pred_file=pred.csv train_file=sample_train.csv test_file= sample_test.csv test_target=true params=params.txt verbose=true threads=7 metric=logloss stackdata=false seed=1 folds=5 bins=3

Note that you can have train and test at the same time. In that case after training, it scores the test data.

Commandline predict Statement

Java -jar stacknet.jar predict sparse=false has_head=true model=model pred_file=pred.csv test_file=sample_test.csv test_target=true verbose=true metric=logloss

Examples

Run StackNet from within Java code

If we wanted to build a 3-level stacknet on a binary target with desne data, we start with initializing a StackNetClassifier Object:

 StackNetClassifier StackNet = new StackNetClassifier (); // Initialise a StackNet

Which is then followed by a 2-dimensional String array with the list of models in each layer along with their hyperparameters in the form of as in "estimator [space delimited hyper parameters]"

String models_per_level[][]=new String[][]; 

            
{//First Level
{"LogisticRegression C:0.5 maxim_Iteration:100 verbose:true", 
"RandomForestClassifier bootsrap:false estimators:100 threads:25 offset:0.00001 cut_off_subsample:1.0 feature_subselection:1.0 max_depth:15 max_features:0.3 max_tree_size:-1 min_leaf:2.0 min_split:5.0 Objective:ENTROPY row_subsample:0.95", 
"LSVC C:3 maxim_Iteration:50",
"LibFmClassifier maxim_Iteration:16 C:0.000001 lfeatures:3 init_values:0.9 learn_rate:0.9 smooth:0.1", 
"NaiveBayesClassifier Shrinkage:0.01", 
"Vanilla2hnnclassifier maxim_Iteration:20 C:0.000001 tolerance:0.01 learn_rate:0.009 smooth:0.02 h1:30 h2:20 connection_nonlinearity:Relu init_values:0.02", 
"GradientBoostingForestClassifier estimators:100 threads:25 verbose:false trees:1 rounding:2 shrinkage:0.1 feature_subselection:0.5 max_depth:8 max_features:1.0 min_leaf:2.0 min_split:5.0 row_subsample:0.9", 
"LinearRegression C:0.00001", 
"AdaboostRandomForestClassifier estimators:100 threads:3 verbose:true trees:1 rounding:2 weight_thresold:0.4 feature_subselection:0.5 max_depth:8 max_features:1.0 min_leaf:2.0 min_split:5.0 row_subsample:0.9", 
"GradientBoostingForestRegressor estimators:100 threads:3 trees:1 rounding:2 shrinkage:0.1 feature_subselection:0.5 max_depth:9 max_features:1.0 min_leaf:2.0 min_split:5.0 row_subsample:0.9", 
"RandomForestRegressor estimators:100 internal_threads:1 threads:25 offset:0.00001 verbose:true cut_off_subsample:1.0 feature_subselection:1.0 max_depth:14 max_features:0.25 max_tree_size:-1 min_leaf:2.0 min_split:5.0 Objective:RMSE row_subsample:1.0", 
"LSVR C:3 maxim_Iteration:50 P:0.2" },
//Second Level                
{"RandomForestClassifier estimators:1000  threads:25 offset:0.0000000001 verbose=false cut_off_subsample:0.1 feature_subselection:1.0 max_depth:7 max_features:0.4  max_tree_size:-1 min_leaf:1.0  min_split:2.0 Objective:ENTROPY row_subsample:1.0",
"GradientBoostingForestClassifier estimators:1000 threads:25 verbose:false trees:1 rounding:4 shrinkage:0.01 feature_subselection:0.5 max_depth:5 max_features:1.0 min_leaf:1.0 min_split:2.0 row_subsample:0.9",    
"Vanilla2hnnclassifier maxim_Iteration:20 C:0.000001 tolerance:0.01 learn_rate:0.009 smooth:0.02 h1:30 h2:20 connection_nonlinearity:Relu init_values:0.02",    
"LogisticRegression C:0.5 maxim_Iteration:100 verbose:false" },
//Third Level                    
{"RandomForestClassifier estimators:1000  threads:25 offset:0.0000000001 verbose=false cut_off_subsample:0.1 feature_subselection:1.0 max_depth:6 max_features:0.7  max_tree_size:-1 min_leaf:1.0  min_split:2.0 Objective:ENTROPY row_subsample:1.0" }
};

Alternatively, we could load directly from a file :

String modellings[][]=io.input.StackNet_Configuration("params.txt");

StackNet.parameters=models_per_level; // adding the models' specifications

The remaining parameters to be specified include the cross validation training schema, the Restacking mode option, setting a random state as well as some other miscellaneous options:

StackNet.threads=4; // models to be run in parallel
StackNet.folds=5; // size of K-Fold
StackNet.stackdata=true; // use Restacking
StackNet.print=true; // this helps to avoid rerunning should the model fail
StackNet.output_name="restack";// prefix for each layer's output.
StackNet.verbose=true; // it outputs 
StackNet.seed=1; // random state
StackNet.metric="logloss"

Ultimately given a data object X and a 1-dimensional vector y, the model can be trained using:

StackNet.target=y; // the target variable        
StackNet.fit(X); // fitting the model on the training data

Predictions are made with :

double preds [][]=StackNet.predict_proba(X_test);

Potential Next Steps

Reference

For now, you may use this:

Marios Michailidis (2017), StackNet, StackNet Meta Modelling Framework, url https://github.com/kaz-Anova/StackNet

News

Special Thanks

To my co-supervisors: