GAparsimony 0.0.9

Combines feature selection, model tuning, and parsimonious model selection with GA optimization. GA selection procedure is based on separate cost and complexity evaluations. Therefore, the best individuals are initially sorted by an error fitness function, and afterwards, models with similar costs are rearranged according to modelcomplexity measurement so as to foster models of lesser complexity. The algorithm can be run sequentially or in parallel.

GAparsimony

GAparsimony

Documentation

GAparsimony for Python is a package for searching with genetic algorithms (GA) accurate parsimonious models by combining feature selection (FS), model hyperparameter optimization (HO), and parsimonious model selection (PMS). It has R implementation R GAparsimony

PMS is based on separate cost and complexity evaluations. The best individuals are initially sorted by an error fitness function, and afterwards, models with similar costs are rearranged according to model complexity measurement so as to foster models of lesser complexity. The algorithm can be run sequentially or in parallel.

Installation

Install these packages:

pip install GAparsimony

How to use this package

Example 1: Classification

This example shows how to search, for the Sonar database, a parsimony SVM classificator with GAparsimony package.

In the next step, a fitness function is created using getFitness. This function return a fitness function for the SVC model, the cohen_kappa_score metric and the predefined svm complexity function for SVC models. We set regression to False beacause is classification example.

A SVM model is trained with these parameters and the selected input features. Finally, fitness() returns a vector with three values: the kappa statistic obtained with the mean of 10 runs of a 10-fold cross-validation process, the kappa measured with the test database to check the model generalization capability, and the model complexity. And the trained model.

The GA-PARSIMONY process begins defining the range of the SVM parameters and their names. Also, rerank_error can be tuned with different ga_parsimony runs to improve the model generalization capability. In this example, rerank_error has been fixed to 0.001 but other values could improve the trade-off between model complexity and model accuracy. For example, with rerank_error=0.01, we can be interested in obtaining models with a smaller number of inputs with a gamma rounded to two decimals.

from sklearn.model_selection import RepeatedKFold
from sklearn.svm import SVC
from sklearn.metrics import cohen_kappa_score
from sklearn.preprocessing import StandardScaler
from sklearn.datasets import load_wine

from GAparsimony import GAparsimony, Population, getFitness
from GAparsimony.util import svm

wine = load_wine()
X, y = wine.data, wine.target 
X = StandardScaler().fit_transform(X)


rerank_error = 0.001
params = {"C":{"range": (00.0001, 99.9999), "type": Population.FLOAT}, 
            "gamma":{"range": (0.00001,0.99999), "type": Population.FLOAT}, 
            "kernel": {"value": "poly", "type": Population.CONSTANT}}


fitness = getFitness(SVC, cohen_kappa_score, svm, regression=False, test_size=0.2, random_state=42, n_jobs=-1)


GAparsimony_model = GAparsimony(fitness=fitness,
                                  params=params,
                                  features=wine.feature_names,
                                  keep_history = True,
                                  rerank_error = rerank_error,
                                  popSize = 40,
                                  maxiter = 5, early_stop=10,
                                  feat_thres=0.90, # Perc selected features in first generation
                                  feat_mut_thres=0.10, # Prob of a feature to be one in mutation
                                  seed_ini = 1234)

With small databases, it is highly recommended to execute GAparsimony with different seeds in order to find the most important input features and model parameters.

In this example, one GA optimization is presented with a training database composed of 60 input features and 167 instances, and a test database with only 41 instances. Hence, a robust validation metric is necessary. Thus, a repeated cross-validation is performed.

Starts the GA optimizaton process with 40 individuals per generation and a maximum number of 5 iterations with an early stopping when validation measure does not increase significantly in 3 generations. Parallel is activated. In addition, history of each iteration is saved in order to use plot and parsimony_importance methods.

GAparsimony_model.fit(X, y)

#output

GA-PARSIMONY | iter = 0
   MeanVal = 0.879549  |  ValBest = 0.9314718  |  TstBest = 0.9574468  |ComplexBest = 10000000045.0| Time(min) = 0.1473163  

GA-PARSIMONY | iter = 1
  MeanVal = 0.9075035  |  ValBest = 0.9496819  |  TstBest = 0.9142857  |ComplexBest = 11000000060.0| Time(min) = 0.0926334  

GA-PARSIMONY | iter = 2
  MeanVal = 0.9183232  |  ValBest = 0.9496819  |  TstBest = 0.9142857  |ComplexBest = 11000000060.0| Time(min) = 0.0817334  

GA-PARSIMONY | iter = 3
  MeanVal = 0.9219764  |  ValBest = 0.9534295  |  TstBest = 0.9568345  |ComplexBest = 10000000043.0| Time(min) = 0.0768833  

GA-PARSIMONY | iter = 4
  MeanVal = 0.8932938  |  ValBest = 0.9534295  |  TstBest = 0.9568345  |ComplexBest = 10000000043.0| Time(min) = 0.0886667 

summary() shows the GA initial settings and two solutions: the solution with the best validation score in the whole GA optimization process, and finally, the best parsimonious individual at the last generation.

GAparsimony_model.summary()

+------------------------------------+
|             GA-PARSIMONY           |
+------------------------------------+

GA-PARSIMONY settings:
 Number of Parameters      = 2
 Number of Features        = 13
 Population size           = 40
 Maximum of generations    = 5
 Number of early-stop gen. = 10
 Elitism                   = 8
 Crossover probability     = 0.8
 Mutation probability      = 0.1
 Max diff(error) to ReRank = 0.001
 Perc. of 1s in first popu.= 0.9
 Prob. to be 1 in mutation = 0.1

 Search domain =
                 C    gamma  alcohol  malic_acid  ash  alcalinity_of_ash  \
Min_param   0.0001  0.00001      0.0         0.0  0.0                0.0
Max_param  99.9999  0.99999      1.0         1.0  1.0                1.0

           magnesium  total_phenols  flavanoids  nonflavanoid_phenols  \
Min_param        0.0            0.0         0.0                   0.0
Max_param        1.0            1.0         1.0                   1.0

           proanthocyanins  color_intensity  hue  \
Min_param              0.0              0.0  0.0
Max_param              1.0              1.0  1.0

           od280/od315_of_diluted_wines  proline
Min_param                           0.0      0.0
Max_param                           1.0      1.0


GA-PARSIMONY results:
 Iterations                = 5
 Best validation score = 0.9534294543460606


Solution with the best validation score in the whole GA process =

  fitnessVal fitnessTst complexity        C     gamma alcohol malic_acid ash  \
0   0.953429   0.956835      1e+10  18.4049  0.667214       1          1   1

  alcalinity_of_ash magnesium total_phenols flavanoids nonflavanoid_phenols  \
0                 1         0             0          1                    1

  proanthocyanins color_intensity hue od280/od315_of_diluted_wines proline
0               0               1   1                            1       1


Results of the best individual at the last generation =

 Best indiv's validat.cost = 0.9534294543460606
 Best indiv's testing cost = 0.9568345323741008
 Best indiv's complexity   = 10000000043.0
 Elapsed time in minutes   = 0.4872331658999125


BEST SOLUTION =

  fitnessVal fitnessTst complexity        C     gamma alcohol malic_acid ash  \
0   0.953429   0.956835      1e+10  18.4049  0.667214       1          1   1

  alcalinity_of_ash magnesium total_phenols flavanoids nonflavanoid_phenols  \
0                 1         0             0          1                    1

  proanthocyanins color_intensity hue od280/od315_of_diluted_wines proline
0               0               1   1                            1       1

Plot GA evolution.

GAparsimony_model.plot()

GA-PARSIMONY evolution

Show percentage of appearance for each feature in elitists

# Percentage of appearance for each feature in elitists
GAparsimony_model.importance()

+--------------------------------------------+
|                  GA-PARSIMONY              |
+--------------------------------------------+

Percentage of appearance of each feature in elitists:

  alcohol malic_acid  hue  ash proline od280/od315_of_diluted_wines  \
0     100        100  100  100     100                       96.875

  alcalinity_of_ash nonflavanoid_phenols color_intensity proanthocyanins  \
0            96.875               96.875           93.75           81.25

  flavanoids magnesium total_phenols
0     65.625    40.625         9.375

Example 2: Regression

This example shows how to search, for the Boston database, a parsimonious ANN model for regression and with GAparsimony package.

In the next step, a fitness function is created using getFitness. This function return a fitness function for the Lasso model, the mean_squared_error(RMSE) metric and the predefined linearModels complexity function for SVC models. We set regression to True beacause is classification example.

A Lasso model is trained with these parameters and the selected input features. Finally, fitness() returns a vector with three negatives values: the RMSE statistic obtained with the mean of 10 runs of a 10-fold cross-validation process, the RMSE measured with the test database to check the model generalization capability, and the model complexity. And the trained model.

The GA-PARSIMONY process begins defining the range of the SVM parameters and their names. Also, rerank_error can be tuned with different ga_parsimony runs to improve the model generalization capability. In this example, rerank_error has been fixed to 0.01 but other values could improve the trade-off between model complexity and model accuracy.

Therefore, PMS considers the most parsimonious model with the lower number of features. Between two models with the same number of features, the lower sum of the squared network weights will determine the most parsimonious model (smaller weights reduce the propagation of disturbances).

from sklearn.model_selection import RepeatedKFold
from sklearn.linear_model import Lasso
from sklearn.preprocessing import StandardScaler
from sklearn.metrics import mean_squared_error

from sklearn.datasets import load_boston

from GAparsimony import GAparsimony, Population, getFitness
from GAparsimony.util import linearModels

boston = load_boston()
X, y = boston.data, boston.target 
X = StandardScaler().fit_transform(X)

# ga_parsimony can be executed with a different set of 'rerank_error' values
rerank_error = 0.01

params = {"alpha":{"range": (1., 25.9), "type": Population.FLOAT}, 
            "tol":{"range": (0.0001,0.9999), "type": Population.FLOAT}}

fitness = getFitness(Lasso, mean_squared_error, linearModels, regression=True, test_size=0.2, random_state=42, n_jobs=-1)


GAparsimony_model = GAparsimony(fitness=fitness,
                                params = params, 
                                features = boston.feature_names,
                                keep_history = True,
                                rerank_error = rerank_error,
                                popSize = 40,
                                maxiter = 5, early_stop=3,
                                feat_thres=0.90, # Perc selected features in first generation
                                feat_mut_thres=0.10, # Prob of a feature to be one in mutation
                                seed_ini = 1234)

GAparsimony_model.fit(X, y)

#output

GA-PARSIMONY | iter = 0
 MeanVal = -79.1813338 | ValBest = -30.3470614 | TstBest = -29.2466835 |ComplexBest = 13000000021.927263| Time(min) = 0.1210119  

GA-PARSIMONY | iter = 1
 MeanVal = -55.0713465 | ValBest = -30.2283235 | TstBest = -29.2267507 |ComplexBest = 12000000022.088743| Time(min) = 0.0713775  

GA-PARSIMONY | iter = 2
 MeanVal = -34.8473723 | ValBest = -30.2283235 | TstBest = -29.2267507 |ComplexBest = 12000000022.088743| Time(min) = 0.0631771  

GA-PARSIMONY | iter = 3
 MeanVal = -38.5251529 | ValBest = -30.0455259 | TstBest = -29.2712578 |ComplexBest = 10000000022.752678| Time(min) = 0.0586402  

GA-PARSIMONY | iter = 4
 MeanVal = -38.1097172 | ValBest = -29.8640867 | TstBest = -29.1833224 |ComplexBest = 8000000022.721948| Time(min) = 0.0682137 

summary() shows the GA initial settings and two solutions: the solution with the best validation score in the whole GA optimization process, and finally, the best parsimonious individual at the last generation.

GAparsimony_model.summary()

+------------------------------------+
|             GA-PARSIMONY           |
+------------------------------------+

GA-PARSIMONY settings:
 Number of Parameters      = 2
 Number of Features        = 13
 Population size           = 40
 Maximum of generations    = 5
 Number of early-stop gen. = 3
 Elitism                   = 8
 Crossover probability     = 0.8
 Mutation probability      = 0.1
 Max diff(error) to ReRank = 0.01
 Perc. of 1s in first popu.= 0.9
 Prob. to be 1 in mutation = 0.1

 Search domain =
           alpha     tol  CRIM   ZN  INDUS  CHAS  NOX   RM  AGE  DIS  RAD  \
Min_param    1.0  0.0001   0.0  0.0    0.0   0.0  0.0  0.0  0.0  0.0  0.0
Max_param   25.9  0.9999   1.0  1.0    1.0   1.0  1.0  1.0  1.0  1.0  1.0

           TAX  PTRATIO    B  LSTAT
Min_param  0.0      0.0  0.0    0.0
Max_param  1.0      1.0  1.0    1.0


GA-PARSIMONY results:
 Iterations                = 5
 Best validation score = -29.864086737831904


Solution with the best validation score in the whole GA process =

  fitnessVal fitnessTst complexity    alpha       tol CRIM ZN INDUS CHAS NOX  \
0   -29.8641   -29.1833      8e+09  1.33745  0.340915    1  0     1    0   1

  RM AGE DIS RAD TAX PTRATIO  B LSTAT
0  1   0   1   0   0       1  1     1


Results of the best individual at the last generation =

 Best indiv's validat.cost = -29.864086737831904
 Best indiv's testing cost = -29.183322365179112
 Best indiv's complexity   = 8000000022.721948
 Elapsed time in minutes   = 0.3824204007784525


BEST SOLUTION =

  fitnessVal fitnessTst complexity    alpha       tol CRIM ZN INDUS CHAS NOX  \
0   -29.8641   -29.1833      8e+09  1.33745  0.340915    1  0     1    0   1

  RM AGE DIS RAD TAX PTRATIO  B LSTAT
0  1   0   1   0   0       1  1     1

Plot GA evolution.

GAparsimony_model.plot()

GA-PARSIMONY evolution

Show percentage of appearance for each feature in elitists

# Percentage of appearance for each feature in elitists
GAparsimony_model.importance()

+--------------------------------------------+
|                  GA-PARSIMONY              |
+--------------------------------------------+

Percentage of appearance of each feature in elitists:

  PTRATIO LSTAT   RM    B     DIS    CRIM      ZN     NOX   INDUS    AGE  \
0     100   100  100  100  96.875  84.375  84.375  84.375  84.375  81.25

      TAX   CHAS RAD
0  71.875  56.25  50

References

Martinez-De-Pison, F.J., Gonzalez-Sendino, R., Ferreiro, J., Fraile, E., Pernia-Espinoza, A. GAparsimony: An R package for searching parsimonious models by combining hyperparameter optimization and feature selection (2018) Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics), 10870 LNAI, pp. 62-73. https://doi.org/10.1007/978-3-319-92639-1_6

Martinez-de-Pison, F.J., Gonzalez-Sendino, R., Aldama, A., Ferreiro-Cabello, J., Fraile-Garcia, E. Hybrid methodology based on Bayesian optimization and GA-PARSIMONY to search for parsimony models by combining hyperparameter optimization and feature selection (2019) Neurocomputing, 354, pp. 20-26. https://doi.org/10.1016/j.neucom.2018.05.136

Urraca R., Sodupe-Ortega E., Antonanzas E., Antonanzas-Torres F., Martinez-de-Pison, F.J. (2017). Evaluation of a novel GA-based methodology for model structure selection: The GA-PARSIMONY. Neurocomputing, Online July 2017. https://doi.org/10.1016/j.neucom.2016.08.154

Sanz-Garcia, A., Fernandez-Ceniceros, J., Antonanzas-Torres, F., Pernia-Espinoza, A.V., Martinez-De-Pison, F.J. GA-PARSIMONY: A GA-SVR approach with feature selection and parameter optimization to obtain parsimonious solutions for predicting temperature settings in a continuous annealing furnace (2015) Applied Soft Computing Journal, 35, art. no. 3006, pp. 13-28. https://doi.org/10.1016/j.asoc.2015.06.012

Fernandez-Ceniceros, J., Sanz-Garcia, A., Antoñanzas-Torres, F., Martinez-de-Pison, F.J. A numerical-informational approach for characterising the ductile behaviour of the T-stub component. Part 2: Parsimonious soft-computing-based metamodel (2015) Engineering Structures, 82, pp. 249-260. https://doi.org/10.1016/j.engstruct.2014.06.047

Antonanzas-Torres, F., Urraca, R., Antonanzas, J., Fernandez-Ceniceros, J., Martinez-De-Pison, F.J. Generation of daily global solar irradiation with support vector machines for regression (2015) Energy Conversion and Management, 96, pp. 277-286. https://doi.org/10.1016/j.enconman.2015.02.086