Grid Searching From Scratch using Python

Grid searching is a method to find the best possible combination of hyper-parameters at which the model achieves the highest accuracy. Before applying Grid Searching on any algorithm, Data is used to divided into training and validation set, a validation set is used to validate the models. A model with all possible combinations of hyperparameters is tested on the validation set to choose the best combination.

Implementation:

Grid Searching can be applied to any hyperparameters algorithm whose performance can be improved by tuning hyperparameter. For example, we can apply grid searching on K-Nearest Neighbors by validating its performance on a set of values of K in it. Same thing we can do with Logistic Regression by using a set of values of learning rate to find the best learning rate at which Logistic Regression achieves the best accuracy.

It has 8 features columns like i.e “Age”, “Glucose” e.t.c, and the target variable “Outcome” for 108 patients. So in this, we will train a Logistic Regression Classifier model to predict the presence of diabetes or not for patients with such information.

Code: Implementation of Grid Searching on Logistic Regression from Scratch

Python3

# Importing libraries

import numpy as np
import pandas as pd
from sklearn.model_selection import train_test_split

# Grid Searching in Logistic Regression
class LogitRegression() :
    def __init__( self, learning_rate, iterations ) :
        self.learning_rate = learning_rate
        self.iterations = iterations

    # Function for model training
    def fit( self, X, Y ) :
        # no_of_training_examples, no_of_features
        self.m, self.n = X.shape

        # weight initialization
        self.W = np.zeros( self.n )
        self.b = 0
        self.X = X
        self.Y = Y

        # gradient descent learning
        for i in range( self.iterations ) :
            self.update_weights()
        return self

    # Helper function to update weights in gradient descent
    def update_weights( self ) :
        A = 1 / ( 1 + np.exp( - ( self.X.dot( self.W ) + self.b ) ) )

        # calculate gradients
        tmp = ( A - self.Y.T )
        tmp = np.reshape( tmp, self.m )
        dW = np.dot( self.X.T, tmp ) / self.m
        db = np.sum( tmp ) / self.m

        # update weights
        self.W = self.W - self.learning_rate * dW
        self.b = self.b - self.learning_rate * db
        return self

    # Hypothetical function  h( x )
    def predict( self, X ) :
        Z = 1 / ( 1 + np.exp( - ( X.dot( self.W ) + self.b ) ) )
        Y = np.where( Z > 0.5, 1, 0 )
        return Y


# Driver code

def main() :

    # Importing dataset
    df = pd.read_csv( "diabetes.csv" )
    X = df.iloc[:,:-1].values
    Y = df.iloc[:,-1:].values

    # Splitting dataset into train and validation set
    X_train, X_valid, Y_train, Y_valid = train_test_split(
      X, Y, test_size = 1/3, random_state = 0 )

    # Model training
    max_accuracy = 0

    # learning_rate choices
    learning_rates = [ 0.1, 0.2, 0.3, 0.4, 0.5,
                      0.01, 0.02, 0.03, 0.04, 0.05 ]

    # iterations choices
    iterations = [ 100, 200, 300, 400, 500 ]

    # available combination of learning_rate and iterations

    parameters = []
    for i in learning_rates :
        for j in iterations :
            parameters.append( ( i, j ) )

    print("Available combinations : ",  parameters )

    # Applying linear searching in list of available combination
    # to achieved maximum accuracy on CV set

    for k in range( len( parameters ) ) :
        model = LogitRegression( learning_rate = parameters[k][0],
                                iterations = parameters[k][1] )

        model.fit( X_train, Y_train )

        # Prediction on validation set
        Y_pred = model.predict( X_valid )

        # measure performance on validation set

        correctly_classified = 0

        # counter
        count = 0

        for count in range( np.size( Y_pred ) ) :
            if Y_valid[count] == Y_pred[count] :
                correctly_classified = correctly_classified + 1

        curr_accuracy = ( correctly_classified / count ) * 100

        if max_accuracy < curr_accuracy :
            max_accuracy = curr_accuracy

    print( "Maximum accuracy achieved by our model through grid searching : ", max_accuracy )

if __name__ == "__main__" :
    main()

Output:

Available combinations :  [(0.1, 100), (0.1, 200), (0.1, 300), (0.1, 400), 
(0.1, 500), (0.2, 100), (0.2, 200), (0.2, 300), (0.2, 400), (0.2, 500), 
(0.3, 100), (0.3, 200), (0.3, 300), (0.3, 400), (0.3, 500), (0.4, 100), 
(0.4, 200), (0.4, 300), (0.4, 400), (0.4, 500), (0.5, 100), (0.5, 200), 
(0.5, 300), (0.5, 400), (0.5, 500), (0.01, 100), (0.01, 200), (0.01, 300),
(0.01, 400), (0.01, 500), (0.02, 100), (0.02, 200), (0.02, 300), (0.02, 400), 
(0.02, 500), (0.03, 100), (0.03, 200), (0.03, 300), (0.03, 400), (0.03, 500), 
(0.04, 100), (0.04, 200), (0.04, 300), (0.04, 400), (0.04, 500), (0.05, 100), 
(0.05, 200), (0.05, 300), (0.05, 400), (0.05, 500)]

Maximum accuracy achieved by our model through grid searching :  60.0

In the above, we applied grid searching on all possible combinations of learning rates and the number of iterations to find the peak of the model at which it achieves the highest accuracy.

Code: Implementation of Grid Searching on Logistic Regression of sklearn

Python3

# Importing Libraries

import pandas as pd
import numpy as np
from sklearn.linear_model import LogisticRegression
from sklearn.model_selection import GridSearchCV

# Driver Code

def main() :
    # Importing dataset
    df = pd.read_csv( "diabetes.csv" )
    X = df.iloc[:,:-1].values
    Y = df.iloc[:,-1:].values

    # Splitting dataset into train and test set
    X_train, X_test, Y_train, Y_test = train_test_split(
      X, Y, test_size = 1/3, random_state = 0 )

    # Model training
    max_accuracy = 0

    # grid searching for learning rate
    parameters = { 'C' : [ 1, 2, 3, 4, 5, 6, 7, 8, 9, 10 ] }

    model = LogisticRegression()
    grid = GridSearchCV( model, parameters )
    grid.fit( X_train, Y_train )

    # Prediction on test set
    Y_pred = grid.predict( X_test )

    # measure performance
    correctly_classified = 0

    # counter
    count = 0

    for count in range( np.size( Y_pred ) ) :
        if Y_test[count] == Y_pred[count] :
            correctly_classified = correctly_classified + 1

    accuracy = ( correctly_classified / count ) * 100

    print( "Maximum accuracy achieved by sklearn model through grid searching : ", np.round( accuracy, 2 ) )

if __name__ == "__main__" :
    main()

Output:

Maximum accuracy achieved by sklearn model through grid searching :  62.86

Note: Grid Searching plays a vital role in tuning hyperparameters for the mathematically complex models.