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204.4.7 Problem of Overfitting

Understanding Over fitting with an example.
Link to the previous post : https://statinfer.com/204-4-6-type-of-datasets-type-of-errors-and-problem-of-overfitting/

The Problem of Over Fitting

  • In search of the best model on the given data we add many predictors, polynomial terms, Interaction terms, variable transformations, derived variables, indicator/dummy variables etc.,
  • Most of the times we succeed in reducing the error. What error is this?
  • So by complicating the model we fit the best model for the training data.
  • Sometimes the error on the training data can reduce to near zero
  • But the same best model on training data fails miserably on test data.
  • Imagine building multiple models with small changes in training data. The resultant set of models will have huge variance in their parameter estimates.
  • The model is made really complicated, that it is very sensitive to minimal changes.
  • By complicating the model the variance of the parameters estimates inflates.
  • Model tries to fit the irrelevant characteristics in the data.
  • Over fitting
    • The model is super good on training data but not so good on test data
    • We fit the model for the noise in the data
    • Less training error, high testing error
    • The model is over complicated with too many predictors
    • Model need to be simplified
    • A model with lot of variance

Practice : Model with huge Variance

  • Data: Fiberbits/Fiberbits.csv
  • Take initial 90% of the data. Consider it as training data. Keep the final 10% of the records for validation.
  • Build the best model(5% error) model on training data.
  • Use the validation data to verify the error rate. Is the error rate on the training data and validation data same?
In [18]:
#Splitting the dataset into training and testing datasets
X = np.array(Fiber_df[features])
y = np.array(Fiber_df['active_cust'])

from sklearn.cross_validation import train_test_split
X_train, X_test, y_train, y_test = train_test_split(X,y, train_size = 0.9)
In [19]:
#Building model on training data.
tree_var = tree.DecisionTreeClassifier(criterion='gini', 
                                              splitter='best', 
                                              max_depth=20, 
                                              min_samples_split=2, 
                                              min_samples_leaf=1, 
                                              max_leaf_nodes=None)
tree_var.fit(X_train,y_train)
Out[19]:
DecisionTreeClassifier(class_weight=None, criterion='gini', max_depth=20,
            max_features=None, max_leaf_nodes=None, min_samples_leaf=1,
            min_samples_split=2, min_weight_fraction_leaf=0.0,
            presort=False, random_state=None, splitter='best')
In [20]:
#Accuracy of the model on training data
tree_var.score(X_train,y_train)
Out[20]:
0.95315555555555553

Validation accuracy :

In [21]:
#Accuracy on the test data
tree_var.score(X_test,y_test)
Out[21]:
0.86550000000000005
  • Error rate on validation data is more than the training data error.

The next post is about  problem of under fitting.

Link to the next post : https://statinfer.com/204-4-8-problem-of-under-fitting/

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