### 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]:

In [20]:

```
#Accuracy of the model on training data
tree_var.score(X_train,y_train)
```

Out[20]:

**Validation accuracy :**

In [21]:

```
#Accuracy on the test data
tree_var.score(X_test,y_test)
```

Out[21]:

- Error rate on validation data is more than the training data error.