Welcome to Machine Learning. Everything is imported from class lectures and backup for future study.

Train_Test_Split:

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Input: X, y, test_size, shuffle, random_state
Output: X_train, X_test, y_train, y_test
  • (X, y): features and the target variable.
  • (test_size): between 0 and 1 - how much to allocate to the test set; the rest goes to the train set.
  • (shuffle): if True, shuffle the dataset, otherwise not.
  • (random_state): integer; if None, then results are random, otherwise fixed to a given seed.

Machine Learning need split for Train Set and Test Set. We train the model from Train Set and use the model for unknowed Test Set.

MSE - Mean Square Error

  • Mean of the square difference between the predicted value and true value.

$$ MSE = \frac{1}{N} \sum_{i=1}^N (y_i - \hat y_i)^2 $$

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# function mse		- return Mean-Squared Error
def mse(y_predicted, y_true):
    return ((y_predicted - y_true)**2).mean()


RMSE - Root Mean Square Error

  • Square root for Mean of the square difference between the predicted value and true value.
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# function rmse		- return Root Mean-Squared Error
def rmse(y_predicted, y_true):
    return np.sqrt(((y_predicted - y_true)**2).mean())


RSQ - R Square Score - $ R^2 $

  • $ 0 \le R^2 \le 1 $

The goal is to make the $ R^2 $ approaching 1 to train the model perfect.

$$ R^2 = 1 - { mse \over value } $$

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# function rsq		- return R^2
def rsq(y_predicted, y_true):
    return 1 - ((y_predicted - y_true)**2).mean() / ((y_true - y_true.mean())**2).mean()

Overfitting

Overfitting means our model fit the trainning set really well, maybe too well. $R^2$ train set way better than $R^2$ test set.

e.g. Train Set $R^2 = 0.97$ , Test Set $R^2 = 0.64$.

Solution: Reduce the complexity of our model from high frequency model to a lower degree polynomial model.

Underfitting

Underfitting mean low $R^2$ on both train set and test set. $R^2$ train set and $R^2$ test set are low.

e.g. Train Set $R^2 = 0.64$, Test Set $R^2 = 0.62$.

Solution: We can try more complex model from low degree polynomial model to a higher degree polynomial model.

2019-03-30