Machine Learning Concept 25: Bias-Variance Tradeoff in the models of Machine Learning.
Bias - Variance Tradeoff:
The bias-variance tradeoff is a fundamental concept in machine learning that refers to the tradeoff between the model’s ability to fit the training data well (low bias) and the ability to generalize well to unseen data (low variance). In other words, bias is the error introduced by approximating a real-world problem with a simpler model, and variance is the error introduced by the model’s sensitivity to small fluctuations in the training data.
Mathematically, we can decompose the expected prediction error (EPE) of a machine learning model into three parts: bias, variance, and irreducible error:
EPE(x) = Bias²(x) + Var(x) + Irreducible error
where x is an input example. Bias represents the difference between the expected prediction of the model and the true value, and it measures how much the model simplifies the real-world problem. Variance, on the other hand, measures how much the model’s predictions vary for different training sets. The irreducible error is the minimum error that the model cannot reduce, and it is due to the noise inherent in the problem or the limitations of the data.
To illustrate this concept with an example, consider a linear regression problem where we want to predict the price of a house based on its size. We can fit a linear model to the training data, and the resulting model has low variance but high bias because it cannot capture the nonlinear relationship between the price and the size of the house. Alternatively, we can fit a high-degree polynomial model to the data, which has low bias but high variance because it fits the training data too closely and does not generalize well to unseen data.
To balance the bias-variance tradeoff, we can use regularization techniques such as L1 or L2 regularization, early stopping, or ensemble methods like bagging or boosting. Regularization methods reduce the model’s complexity and prevent overfitting to the training data, thereby reducing the variance. Ensemble methods combine multiple models to reduce the variance and improve the generalization performance.
