The Bias and Variance Tradeoff in Machine Learning

In order to understand the bias-variance tradeoff, we must first understand the two types of error made by machine learning models; bias and variance. Bias occurs when the model is too simple and fails to capture the underlying relationship in the data. Variance occurs when the model is unstable and doesn't generalize well to unseen new data. Both of these errors contribute to the overall error of the model, so it is an important concept to understand.

In this article, I will explain the bias and variance tradeoff in detail. I will discuss how overfitting and underfitting can lead to high variance and bias, respectively. In addition, I will explore techniques such as regularization and cross-validation that can be used to address the tradeoff.

Overfitting

Overfitting occurs when we have a complex model that fits the training data too closely. In this case, the model will have high variance since it will perform well on the training data but will not generalize well to new data. Examples of overfitting include:

• A linear regression model with too many variables can lead to a model that fits the training data very well but is unable to generalize to new data.

• A decision tree model with too many branches can lead to a model that fits the training data perfectly but cannot generalize to new data.

Underfitting

Underfitting occurs when a simple model fails to fit the training data well. In this case, the model will be unable to make predictions accurately and will have a high bias.

• Fitting a model with fewer features compared to the number of training examples available.

• Fitting a linear regression model to a non-linear dataset.

• Using a single-layer neural network to fit a complex dataset.

Regularization

Regularization is an important statistical technique in machine learning. It's a technique used to reduce the complexity of the model, which reduces the risk of overfitting. It is achieved by adding noise into your model and influencing the algorithm to build a less complex model. There are two common ways of controlling the complexity of a model; L2 and L1 regularization.

L2 regularization helps to reduce the risk of overfitting by adding a squared magnitude of the coefficients to the cost function. This influences the model to select smaller model coefficients, which helps reduce the model complexity. However, since L2 regularization uses all features in the model, it is computationally expensive and is not very useful in cases with high dimensionality.

Similarly, L1 regularization adds noise to your model by adding an absolute value of the coefficients to the cost function, which influences the model to find a subset of features with non-zero coefficients. However, since L1 finds a subset of optimal features, L1 regularization is unstable since it can select any correlated features when reducing the model coefficients to zero, which can change across training.

Cross-Validation

Cross-validation is a technique used in machine learning to evaluate the stability of a model, determine the model's predictive power, and reduce the risk of overfitting. At its core, the basic idea of cross-validation is to use a subset of the training data to train a model and the remaining data to estimate its predictive power. By doing this, cross-validation allows us to identify the optimal model complexity while avoiding the risk of overfitting. Furthermore, by using cross-validation, we can better manage the bias-variance tradeoff and ensure that our model is not overfitted and can generalize to unseen data. In future articles, I will write an article dedicated to the different types of cross-validation techniques and how they can be used to address the bias-variance tradeoff.

Conclusion

In conclusion, the bias-variance tradeoff is important to understand when developing machine learning models. Overfitting and underfitting can lead to high variance and high bias, so it's important to find right methods to address the tradeoff. Regularization and cross-validation are two techniques that can help reduce the risk of overfitting and ensure the model generalizes well to unseen data. Understanding the bias-variance tradeoff and using the proper techniques can help you create more accurate and stable machine learning models.