Empirical Risk Minimization (ERM)
Empirical risk minimization, or ERM, is a central principle in statistical learning theory. When you use ERM, you choose a function from a set of possible hypotheses that minimizes the average loss on your observed training data. The motivation for ERM comes from the fact that, in real-world situations, the true distribution of the data is unknown. You cannot directly minimize the expected loss (the true risk) because you do not have access to all possible data pointsβonly to a finite sample. ERM offers a practical approach: instead of minimizing the true risk, you minimize the empirical risk, which is the average loss over your sample. This makes ERM the default strategy for many learning algorithms that need to select the best hypothesis based solely on the available data.
You start with a set of possible functions (hypothesis class) and a loss function that measures how well a function predicts the correct output. The hypothesis class could include models like linear functions, decision trees, or neural networks. The loss function, such as mean_squared_error or zero_one_loss, quantifies prediction errors.
You collect a set of labeled examples drawn from the unknown data distribution. This training sample is your only source of information about the underlying process, since the true distribution is not accessible.
For each function in your hypothesis class, calculate the average loss over the training data. This value is called the empirical risk:
EmpiricalΒ Risk(h)=n1βi=1βnβloss(h(xiβ),yiβ)where h is a hypothesis, (xiβ,yiβ) are the training examples, and n is the number of examples.
Choose the function from your hypothesis class that achieves the lowest empirical risk on the observed sample. This is the hypothesis that best fits your training data according to the chosen loss function.
The chosen function is then used to make predictions on new, unseen data. The hope is that minimizing empirical risk will also lead to low true risk on future data.
While ERM is intuitive and widely used, it has important limitations. The most significant is its sensitivity to overfitting: a hypothesis that perfectly fits the training data may perform poorly on new data if it simply memorizes the sample rather than capturing the underlying pattern. This happens especially when the hypothesis class is very large or flexible compared to the amount of available data.
Thanks for your feedback!
Ask AI
Ask AI
Ask anything or try one of the suggested questions to begin our chat
Can you explain the difference between empirical risk and true risk?
What are some common loss functions used in ERM?
How does ERM relate to overfitting in machine learning?
Awesome!
Completion rate improved to 7.69Empirical Risk Minimization (ERM)
Swipe to show menu
Empirical risk minimization, or ERM, is a central principle in statistical learning theory. When you use ERM, you choose a function from a set of possible hypotheses that minimizes the average loss on your observed training data. The motivation for ERM comes from the fact that, in real-world situations, the true distribution of the data is unknown. You cannot directly minimize the expected loss (the true risk) because you do not have access to all possible data pointsβonly to a finite sample. ERM offers a practical approach: instead of minimizing the true risk, you minimize the empirical risk, which is the average loss over your sample. This makes ERM the default strategy for many learning algorithms that need to select the best hypothesis based solely on the available data.
You start with a set of possible functions (hypothesis class) and a loss function that measures how well a function predicts the correct output. The hypothesis class could include models like linear functions, decision trees, or neural networks. The loss function, such as mean_squared_error or zero_one_loss, quantifies prediction errors.
You collect a set of labeled examples drawn from the unknown data distribution. This training sample is your only source of information about the underlying process, since the true distribution is not accessible.
For each function in your hypothesis class, calculate the average loss over the training data. This value is called the empirical risk:
EmpiricalΒ Risk(h)=n1βi=1βnβloss(h(xiβ),yiβ)where h is a hypothesis, (xiβ,yiβ) are the training examples, and n is the number of examples.
Choose the function from your hypothesis class that achieves the lowest empirical risk on the observed sample. This is the hypothesis that best fits your training data according to the chosen loss function.
The chosen function is then used to make predictions on new, unseen data. The hope is that minimizing empirical risk will also lead to low true risk on future data.
While ERM is intuitive and widely used, it has important limitations. The most significant is its sensitivity to overfitting: a hypothesis that perfectly fits the training data may perform poorly on new data if it simply memorizes the sample rather than capturing the underlying pattern. This happens especially when the hypothesis class is very large or flexible compared to the amount of available data.
Thanks for your feedback!
