What is Cost Function?
Cost function, also known as the loss function, is a mathematical function that measures the difference between the predicted values of a machine learning model and the actual values of the target variable. In other words, it calculates how well the model is performing on a given dataset. The goal of the cost function is to minimize the error between the predicted values and the actual values.
The cost function is an essential part of machine learning because it provides a quantitative measure of how well the model is performing. By minimizing the cost function, we can improve the accuracy of the model and make better predictions.
In supervised learning, we have a training dataset with inputs and corresponding target outputs. We use the training dataset to train the machine learning model by minimizing the cost function. The model is trained to minimize the cost function so that it can make accurate predictions on new, unseen data.
There are different types of cost functions used in machine learning. The choice of cost function depends on the problem we are trying to solve and the type of machine learning model we are using. Here are some commonly used cost functions:
Mean Squared Error (MSE) is the most commonly used cost function for regression problems. It calculates the average squared difference between the predicted values and the actual values. The formula for MSE is:
MSE = (1/n) * Σ(y - y_hat)^2
where y is the actual value, y_hat is the predicted value, and n is the number of data points.
Cross-entropy is a cost function used for classification problems. It measures the difference between the predicted probability distribution and the actual probability distribution. The formula for cross-entropy is:
CE = - Σ(y * log(y_hat) + (1 - y) * log(1 - y_hat))
where y is the actual probability distribution, y_hat is the predicted probability distribution.
Hinge loss is a cost function used for binary classification problems. It measures the difference between the predicted output and the actual output. The formula for hinge loss is:
HL = max(0, 1 - y * y_hat)
where y is the actual output, and y_hat is the predicted output.
The goal of machine learning is to minimize the cost function. This is done by adjusting the parameters of the model to find the optimal values that minimize the cost function. This process is called optimization.
Gradient descent is a popular optimization algorithm used to minimize the cost function. It works by iteratively adjusting the parameters of the model in the direction of the negative gradient of the cost function until the cost function is minimized.
Story in a nut shell, the cost function is a mathematical function used to measure the difference between the predicted values and the actual values of a machine learning model. By minimizing the cost function, we can improve the accuracy of the model and make better predictions. There are different types of cost functions used in machine learning, depending on the problem we are trying to solve and the type of machine learning model we are using. The goal of machine learning is to minimize the cost function, and this is done through optimization algorithms like gradient descent.
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