Negative Log-Likelihood

What is Negative log-likelihood (NLL)? NLL Explained

Negative log-likelihood (NLL), also known as cross-entropy loss, is a commonly used loss function in machine learning, particularly in classification tasks. It is often used in conjunction with probabilistic models and maximum likelihood estimation (MLE) to train models.

Here's how negative log-likelihood works:

Probability distribution: Negative log-likelihood is typically used when modeling the probability distribution of the target variable. The model, such as a neural network or a logistic regression model, predicts the probability distribution over classes for each input.

Loss calculation: To measure the difference between the predicted probability distribution and the true labels, the negative log-likelihood is computed. For each training example, the negative logarithm of the predicted probability for the correct class is taken. The negative sign is used to convert the likelihood (a value between 0 and 1) to a loss value (non-negative).

Minimization: The goal is to minimize the negative log-likelihood loss across the entire training dataset. This is typically achieved by using optimization algorithms, such as stochastic gradient descent (SGD) or its variants, which iteratively adjust the model parameters to minimize the loss.

The negative log-likelihood loss has several desirable properties:

Convexity: The negative log-likelihood loss is convex, which means it has a unique minimum and gradient descent methods can effectively find the optimal solution.

Maximum likelihood estimation: Minimizing the negative log-likelihood loss is equivalent to maximizing the likelihood of the observed data given the model parameters. This is known as maximum likelihood estimation (MLE) and is a common approach for training probabilistic models.

Emphasizing correct predictions: The negative log-likelihood loss puts higher emphasis on minimizing the loss for incorrect predictions, as it penalizes larger deviations from the true class probabilities. This helps the model to focus on improving its predictions for misclassified examples.

The negative log-likelihood loss is widely used in classification tasks, such as multi-class classification or binary classification, where the goal is to predict the class probabilities for each input. It provides a measure of the discrepancy between predicted probabilities and true labels, and serves as an objective function to guide model training. By minimizing the negative log-likelihood loss, the model learns to make more accurate and confident predictions.