📉Negative Log-Likelihood

NEW

Also known as: NLL

A loss function equal to the negative logarithm of the likelihood, penalizing improbable predictions under the model’s distribution.

DESCRIPTION

Negative log-likelihood is widely used to train probabilistic models by maximizing data likelihood via minimization. For classification with softmax, it corresponds to cross-entropy, while for Gaussian regression it becomes log-variance-weighted error. NLL encourages calibrated probabilistic outputs and supports uncertainty-aware modeling. Properly handling class imbalance, label smoothing, and regularization improves stability and generalization.

ALTERNATIVE DEFINITIONS

Wikipedia

In statistics, the log-likelihood of a model is the logarithm of the likelihood function.

Defines log-likelihood, the basis for NLL as its negation during optimization.

Source

PyTorch

The negative log likelihood loss.

Provides the canonical implementation used with log-probabilities and class targets.

Source

Stanford CS229

Maximizing likelihood is equivalent to minimizing negative log-likelihood, which is often easier to optimize.

Connects NLL minimization to maximum likelihood estimation in practice.

Source

RELATED TERMS

Maximum Likelihood Estimation Softmax Logistic Regression Probabilistic Modeling Entropy KL Divergence Gaussian NLL Loss Loss Function Likelihood

COMPETING TERMS

Mean Squared Error Hinge Loss Cross-Entropy Loss

RELATIONS

• Broader: Log-Likelihood

KNOWLEDGE AREAS

Mathematics AI Data Science MLOps

TARGET AUDIENCE

Data Scientist AI Engineer MLOps Engineer

EXTERNAL SOURCES

• Wikipedia - Log-likelihood
• PyTorch - API for NLLLoss
• scikit-learn - Log loss for classification
• Deep Learning (Goodfellow et al.) - Probability and likelihood

TOP QUESTIONS

Why use Negative Log-Likelihood in classification?

NLL aligns with maximum likelihood and encourages calibrated probabilities. With softmax, it is equivalent to cross-entropy, a robust choice for multi-class tasks.

Category: Relevancy

How does NLL compare to MSE in probabilistic models?

NLL respects the model’s distribution and uncertainty, while MSE penalizes squared error. NLL is preferred when probabilistic calibration matters.

Category: Alternatives

What are common mistakes using NLL?

Feeding raw logits instead of log-probabilities to NLLLoss in PyTorch results in incorrect optimization. Also neglecting class imbalance harms performance.

Category: Mistakes

Why is NLL numerically stable?

Logarithms convert products to sums and avoid underflow. Log-sum-exp tricks further stabilize softmax computations.

Category: Example

How does label smoothing affect NLL?

It reduces overconfidence by distributing small probability mass across non-target classes, improving generalization and calibration.

Category: Opinion

When is Gaussian NLL appropriate?

For regression with heteroscedastic noise, modeling variance and mean allows uncertainty-aware predictions and principled likelihood optimization.

Category: Requirements

What risks arise from miscalibrated NLL outputs?

Overconfident wrong probabilities mislead downstream decisions. Monitoring calibration and using temperature scaling helps mitigate.

Category: Risk

Is NLL suitable for imbalanced classes?

Yes, with class weights or focal variants. Unweighted NLL can bias toward majority classes.

Category: HowTo

What’s a hot topic around NLL?

Distribution-aware training and uncertainty quantification in deep learning, including evidential models and calibration techniques.

Category: Topic