Negative log-likelihood

As explained in Optimization Algorithms: AI techniques for design, planning, and control problems

Negative log likelihood is a loss equal to the negative logarithm of the probability assigned to the true label.

How Optimization Algorithms: AI techniques for design, planning, and control problems covers it

How deep it goes

Defines NLL and explains its behavior, then demonstrates batch computation but stops short of deriving optimization details.

Examples

Demonstrates NLL inside NumPy forward propagation for a neural network trained on the Penguins classification dataset.

What it assumes

Assumes multiclass labels and predicted probabilities while introducing the loss formula and its confidence interpretation.

What you can do after

Apply it via NumPy to compute and average classification loss from logits, probabilities, and true labels.

How it connects

Connects NLL with cross-entropy loss, probability distributions, logits, feedforward networks, and particle swarm optimization.

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Also explained in

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  Reinforcement Learning from Human FeedbackNegative log-likelihood is the negation of a model's log-likelihood, used as a loss for probabilistic predictions.
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  Deep Learning with PyTorch, Second EditionA loss function that penalizes low predicted probability assigned to the correct class by taking the negative logarithm of that probability and summing over samples.
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  Natural Language Processing in Action, Second EditionNegative log likelihood is the negative of the logarithm of a model-assigned likelihood, commonly minimized as a probabilistic prediction loss.
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  Causal AIThe negative log-likelihood loss function is the negative logarithm of the likelihood and is minimized to estimate parameters.
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  Machine Learning Algorithms in DepthA negative log likelihood is a loss equal to the negative logarithm of the likelihood assigned to observed outcomes by a probabilistic model.
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  Ensemble Methods for Machine LearningNegative log-likelihood is the negative logarithm of the likelihood assigned by a probabilistic model to observed data.

Compare how 7 books explain negative log-likelihood →

Related concepts

• cross entropy lossequivalent to · Cross-entropy loss measures the expected negative log probability that a predicted distribution assigns to outcomes drawn from a target distribution.
• mean squared errorequivalent to · Mean squared error is the arithmetic mean of the squared differences between corresponding predicted and target numerical values.
• DPO lossused by · The DPO loss is a preference-training objective that optimizes a policy to assign higher relative likelihood to preferred responses than to rejected responses compared with a reference policy.
• NLLLossused by · NLLLoss is a PyTorch loss function that computes negative log-likelihood loss from log-probability outputs and target classes.
• mixture density networkused by · A mixture density network is a neural network that predicts the parameters of a conditional mixture probability distribution, optionally at each sequence step.
• variational lossy autoencodermeasures · A variational lossy autoencoder is an autoencoder variant that intentionally constrains its latent representation so reconstruction preserves selected information rather than every input detail.

This explainer was generated by Manning's knowledge graph from the text of Optimization Algorithms: AI techniques for design, planning, and control problems. The section links point to the parts of the book it draws on.