How deeply does Causal AI cover negative log-likelihood?

Defines the likelihood transformation and optimization role, then connects it to numerical optimization and regularization.

Negative log-likelihood

As explained in Causal AI

The negative log-likelihood loss function is the negative logarithm of the likelihood and is minimized to estimate parameters.

Negative log-likelihood is a loss function equal to the negative logarithm of a model’s likelihood. Minimizing it estimates parameters just as maximizing likelihood or log-likelihood does, while fitting naturally into machine-learning optimization workflows. section 2.3.4

Its practical role follows from how parameter estimation is performed:

Use numerical optimization when no closed-form maximum-likelihood solution is available. section 2.3.4
Fit neural-network parameters by seeking a candidate with relatively high likelihood, expressed as low negative log-likelihood. section 2.3.4
Add regularization when optimization should discourage extreme parameter values; L2 regularization penalizes the sum of squared parameters. section 2.3.4

How Causal AI covers it

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Also explained in

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Optimization Algorithms: AI techniques for design, planning, and control problemsNegative log likelihood is a loss equal to the negative logarithm of the probability assigned to the true label.
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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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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.

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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 Causal AI. The section links point to the parts of the book it draws on.