Contrastive divergence is a human-made approximate learning algorithm for energy-based models, especially Boltzmann machines, that estimates the gradient of the log-likelihood by running a short Gibbs chain initialized from data and contrasting the data statistics with the statistics after k steps of Markov chain Monte Carlo. Parameters: (1) the energy-based model with parameters θ defining p_θ(x) ∝ exp(-E_θ(x)), (2) the number of Gibbs steps k (typically k=1), (3) the data distribution p_data, (4) the model distribution p_θ. The algorithm persists through machine learning literature and software libraries as a computationally tractable alternative to full maximum-likelihood, with the update Δθ ∝ ∂/∂θ [E_{p_data}[E_θ(x)] - E_{p_θ^k}[E_θ(x)]]. [formal: divergentia contrastiva | substrate: mind | horizon: hours | explicit: yes | epoch: 0.02]
Accepted ontology entry
contrastive-divergence
Contrastive divergence is a human-made approximate learning algorithm for energy-based models, especially Boltzmann machines, that estimates the gradient of the log-likelihood by running a short Gibbs chain initialized from data and contra…
Definition
Why it is in scope
A human-made learning algorithm used to approximate maximum-likelihood training for Boltzmann machines by contrasting data distribution with model distribution, persisting through machine learning practice and computational implementations.
Names and aliases
- contrastive-divergenceen · CANONICAL
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Contrastive divergence estimates log-likelihood gradient by contrasting data statistics with model statistics under a probability distribution. Remove probability distributions and the Gibbs chain has no density p_θ(x) to sample, the expectation E_{p_data}[E_θ] and E_{p_θ^k}[E_θ] become inoperable, and the algorithm ceases to operate. Operational cessation per Law 8b.
- cmsllb31s07h4nobp1h0i7lu3INSTANCE_OF →
Contrastive divergence is a specific learning algorithm that iteratively adjusts model parameters to approximate maximum-likelihood, i.e., an optimization procedure for energy-based models. A competent speaker would call it an optimization algorithm. Nearest kind is optimization algorithm per Law 9.
- cmsi4l2p80452ywh500rxvdvfSERVES →
Contrastive divergence is an approximation algorithm for maximum likelihood estimation in energy-based models. It is built for the sake of optimization — providing a tractable optimization objective where exact gradient computation is intractable.
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- Sep 5, 2026, 8:06 AM UTC
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