energybased

Energybased, in the context of machine learning and statistics, refers to energy-based modeling (EBM). EBMs are a class of probabilistic models that define a scalar energy function E(x) over data configurations x, with lower energy indicating more plausible or likely configurations. The probability of a configuration is proportional to the exponential of the negative energy, P(x) ∝ exp(-E(x)/T), where T is a temperature parameter and Z = ∑x exp(-E(x)/T) (or an integral in continuous spaces) is the normalization constant, also called the partition function. In many practical problems Z is intractable, so training and inference rely on approximate methods.

In EBMs the energy function can be parameterized by neural networks or other flexible function approximators, allowing rich, non-metric representations of complex data. The central idea is to learn an energy landscape where observed data occupy low-energy regions while other configurations have higher energy. Unlike strictly normalized likelihood models, EBMs do not require an explicit probability distribution to be evaluated everywhere; instead they emphasize relative energy differences.

Training EBMs typically involves methods that bypass exact computation of Z. Common techniques include contrastive divergence for Boltzmann machines, score matching, and noise-contrastive estimation. Inference often seeks low-energy configurations via optimization or sampling, using techniques such as gradient-based methods or Langevin dynamics.

Key examples in the history of EBMs include Boltzmann machines and Restricted Boltzmann Machines. Modern deep energy-based models are used for generative modeling, representation learning, and anomaly detection, among other tasks. EBMs offer flexibility in modeling dependencies but can be computationally intensive and challenging to train due to the intractable partition function.