 Generative model

A generative model describes how observations can be produced. It can specify a probability distribution $p_{\theta }(x)$ explicitly, or provide a procedure that generates samples whose distribution is determined by parameters $\theta$. Producing observations and assigning a tractable numerical probability to every observation are separate capabilities.

An original two-bit example defines a joint probability distribution through conditional probabilities. LetGenerate $X_1$ first, then generate $X_2$ using the applicable conditional probability. The four possible outputs have probabilitieswhich sum to one. The procedure generates both complete observations and a dependence between their components. Always outputting the most probable observation, 11, would produce a different distribution: it would discard all the other outcomes rather than sample the stipulated model.

A generative adversarial network gives a different implementation. A generator transforms an input random variable into a candidate observation, while a discriminator supplies a training signal by distinguishing generated samples from training examples. The original paper develops this as an adversarial learning procedure.^[ref]

The model's samples must be assessed against the intended distribution or task. A visually plausible observation alone does not establish that the model represents the full range of observations well; distributional coverage and the probability of different outcomes matter alongside individual sample appearance.

A generative model is a type of statistical model that is designed to generate new data points from the same distribution as the training data. In contrast to discriminative models, which learn to identify or classify data points by modeling the boundary between classes, generative models attempt to capture the underlying probabilities and structures of the data itself. Generative models can be used for various tasks, including: 1. **Data Generation**: Creating new samples that mimic the original dataset.