Reparameterisation

Reparameterization is a technique used in various fields, including machine learning and optimization, to transform the parameters of a model or function into a different set of parameters. This transformation can simplify the optimization process, improve numerical stability, or enable the use of specific optimization algorithms. The key idea is to re-express the original parameters in terms of new parameters, which may have different properties or constraints.

In machine learning, reparameterization is often used in variational inference and generative models. For example, in variational autoencoders (VAEs), the reparameterization trick is employed to make the stochastic gradient variational bayes (SGVB) estimator unbiased. This involves expressing the latent variables in terms of a deterministic function of the parameters and a noise variable, allowing for efficient backpropagation through the reparameterized variables.

Reparameterization can also be applied in optimization problems to transform the objective function into a more tractable form. For instance, in constrained optimization, reparameterization can be used to convert a constrained problem into an unconstrained one, making it easier to apply gradient-based optimization methods.

The choice of reparameterization depends on the specific problem and the desired properties of the new parameters. It is important to ensure that the reparameterization is invertible and that the transformation preserves the essential characteristics of the original problem. Additionally, the reparameterization should be chosen to facilitate the optimization process or to meet the requirements of the specific application.