Variational Autoencoders (VAEs)

Variational Autoencoders (VAEs) are a type of generative model that combines principles from deep learning and Bayesian inference. They are designed to learn a probabilistic mapping from a high-dimensional input space to a lower-dimensional latent space, and then back to the input space. VAEs are particularly useful for generating new data samples that resemble the training data.

Key components of VAEs include:

• Encoder: This network maps the input data to a latent space, producing a distribution (usually Gaussian) rather than a single point. It outputs the mean and variance of the distribution for each dimension in the latent space.

• Latent Space: A lower-dimensional space where the data is represented in terms of probability distributions. The encoder outputs parameters of these distributions, allowing for sampling.

• Decoder: This network maps points from the latent space back to the input space, reconstructing the original data. It takes samples from the latent distribution and attempts to generate data that resembles the input.

• Loss Function: VAEs use a loss function that combines reconstruction loss (to ensure the output is similar to the input) and a regularization term (to ensure the latent space distribution is close to a standard normal distribution).

VAEs are widely used for tasks such as image generation, data compression, and anomaly detection. They are valued for their ability to learn meaningful and interpretable latent representations of data.