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The encoder part of the VAE takes an image as input and outputs a lower-dimensional latent representation of the image. This latent representation is then used as input to the U-Net. Once the model is trained, the encoder is used to encode images into latent representations, and the decoder is used to decode latent representations back into images.
Diffusion models were introduced in 2015 as a method to learn a model that can sample from a highly complex probability distribution. They used techniques from non-equilibrium thermodynamics, especially diffusion. [15] Consider, for example, how one might model the distribution of all naturally-occurring photos.
Hierarchical latent tree analysis is an alternative to LDA, which models word co-occurrence using a tree of latent variables and the states of the latent variables, which correspond to soft clusters of documents, are interpreted as topics. Animation of the topic detection process in a document-word matrix through biclustering. Every column ...
discount recursively through the tree using the rate at each node, i.e. via "backwards induction", from the time-step in question to the first node in the tree (i.e. i=0); repeat until the discounted value at the first node in the tree equals the zero-price corresponding to the given spot interest rate for the i-th time-step. Step 2.
As it maps from a known input space to the low-dimensional latent space, it is called the encoder. The decoder is the second neural network of this model. It is a function that maps from the latent space to the input space, e.g. as the means of the noise distribution.
Other latent variables correspond to abstract concepts, like categories, behavioral or mental states, or data structures. The terms hypothetical variables or hypothetical constructs may be used in these situations. The use of latent variables can serve to reduce the dimensionality of data. Many observable variables can be aggregated in a model ...
A latent variable model is a statistical model that relates a set of observable variables (also called manifest variables or indicators) [1] to a set of latent variables. Latent variable models are applied across a wide range of fields such as biology, computer science, and social science. [ 2 ]
A link/cut tree is a data structure for representing a forest, a set of rooted trees, and offers the following operations: Add a tree consisting of a single node to the forest. Given a node in one of the trees, disconnect it (and its subtree) from the tree of which it is part. Attach a node to another node as its child.