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A variational autoencoder is a generative model with a prior and noise distribution respectively. Usually such models are trained using the expectation-maximization meta-algorithm (e.g. probabilistic PCA , (spike & slab) sparse coding).
Gradient descent with momentum remembers the solution update at each iteration, and determines the next update as a linear combination of the gradient and the previous update. For unconstrained quadratic minimization, a theoretical convergence rate bound of the heavy ball method is asymptotically the same as that for the optimal conjugate ...
An autoencoder is a type of artificial neural network used to learn efficient codings of unlabeled data (unsupervised learning).An autoencoder learns two functions: an encoding function that transforms the input data, and a decoding function that recreates the input data from the encoded representation.
The calculus of variations began with the work of Isaac Newton, such as with Newton's minimal resistance problem, which he formulated and solved in 1685, and published in his Principia in 1687, [2] which was the first problem in the field to be clearly formulated and correctly solved, and was one of the most difficult problems tackled by variational methods prior to the twentieth century.
In 2014, advancements such as the variational autoencoder and generative adversarial network produced the first practical deep neural networks capable of learning generative models, as opposed to discriminative ones, for complex data such as images. These deep generative models were the first to output not only class labels for images but also ...
Because free energy can be expressed as the expected energy of observations under the variational density minus its entropy, it is also related to the maximum entropy principle. [19] Finally, because the time average of energy is action, the principle of minimum variational free energy is a principle of least action. Active inference allowing ...
In statistics, econometrics, and signal processing, an autoregressive (AR) model is a representation of a type of random process; as such, it can be used to describe certain time-varying processes in nature, economics, behavior, etc.
The on-line textbook: Information Theory, Inference, and Learning Algorithms, by David J.C. MacKay includes simple examples of the EM algorithm such as clustering using the soft k-means algorithm, and emphasizes the variational view of the EM algorithm, as described in Chapter 33.7 of version 7.2 (fourth edition). Variational Algorithms for ...