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Ordination or gradient analysis, in multivariate analysis, is a method complementary to data clustering, and used mainly in exploratory data analysis (rather than in hypothesis testing). In contrast to cluster analysis, ordination orders quantities in a (usually lower-dimensional) latent space. In the ordination space, quantities that are near ...
In optimization, a gradient method is an algorithm to solve problems of the form min x ∈ R n f ( x ) {\displaystyle \min _{x\in \mathbb {R} ^{n}}\;f(x)} with the search directions defined by the gradient of the function at the current point.
The adjoint state method is a numerical method for efficiently computing the gradient of a function or operator in a numerical optimization problem. [1] It has applications in geophysics, seismic imaging, photonics and more recently in neural networks. [2] The adjoint state space is chosen to simplify the physical interpretation of equation ...
In this way, it is possible to backpropagate the gradient without involving stochastic variable during the update. The scheme of a variational autoencoder after the reparameterization trick. In Variational Autoencoders (VAEs), the VAE objective function, known as the Evidence Lower Bound (ELBO), is given by:
The Bregman-Lagrangian framework permits a systematic understanding of the matching rates associated with higher-order gradient methods in discrete and continuous time. [1] Based on Bregman divergence , the Lagrangian is a continuous time dynamical system whose Euler-Lagrange equations can be linked to Nesterov's accelerated gradient method for ...
The optimized gradient method (OGM) [26] reduces that constant by a factor of two and is an optimal first-order method for large-scale problems. [27] For constrained or non-smooth problems, Nesterov's FGM is called the fast proximal gradient method (FPGM), an acceleration of the proximal gradient method.
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