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Stochastic gradient descent competes with the L-BFGS algorithm, [citation needed] which is also widely used. Stochastic gradient descent has been used since at least 1960 for training linear regression models, originally under the name ADALINE. [25] Another stochastic gradient descent algorithm is the least mean squares (LMS) adaptive filter.
This technique is used in stochastic gradient descent and as an extension to the backpropagation algorithms used to train artificial neural networks. [29] [30] In the direction of updating, stochastic gradient descent adds a stochastic property. The weights can be used to calculate the derivatives.
The first deep learning multilayer perceptron trained by stochastic gradient descent [22] was published in 1967 by Shun'ichi Amari. [23] In computer experiments conducted by Amari's student Saito, a five layer MLP with two modifiable layers learned internal representations to classify non-linearily separable pattern classes. [24]
[8] [12] In February 2011, some of the authors of the original L-BFGS-B code posted a major update (version 3.0). A reference implementation in Fortran 77 (and with a Fortran 90 interface). [13] [14] This version, as well as older versions, has been converted to many other languages. An OWL-QN C++ implementation by its designers. [3] [15]
[1] It's also important to apply feature scaling if regularization is used as part of the loss function (so that coefficients are penalized appropriately). Empirically, feature scaling can improve the convergence speed of stochastic gradient descent. In support vector machines, [2] it can reduce the time to find support vectors. Feature scaling ...
When the objective function is differentiable, sub-gradient methods for unconstrained problems use the same search direction as the method of gradient descent. Subgradient methods are slower than Newton's method when applied to minimize twice continuously differentiable convex functions.
Among the most used adaptive algorithms is the Widrow-Hoff’s least mean squares (LMS), which represents a class of stochastic gradient-descent algorithms used in adaptive filtering and machine learning. In adaptive filtering the LMS is used to mimic a desired filter by finding the filter coefficients that relate to producing the least mean ...
Neighbourhood components analysis is a supervised learning method for classifying multivariate data into distinct classes according to a given distance metric over the data. . Functionally, it serves the same purposes as the K-nearest neighbors algorithm and makes direct use of a related concept termed stochastic nearest neighbo