Search results
Results from the WOW.Com Content Network
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.
Strictly speaking, the term backpropagation refers only to an algorithm for efficiently computing the gradient, not how the gradient is used; but the term is often used loosely to refer to the entire learning algorithm – including how the gradient is used, such as by stochastic gradient descent, or as an intermediate step in a more ...
The properties of gradient descent depend on the properties of the objective function and the variant of gradient descent used (for example, if a line search step is used). The assumptions made affect the convergence rate, and other properties, that can be proven for gradient descent. [ 33 ]
The algorithm starts with an initial estimate of the optimal value, , and proceeds iteratively to refine that estimate with a sequence of better estimates ,, ….The derivatives of the function := are used as a key driver of the algorithm to identify the direction of steepest descent, and also to form an estimate of the Hessian matrix (second derivative) of ().
Specific approaches include the projected gradient descent methods, [29] [30] the active set method, [6] [31] the optimal gradient method, [32] and the block principal pivoting method [33] among several others. [34] Current algorithms are sub-optimal in that they only guarantee finding a local minimum, rather than a global minimum of the cost ...
Consequently, the hinge loss function cannot be used with gradient descent methods or stochastic gradient descent methods which rely on differentiability over the entire domain. However, the hinge loss does have a subgradient at y f ( x → ) = 1 {\displaystyle yf({\vec {x}})=1} , which allows for the utilization of subgradient descent methods ...
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.
Another computational approach is to directly seek the minima of the MSE using techniques such as the stochastic gradient descent methods; but this method still requires the evaluation of expectation. While these numerical methods have been fruitful, a closed form expression for the MMSE estimator is nevertheless possible if we are willing to ...