Search results
Results From The WOW.Com Content Network
The number of gradient descent iterations is commonly proportional to the spectral condition number of the system matrix (the ratio of the maximum to minimum eigenvalues of ), while the convergence of conjugate gradient method is typically determined by a square root of the condition number, i.e., is much faster.
In optimization, a gradient method is an algorithm to solve problems of the form with the search directions defined by the gradient of the function at the current point. Examples of gradient methods are the gradient descent and the conjugate gradient.
As observed above, is the negative gradient of at , so the gradient descent method would require to move in the direction r k. Here, however, we insist that the directions must be conjugate to each other. A practical way to enforce this is by requiring that the next search direction be built out of the current residual and all previous search ...
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.
The line-search method first finds a descent direction along which the objective function will be reduced, and then computes a step size that determines how far should move along that direction. The descent direction can be computed by various methods, such as gradient descent or quasi-Newton method. The step size can be determined either ...
Numerous methods exist to compute descent directions, all with differing merits, such as gradient descent or the conjugate gradient method. More generally, if is a positive definite matrix, then = is a descent direction at . [1]
The Barzilai-Borwein method [1] is an iterative gradient descent method for unconstrained optimization using either of two step sizes derived from the linear trend of the most recent two iterates. This method, and modifications, are globally convergent under mild conditions, [ 2 ] [ 3 ] and perform competitively with conjugate gradient methods ...
In machine learning, early stopping is a form of regularization used to avoid overfitting when training a model with an iterative method, such as gradient descent. Such methods update the model to make it better fit the training data with each iteration. Up to a point, this improves the model's performance on data outside of the training set (e ...