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Gradient descent is a method for unconstrained mathematical optimization. It is a first-order iterative algorithm for finding a local minimum of a differentiable multivariate function . The idea is to take repeated steps in the opposite direction of the gradient (or approximate gradient) of the function at the current point, because this is the ...
Conjugate gradient method. A comparison of the convergence of gradient descent with optimal step size (in green) and conjugate vector (in red) for minimizing a quadratic function associated with a given linear system. Conjugate gradient, assuming exact arithmetic, converges in at most n steps, where n is the size of the matrix of the system ...
Stochastic gradient descent is a popular algorithm for training a wide range of models in machine learning, including (linear) support vector machines, logistic regression (see, e.g., Vowpal Wabbit) and graphical models. [21] When combined with the back propagation algorithm, it is the de facto standard algorithm for training artificial neural ...
In mathematics and computing, the Levenberg–Marquardt algorithm ( LMA or just LM ), also known as the damped least-squares ( DLS) method, is used to solve non-linear least squares problems. These minimization problems arise especially in least squares curve fitting. The LMA interpolates between the Gauss–Newton algorithm (GNA) and the ...
In machine learning and statistics, the learning rate is a tuning parameter in an optimization algorithm that determines the step size at each iteration while moving toward a minimum of a loss function. [1] Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a ...
Indeed, it's the only well-behaved gradient, which explains why early researches focused on learning or designing recurrent networks systems that could perform long-ranged computations (such as outputting the first input it sees at the very end of an episode) by shaping its stable attractors.
Coordinate descent is an optimization algorithm that successively minimizes along coordinate directions to find the minimum of a function. At each iteration, the algorithm determines a coordinate or coordinate block via a coordinate selection rule, then exactly or inexactly minimizes over the corresponding coordinate hyperplane while fixing all other coordinates or coordinate blocks.
Mean-shift is a hill climbing algorithm which involves shifting this kernel iteratively to a higher density region until convergence. Every shift is defined by a mean shift vector. The mean shift vector always points toward the direction of the maximum increase in the density. At every iteration the kernel is shifted to the centroid or the mean ...