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Gradient descent

Index Gradient descent

Gradient descent is a first-order iterative optimization algorithm for finding the minimum of a function. [1]

63 relations: Accuracy and precision, Algorithm, Artificial neural network, Backpropagation, Big O notation, Bowl, Broyden–Fletcher–Goldfarb–Shanno algorithm, Concentric objects, Conjugate gradient method, Constraint (mathematics), Contour line, Convex function, Convex optimization, Coursera, Curvature, Delta rule, Derivative, Differentiable function, Differential calculus, Eigenvalues and eigenvectors, Euler method, Fréchet derivative, Function of several real variables, Function space, Gauss–Newton algorithm, Geoffrey Hinton, Gradient, Hessian matrix, Hill climbing, Iterative method, Jacobian matrix and determinant, Limited-memory BFGS, Line search, Linear least squares (mathematics), Lipschitz continuity, Mathematical analysis, Mathematical optimization, MATLAB, Maxima and minima, Method of steepest descent, Nelder–Mead method, Neural Networks (journal), Newton's method in optimization, Norm (mathematics), Ordinary differential equation, Orthogonality, Preconditioner, Projection (linear algebra), Proximal gradient method, Python (programming language), ..., Regina S. Burachik, Rosenbrock function, Rprop, Slope, Stochastic gradient descent, Subgradient method, Undefined (mathematics), Variational inequality, Vector field, Willamette University, Wolfe conditions, YouTube, Yurii Nesterov. Expand index (13 more) »

Accuracy and precision

Precision is a description of random errors, a measure of statistical variability.

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Algorithm

In mathematics and computer science, an algorithm is an unambiguous specification of how to solve a class of problems.

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Artificial neural network

Artificial neural networks (ANNs) or connectionist systems are computing systems vaguely inspired by the biological neural networks that constitute animal brains.

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Backpropagation

Backpropagation is a method used in artificial neural networks to calculate a gradient that is needed in the calculation of the weights to be used in the network.

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Big O notation

Big O notation is a mathematical notation that describes the limiting behaviour of a function when the argument tends towards a particular value or infinity.

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Bowl

A bowl is a round, open-top container used in many cultures to serve hot and cold food.

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Broyden–Fletcher–Goldfarb–Shanno algorithm

In numerical optimization, the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm is an iterative method for solving unconstrained nonlinear optimization problems.

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Concentric objects

In geometry, two or more objects are said to be concentric, coaxal, or coaxial when they share the same center or axis.

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Conjugate gradient method

In mathematics, the conjugate gradient method is an algorithm for the numerical solution of particular systems of linear equations, namely those whose matrix is symmetric and positive-definite.

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Constraint (mathematics)

In mathematics, a constraint is a condition of an optimization problem that the solution must satisfy.

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Contour line

A contour line (also isocline, isopleth, isarithm, or equipotential curve) of a function of two variables is a curve along which the function has a constant value, so that the curve joins points of equal value.

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Convex function

In mathematics, a real-valued function defined on an ''n''-dimensional interval is called convex (or convex downward or concave upward) if the line segment between any two points on the graph of the function lies above or on the graph, in a Euclidean space (or more generally a vector space) of at least two dimensions.

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Convex optimization

Convex optimization is a subfield of optimization that studies the problem of minimizing convex functions over convex sets.

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Coursera

Coursera is an online learning platform founded by Stanford professors Andrew Ng and Daphne Koller that offers courses, specializations, and degrees.

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Curvature

In mathematics, curvature is any of a number of loosely related concepts in different areas of geometry.

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Delta rule

In machine learning, the Delta rule is a gradient descent learning rule for updating the weights of the inputs to artificial neurons in a single-layer neural network.

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Derivative

The derivative of a function of a real variable measures the sensitivity to change of the function value (output value) with respect to a change in its argument (input value).

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Differentiable function

In calculus (a branch of mathematics), a differentiable function of one real variable is a function whose derivative exists at each point in its domain.

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Differential calculus

In mathematics, differential calculus is a subfield of calculus concerned with the study of the rates at which quantities change.

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Eigenvalues and eigenvectors

In linear algebra, an eigenvector or characteristic vector of a linear transformation is a non-zero vector that changes by only a scalar factor when that linear transformation is applied to it.

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Euler method

In mathematics and computational science, the Euler method (also called forward Euler method) is a first-order numerical procedure for solving ordinary differential equations (ODEs) with a given initial value.

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Fréchet derivative

In mathematics, the Fréchet derivative is a derivative defined on Banach spaces.

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Function of several real variables

In mathematical analysis, and applications in geometry, applied mathematics, engineering, natural sciences, and economics, a function of several real variables or real multivariate function is a function with more than one argument, with all arguments being real variables.

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Function space

In mathematics, a function space is a set of functions between two fixed sets.

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Gauss–Newton algorithm

The Gauss–Newton algorithm is used to solve non-linear least squares problems.

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Geoffrey Hinton

Geoffrey Everest Hinton One or more of the preceding sentences incorporates text from the royalsociety.org website where: (born 6 December 1947) is a British cognitive psychologist and computer scientist, most noted for his work on artificial neural networks.

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Gradient

In mathematics, the gradient is a multi-variable generalization of the derivative.

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Hessian matrix

In mathematics, the Hessian matrix or Hessian is a square matrix of second-order partial derivatives of a scalar-valued function, or scalar field.

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Hill climbing

In numerical analysis, hill climbing is a mathematical optimization technique which belongs to the family of local search.

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Iterative method

In computational mathematics, an iterative method is a mathematical procedure that uses an initial guess to generate a sequence of improving approximate solutions for a class of problems, in which the n-th approximation is derived from the previous ones.

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Jacobian matrix and determinant

In vector calculus, the Jacobian matrix is the matrix of all first-order partial derivatives of a vector-valued function.

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Limited-memory BFGS

Limited-memory BFGS (L-BFGS or LM-BFGS) is an optimization algorithm in the family of quasi-Newton methods that approximates the Broyden–Fletcher–Goldfarb–Shanno (BFGS) algorithm using a limited amount of computer memory.

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Line search

In optimization, the line search strategy is one of two basic iterative approaches to find a local minimum \mathbf^* of an objective function f:\mathbb R^n\to\mathbb R. The other approach is trust region.

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Linear least squares (mathematics)

In statistics and mathematics, linear least squares is an approach to fitting a mathematical or statistical model to data in cases where the idealized value provided by the model for any data point is expressed linearly in terms of the unknown parameters of the model.

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Lipschitz continuity

In mathematical analysis, Lipschitz continuity, named after Rudolf Lipschitz, is a strong form of uniform continuity for functions.

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Mathematical analysis

Mathematical analysis is the branch of mathematics dealing with limits and related theories, such as differentiation, integration, measure, infinite series, and analytic functions.

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Mathematical optimization

In mathematics, computer science and operations research, mathematical optimization or mathematical programming, alternatively spelled optimisation, is the selection of a best element (with regard to some criterion) from some set of available alternatives.

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MATLAB

MATLAB (matrix laboratory) is a multi-paradigm numerical computing environment and proprietary programming language developed by MathWorks.

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Maxima and minima

In mathematical analysis, the maxima and minima (the respective plurals of maximum and minimum) of a function, known collectively as extrema (the plural of extremum), are the largest and smallest value of the function, either within a given range (the local or relative extrema) or on the entire domain of a function (the global or absolute extrema).

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Method of steepest descent

In mathematics, the method of steepest descent or stationary-phase method or saddle-point method is an extension of Laplace's method for approximating an integral, where one deforms a contour integral in the complex plane to pass near a stationary point (saddle point), in roughly the direction of steepest descent or stationary phase.

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Nelder–Mead method

The Nelder–Mead method or downhill simplex method or amoeba method is a commonly applied numerical method used to find the minimum or maximum of an objective function in a multidimensional space.

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Neural Networks (journal)

Neural Networks is a monthly peer-reviewed scientific journal and an official journal of the International Neural Network Society, European Neural Network Society, and Japanese Neural Network Society.

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Newton's method in optimization

In calculus, Newton's method is an iterative method for finding the roots of a differentiable function (i.e. solutions to the equation). In optimization, Newton's method is applied to the derivative of a twice-differentiable function to find the roots of the derivative (solutions to), also known as the stationary points of.

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Norm (mathematics)

In linear algebra, functional analysis, and related areas of mathematics, a norm is a function that assigns a strictly positive length or size to each vector in a vector space—save for the zero vector, which is assigned a length of zero.

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Ordinary differential equation

In mathematics, an ordinary differential equation (ODE) is a differential equation containing one or more functions of one independent variable and its derivatives.

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Orthogonality

In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.

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Preconditioner

In mathematics, preconditioning is the application of a transformation, called the preconditioner, that conditions a given problem into a form that is more suitable for numerical solving methods.

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Projection (linear algebra)

In linear algebra and functional analysis, a projection is a linear transformation P from a vector space to itself such that.

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Proximal gradient method

Proximal gradient methods are a generalized form of projection used to solve non-differentiable convex optimization problems.

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Python (programming language)

Python is an interpreted high-level programming language for general-purpose programming.

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Regina S. Burachik

Regina Sandra Burachik is an Argentine mathematician who works on optimization and analysis (particularly: convex analysis, functional analysis and non-smooth analysis).

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Rosenbrock function

In mathematical optimization, the Rosenbrock function is a non-convex function, introduced by Howard H. Rosenbrock in 1960, which is used as a performance test problem for optimization algorithms.

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Rprop

Rprop, short for resilient backpropagation, is a learning heuristic for supervised learning in feedforward artificial neural networks.

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Slope

In mathematics, the slope or gradient of a line is a number that describes both the direction and the steepness of the line.

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Stochastic gradient descent

Stochastic gradient descent (often shortened to SGD), also known as incremental gradient descent, is an iterative method for optimizing a differentiable objective function, a stochastic approximation of gradient descent optimization.

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Subgradient method

Subgradient methods are iterative methods for solving convex minimization problems.

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Undefined (mathematics)

In mathematics, undefined has several different meanings, depending on the context.

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Variational inequality

In mathematics, a variational inequality is an inequality involving a functional, which has to be solved for all possible values of a given variable, belonging usually to a convex set.

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Vector field

In vector calculus and physics, a vector field is an assignment of a vector to each point in a subset of space.

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Willamette University

Willamette University is a private liberal arts college located in Salem, Oregon, United States.

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Wolfe conditions

In the unconstrained minimization problem, the Wolfe conditions are a set of inequalities for performing inexact line search, especially in quasi-Newton methods, first published by Philip Wolfe in 1969.

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YouTube

YouTube is an American video-sharing website headquartered in San Bruno, California.

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Yurii Nesterov

Yurii Nesterov is a Russian mathematician, an internationally recognized expert in convex optimization, especially in the development of efficient algorithms and numerical optimization analysis.

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Gradient Descent, Gradient ascent, Gradient descent method, Gradient descent optimization, Steepest ascent, Steepest descent.

References

[1] https://en.wikipedia.org/wiki/Gradient_descent

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