BackpropagationAs a machine-learning algorithm, backpropagation performs a backward pass to adjust the model's parameters, aiming to minimize the mean squared error (MSE). In a single-layered network, backpropagation uses the following steps: Traverse through the network from the input to the output by computing the hidden layers' output and the output layer. (the feedforward step) In the output layer, calculate the derivative of the cost function with respect to the input and the hidden layers.
Convex optimizationConvex optimization is a subfield of mathematical optimization that studies the problem of minimizing convex functions over convex sets (or, equivalently, maximizing concave functions over convex sets). Many classes of convex optimization problems admit polynomial-time algorithms, whereas mathematical optimization is in general NP-hard.
Mathematical optimizationMathematical optimization (alternatively spelled optimisation) or mathematical programming is the selection of a best element, with regard to some criterion, from some set of available alternatives. It is generally divided into two subfields: discrete optimization and continuous optimization. Optimization problems arise in all quantitative disciplines from computer science and engineering to operations research and economics, and the development of solution methods has been of interest in mathematics for centuries.
Stochastic gradient descentStochastic gradient descent (often abbreviated SGD) is an iterative method for optimizing an objective function with suitable smoothness properties (e.g. differentiable or subdifferentiable). It can be regarded as a stochastic approximation of gradient descent optimization, since it replaces the actual gradient (calculated from the entire data set) by an estimate thereof (calculated from a randomly selected subset of the data).
Lagrange multiplierIn mathematical optimization, the method of Lagrange multipliers is a strategy for finding the local maxima and minima of a function subject to equation constraints (i.e., subject to the condition that one or more equations have to be satisfied exactly by the chosen values of the variables). It is named after the mathematician Joseph-Louis Lagrange. The basic idea is to convert a constrained problem into a form such that the derivative test of an unconstrained problem can still be applied.
Newton's method in optimizationIn calculus, Newton's method (also called Newton–Raphson) is an iterative method for finding the roots of a differentiable function F, which are solutions to the equation F (x) = 0. As such, Newton's method can be applied to the derivative f ′ of a twice-differentiable function f to find the roots of the derivative (solutions to f ′(x) = 0), also known as the critical points of f. These solutions may be minima, maxima, or saddle points; see section "Several variables" in Critical point (mathematics) and also section "Geometric interpretation" in this article.
Learning rateIn 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. Since it influences to what extent newly acquired information overrides old information, it metaphorically represents the speed at which a machine learning model "learns". In the adaptive control literature, the learning rate is commonly referred to as gain. In setting a learning rate, there is a trade-off between the rate of convergence and overshooting.
Non-linear least squaresNon-linear least squares is the form of least squares analysis used to fit a set of m observations with a model that is non-linear in n unknown parameters (m ≥ n). It is used in some forms of nonlinear regression. The basis of the method is to approximate the model by a linear one and to refine the parameters by successive iterations. There are many similarities to linear least squares, but also some significant differences.
Regularization (mathematics)In mathematics, statistics, finance, computer science, particularly in machine learning and inverse problems, regularization is a process that changes the result answer to be "simpler". It is often used to obtain results for ill-posed problems or to prevent overfitting. Although regularization procedures can be divided in many ways, the following delineation is particularly helpful: Explicit regularization is regularization whenever one explicitly adds a term to the optimization problem.
Quasiconvex functionIn mathematics, a quasiconvex function is a real-valued function defined on an interval or on a convex subset of a real vector space such that the of any set of the form is a convex set. For a function of a single variable, along any stretch of the curve the highest point is one of the endpoints. The negative of a quasiconvex function is said to be quasiconcave. All convex functions are also quasiconvex, but not all quasiconvex functions are convex, so quasiconvexity is a generalization of convexity.
