Federated stochastic gradient descent - Federated stochastic gradient descent, or FedSGD, is a federated training method that uses stochastic or approximate local gradients rather than requiring...
Finite-dimensional distribution - A finite-dimensional distribution of a stochastic process is the joint probability distribution of its values at a finite selection of indices.
Fireworks algorithm - The fireworks algorithm, or FWA, is a population-based optimization method that generates candidate solutions around several current solutions using an...
Firmly non-expansive operator - A firmly non-expansive operator is a mapping with a stronger geometric stability property than simply not increasing distances.
Fixed point - A fixed point of a mapping is an input that the mapping leaves unchanged. If the mapping is T, a value x* is a fixed point when T(x*) = x*.
Fixed-point characterization - A fixed-point characterization expresses the solutions of a problem as exactly the points left unchanged by a suitable mapping.
Fixed-point computation - Fixed-point computation is the task of finding a value x such that applying a specified mapping G leaves it unchanged: G(x) = x.
Fixed-point equation - A fixed-point equation is an equation of the form x = T(x), where T maps an allowed space into itself. A solution is a value left unchanged by the mapping.
Fixed-point iteration - Fixed-point iteration is a numerical procedure that repeatedly applies a mapping to its current estimate: x_(k+1) = T(x_k).
Fixed-point solving - Fixed-point solving is the task of finding a value x such that applying a given function returns the same value: T(x) = x.
Flat pseudospectral method - The flat pseudospectral method combines differential flatness with pseudospectral numerical optimization to plan trajectories for suitable controlled systems.
Fly algorithm - The Fly algorithm is an evolutionary optimization approach in which many simple candidate components cooperate to represent a solution.
Formation matrix - In likelihood-based statistics, a formation matrix is an inverse information matrix: the expected formation matrix is the inverse of Fisher information...
Forward algorithm - The forward algorithm is a dynamic programming method for computing the likelihood of an observation sequence under a hidden Markov model.
Frank - Wolfe algorithm - The Frank - Wolfe algorithm, also called the conditional gradient method, solves constrained optimization problems by repeatedly minimizing a linear...
Full-rank - A matrix is full-rank when its rank equals the largest value possible for its dimensions. For an m-by-n matrix, that maximum is min(m, n).
Gauss - Newton algorithm - The Gauss - Newton algorithm is an iterative method for nonlinear least squares.
Generalization gap - The generalization gap is the difference between a model's performance on its training data and its performance beyond those data.
Generalized Gauss - Newton method - In the constrained least-squares sense used here, the generalized Gauss - Newton method extends Gauss - Newton fitting to problems with equality or...
Generalized minimum-distance decoding - Generalized minimum-distance decoding, or GMD decoding, uses reliability information alongside hard symbol decisions to generate candidate codewords through...
Generalized total variation - Generalized total variation, or GTV, measures how much models differ across the connections of a weighted graph.
Generalized total variation minimization - Generalized total variation minimization, or GTVMin, is a learning formulation that balances local model fit with a penalty for differences between models...
Global optimization - Global optimization seeks the best objective value over the entire allowed set of choices.
Golden-section search - Golden-section search is a derivative-free method for locating a minimum of a unimodal function on an interval.
Gradient - The gradient of a differentiable scalar-valued function is the vector of its partial derivatives.
Gradient accumulation - Gradient accumulation is a training technique that combines gradients from several smaller batches before performing one optimizer update.
Gradient-based method - A gradient-based method is an optimization procedure that uses derivatives of an objective to guide its search.
Gradient boosted (decision) trees - Gradient boosted decision trees are an ensemble model built by adding decision trees in stages, with each new tree trained to improve the current ensemble...
Gradient descent - Gradient descent is an iterative method for minimizing a differentiable function.
Gradient step - A gradient step is one update of a variable using the gradient of an objective.
Graduated optimization - Graduated optimization tackles a difficult objective through a sequence of simpler approximations.
Graph Coarsening Algorithm - A graph coarsening algorithm creates a smaller graph by combining selected vertices into groups and aggregating their connections.
Graph entropy - In the information-theoretic sense associated with Körner, graph entropy measures a graph together with a probability distribution over its vertices.
Great deluge algorithm - The Great deluge algorithm is a local-search optimization heuristic that accepts candidate solutions according to a changing quality threshold.
Ground resolution theorem - The ground resolution theorem states that an unsatisfiable set of ground clauses has a resolution derivation of the empty clause.
Group - In mathematics, a group is a set together with a binary operation that is closed and associative, has an identity element, and gives every element an inverse.
Hermitian - A square matrix is Hermitian when it equals its conjugate transpose: A = Aᴴ.
Hessian - The Hessian of a scalar-valued function is the matrix of its second-order partial derivatives.
High-dimensional regime - The high-dimensional regime is a statistical setting in which model dimensionality is large relative to the amount of training information.
Hinge loss - Hinge loss is a margin-based loss used in classification. For a binary label y in {−1, +1} and a real-valued prediction score s, it is max(0, 1 − ys).
Horizontal federated learning - Horizontal federated learning is collaborative model training across participants that hold different examples described using a compatible feature space...
Horner's method - Horner's method evaluates a polynomial by rewriting it as nested multiplication and addition.
Hypertext Transfer Protocol - Hypertext Transfer Protocol, or HTTP, is the application-level request-and-response protocol family used to communicate with web resources and many online...
Identity matrix - An identity matrix is a square matrix with ones on its main diagonal and zeros everywhere else.
In-crowd algorithm - The In-crowd algorithm is an active-set method for solving an L1-regularized least-squares problem, commonly called basis pursuit denoising.
Incompleteness theorem - An incompleteness theorem establishes limits on what certain formal mathematical systems can prove.