Mathematics and optimization

447 terms

# A B C D E F G H I J K L M N O P Q R S T U V W X Y Z

  • 0/1 loss - The 0/1 loss assigns zero to a correct classification and one to an incorrect classification.
  • 3D projection - 3D projection is the mathematical mapping of three-dimensional points or objects onto a two-dimensional surface, such as a screen or image plane.
  • Absolute error loss - Absolute error loss measures a numerical prediction's error as the absolute difference between its predicted and reference values: L(y,y-hat)=|y-y-hat|.
  • Active-set method - An active-set method is an optimization approach that works with a changing subset of constraints believed to be tight at the solution.
  • Adjoint state method - The adjoint state method computes how a chosen objective changes when the parameters of a mathematical model change.
  • Σ-algebra
  • Algebraic connectivity - Algebraic connectivity is the second-smallest eigenvalue of a graph's Laplacian matrix.
  • Algorithm IMED - Algorithm IMED, short for Indexed Minimum Empirical Divergence, is a method for choosing actions in a stochastic multi-armed bandit problem.
  • Alternating direction method of multipliers - The alternating direction method of multipliers, or ADMM, is an iterative optimization method that splits a structured problem into subproblems and...
  • Ant Colony Optimization - Ant Colony Optimization, usually abbreviated ACO, is a family of optimization algorithms inspired by how some ant species use pheromone trails.
  • Application programming interface endpoint - An application programming interface endpoint is a specific access point through which software uses an API's resource or operation.
  • Assignment problems - Assignment problems allocate items from one set to items in another while optimizing an objective and satisfying matching constraints.
  • Auction algorithm - The auction algorithm is an optimization method that solves assignment problems through a sequence of bids and price updates.
  • Automated decision-making - Automated decision-making uses a computer system to determine an action or outcome according to rules, model outputs, or both.
  • Automaton - An automaton is a mathematical model of a computing system whose behavior is described through states and transition rules, sometimes with additional memory.
  • Backdoor - In machine learning, a backdoor is an intentionally introduced model behavior that is activated by a particular trigger or input condition.
  • Backtracking line search - Backtracking line search is a procedure for choosing how far an optimization algorithm should move along a proposed direction.
  • Backus - Gilbert method - The Backus - Gilbert method is an approach to inverse problems that estimates local averages of an unknown quantity from indirect measurements.
  • Bacterial colony optimization - Bacterial colony optimization is a population-based optimization method inspired by selected behaviors of bacteria.
  • Barzilai - Borwein method - The Barzilai - Borwein method is a gradient-based optimization approach that chooses its step size from the changes between two successive points and their...
  • Base learner - A base learner is a learning method used as a component of an ensemble.
  • Basis - A basis is a set of linearly independent vectors whose linear combinations produce every vector in a specified vector space.
  • Batch gradient descent - Batch gradient descent updates a model's parameters using the gradient of the loss calculated across the entire training dataset at the current parameter...
  • Baum - Welch algorithm - The Baum - Welch algorithm estimates the parameters of a hidden Markov model from observed sequences whose underlying states are unknown.
  • Bellman pseudospectral method - The Bellman pseudospectral method is an optimal-control computation approach that combines pseudospectral trajectory optimization with Bellman's principle...
  • Benson's algorithm - Benson's algorithm is an optimization approach that constructs the trade-off geometry of a multi-objective problem by successively refining a polyhedral...
  • Berlekamp - Welch algorithm - The Berlekamp - Welch algorithm recovers a low-degree polynomial from evaluations that include a limited number of incorrect values.
  • Berndt - Hall - Hall - Hausman algorithm - The Berndt - Hall - Hall - Hausman algorithm, usually called BHHH, is a numerical method for maximum-likelihood estimation.
  • Bidiagonal matrix - A bidiagonal matrix is a matrix whose only potentially nonzero entries lie on the main diagonal and one immediately neighboring diagonal.
  • Big M method - The Big M method is a linear-programming technique that adds artificial variables to obtain a convenient starting basis and assigns them a very large...
  • Bilevel optimization - Bilevel optimization is optimization in which one decision problem contains another decision problem as a constraint.
  • Bounded minimization - Bounded minimization seeks a minimum of an objective while restricting its input to specified lower and upper limits.
  • Bregman divergence - A Bregman divergence measures the gap between a convex function's value at one point and its first-order linear approximation around another point.
  • Bregman method - The Bregman method is a family of iterative projection techniques for convex feasibility and related convex optimization problems.
  • Broyden - Fletcher - Goldfarb - Shanno algorithm - The Broyden - Fletcher - Goldfarb - Shanno algorithm, usually called BFGS, is a quasi-Newton method for minimizing smooth functions.
  • Buffered probability of exceedance - Buffered probability of exceedance, abbreviated bPOE, measures the size of an upper tail whose average outcome reaches a chosen threshold.
  • Byzantine device - A Byzantine device is a participant in a distributed system that can deviate arbitrarily from the prescribed protocol.
  • Cauchy-Schwarz inequality - The Cauchy-Schwarz inequality states that the absolute value of the inner product of two vectors cannot exceed the product of their lengths.
  • Cauchy sequence - A Cauchy sequence is a sequence whose terms eventually become arbitrarily close to one another.
  • Central limit theorem - The central limit theorem explains why suitably standardized sums or averages often have distributions close to a normal distribution.
  • Chain rule of calculus - The chain rule of calculus gives the derivative of a composite function: a function whose input is the output of another function.
  • Chambolle - Pock algorithm - The Chambolle - Pock algorithm is a first-order primal-dual method for structured convex optimization.
  • Characteristic function - In probability theory, the characteristic function of a real-valued random variable X is the function phi_X(t)=E[exp(i×t×X)], where t is real and i is the...
  • Chebyshev pseudospectral method - The Chebyshev pseudospectral method approximates a continuous function by a polynomial represented through values at Chebyshev nodes, then enforces...
  • Chernoff bound - A Chernoff bound is an upper bound on a tail probability obtained by applying Markov's inequality to an exponential transformation of a random variable.
  • Chernoff's distribution - Chernoff's distribution is the probability distribution of the location at which a two-sided Brownian motion minus a quadratic curve achieves its maximum.
  • Cluster centroid - A cluster centroid is a representative center used to summarize a cluster of data points.
  • Clustered federated learning - Clustered federated learning is an approach to collaborative machine learning that groups clients with compatible learning needs and trains models for those...

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