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Mathematical method that minimizes maximum error
A minimax approximation algorithm (or L∞ approximation or uniform approximation) is a method to find an approximation of a mathematical function that
Minimax approximation algorithm
Minimax_approximation_algorithm
Algorithm to approximate functions
polynomial of best approximation or the minimax approximation algorithm. A review of technicalities in implementing the Remez algorithm is given by W. Fraser
Remez_algorithm
Topics referred to by the same term
refer to: Minimax estimator, an estimator whose maximal risk is minimal between all possible estimators Minimax approximation algorithm, algorithms to approximate
Minimax_(disambiguation)
Topics referred to by the same term
analysis Minimal element of a partial order, in mathematics Minimax approximation algorithm Minimisation operator ("μ operator"), the add-on to primitive
Minimisation
Search algorithm
Alpha–beta pruning is a tree search algorithm that seeks to decrease the number of nodes that are evaluated by the minimax algorithm in its search tree. It is an
Alpha–beta_pruning
method: 2-point, 1-sided Hybrid Algorithms Alpha–beta pruning: search to reduce number of nodes in minimax algorithm A hybrid BFGS-Like method (see more
List_of_algorithms
Theorem
} is either -1 or +1. Several minimax approximation algorithms are available, the most common being the Remez algorithm. Golomb, Michael (1962). Lectures
Equioscillation_theorem
Field of machine learning
characterization of optimal solutions, and algorithms for their exact computation, and less with learning or approximation (particularly in the absence of a mathematical
Reinforcement_learning
function Least squares (function approximation) — minimizes the error in the L2-norm Minimax approximation algorithm — minimizes the maximum error over
List of numerical analysis topics
List_of_numerical_analysis_topics
Model-free reinforcement learning algorithm
environment is passive. Littman proposes the minimax Q learning algorithm. The standard Q-learning algorithm (using a Q {\displaystyle Q} table) applies
Q-learning
Measure of similarity between curves
Godau describe a simpler algorithm to compute the weak Fréchet distance between polygonal curves, based on computing minimax paths in an associated grid
Fréchet_distance
Overview of and topical guide to algorithms
algorithm Ant colony optimization algorithms Particle swarm optimization Evolutionary algorithm A* search algorithm Minimax Alpha–beta pruning Graphplan Monte
Outline_of_algorithms
Path-finding using high-weight graph edges
transportation planning. Any algorithm for the widest path problem can be transformed into an algorithm for the minimax path problem, or vice versa, by
Widest_path_problem
Lists of values of mathematical functions
trigonometric function is generated ahead of time using some approximation of a minimax approximation algorithm. For very high precision calculations, when series-expansion
Trigonometric_table
Problem in computational complexity theory
state-of-the-art algorithm is due to Avidor, Berkovitch and Zwick, and its approximation ratio is 0.7968. They also give another algorithm whose approximation ratio
Maximum satisfiability problem
Maximum_satisfiability_problem
Criterion of fair item allocation
(2018-11-01). "Approximation and complexity of the optimization and existence problems for maximin share, proportional share, and minimax share allocation
Maximin_share
ramifications. Common algorithms for solving combinatorial search problems include: A* search algorithm Alpha–beta pruning Branch-and-bound Minimax Lookahead is
Combinatorial_search
Technique for finding an extremum of a function
(1953) as a minimax search for the maximum (minimum) of a unimodal function in an interval. The Bisection method is a similar algorithm for finding a
Golden-section_search
Optimization method
(1999-06-01). "On Equitable Resource Allocation Problems: A Lexicographic Minimax Approach". Operations Research. 47 (3): 361–378. doi:10.1287/opre.47.3
Lexicographic max-min optimization
Lexicographic_max-min_optimization
Algorithm for computing trigonometric, hyperbolic, logarithmic and exponential functions
exhibit well behaved relative error. Other means of polynomial approximation, such as minimax optimization, may be used to control both kinds of error. Many
CORDIC
American mathematician (1927 to 1992)
they made the Pierce-Birkhoff conjecture, which concerned a minimax approximation algorithm for polynomials. In 1955, he commenced his teaching career
Richard_S._Pierce
Optimization problem
better than 1.463. The currently best known approximation algorithm achieves approximation ratio of 1.488. A minimax facility location problem is an OFL in
Optimal_facility_location
Machine learning optimization algorithm
objective by minimizing a "sharpness-aware" loss. This is formulated as a minimax problem where the inner objective seeks to find the highest loss value
Sharpness_aware_minimization
Pair of polynomial sequences
provides an approximation that is close to the best polynomial approximation to a continuous function under the maximum norm, also called the "minimax" criterion
Chebyshev_polynomials
Least-weight tree connecting graph vertices
(2005), "Approximation Algorithms for the Capacitated Minimum Spanning Tree Problem and Its Variants in Network Design", ACM Trans. Algorithms, 1 (2):
Minimum_spanning_tree
Mathematical concept
are listed below: Approximation-Guided Evolution (first algorithm to directly implement and optimize the formal concept of approximation from theoretical
Multi-objective_optimization
American computer scientist
1986-1987. He has been active in research on Design and Analysis of Approximation Algorithm for 30 years. And over these years he has published 177 Journal
Ding-Zhu_Du
Sigmoid shape special function
solve the numerical coefficients {(an,bn)}N n = 1 that yield a minimax approximation or bound for the closely related Q-function: Q(x) ≈ Q̃(x), Q(x)
Error_function
Optimization algorithm in computer science
"Determining the Performance Ratio of Algorithm Multifit for Scheduling", in Du, Ding-Zhu; Pardalos, Panos M. (eds.), Minimax and Applications, Nonconvex Optimization
Multifit_algorithm
Economical computational problem
They present an algorithm that computes a constant-factor approximation PNE. In particular: With linear delay functions, the approximation ratio is 2+ε,
Nash_equilibrium_computation
Discrete probability distribution
{\hat {\lambda }}_{i}=X_{i}} is inadmissible. In this case, a family of minimax estimators is given for any 0 < c ≤ 2 ( p − 1 ) {\displaystyle 0<c\leq
Poisson_distribution
Computer programming concept
difference learning can be used to learn state evaluation constants for a minimax AI playing a simple board game. Reinforcement Learning Problem, document
Temporal_difference_learning
assignment to the variables in the clauses. We say that an algorithm A provides an α-approximation to MAXEkSAT if, for some fixed positive α less than or
MAXEkSAT
Extension of Laplace's method for approximating integrals
about hypergeometric functions. The contour of steepest descent has a minimax property, see Fedoryuk (2001). Siegel (1932) described some other unpublished
Method_of_steepest_descent
Notion in combinatorial game theory
an estimate of the number of positions one would have to evaluate in a minimax search to determine the value of the initial position. It is hard even
Game_complexity
Edges that hit all cycles in a graph
that have a polynomial time approximation algorithm that achieves a constant approximation ratio. Although such approximations are not known for the feedback
Feedback_arc_set
Overview of and topical guide to statistics
Jackknife resampling Integrated nested Laplace approximations Nested sampling algorithm Metropolis–Hastings algorithm Importance sampling Mathematical optimization
Outline_of_statistics
Type of polynomial used in Numerical Analysis
first used by Bernstein in a constructive proof of the Weierstrass approximation theorem. With the advent of computer graphics, Bernstein polynomials
Bernstein_polynomial
Mathematical optimization concept
using the strong duality theorem, in particular, Konig's theorem. The Minimax theorem for zero-sum games can be proved using the strong-duality theorem
Dual_linear_program
Algorithm for trajectory optimization
dynamic programming (DDP) is an optimal control algorithm of the trajectory optimization class. The algorithm was introduced in 1966 by Mayne and subsequently
Differential dynamic programming
Differential_dynamic_programming
Algorithm for modelling sequential data
chess board positions. Using static evaluation alone (that is, with no Minimax search) transformer achieved an Elo of 2895, putting it at grandmaster
Transformer_(deep_learning)
On bipartite matching and vertex cover
for approximation algorithms. Bipartite maximum matchings can be approximated arbitrarily accurately in constant time by distributed algorithms; in contrast
Kőnig's theorem (graph theory)
Kőnig's_theorem_(graph_theory)
On point sets with no small-area triangles
in a planar convex body", in Du, Ding-Zhu; Pardalos, Panos M. (eds.), Minimax and Applications, Nonconvex Optim. Appl., vol. 4, Kluwer Acad. Publ., Dordrecht
Heilbronn_triangle_problem
Cache of previously seen positions, and associated evaluations in a game tree
enumerated. These are commonly used in bitboard implementations. Minimax algorithm Alpha-beta pruning Zobrist hashing Transposition Tables, Gamedev.net
Transposition_table
"disagreement points" or "status quo points". Minimax theorem - gives conditions on games, guaranteeing that the minimax value equals the maximin value. Daskalakis
Min-max_optimization
Greek-American electrical engineer (1942–2026)
extends the framework for applications to sequential zero-sum games and minimax problems, was published in 2022. "Reinforcement Learning and Optimal Control"
Dimitri_Bertsekas
of theorems and similar statements include: List of algebras List of algorithms List of axioms List of conjectures List of data structures List of derivatives
List_of_theorems
support Metropolis–Hastings algorithm Mexican paradox Microdata (statistics) Midhinge Mid-range MinHash Minimax Minimax estimator Minimisation (clinical
List_of_statistics_articles
Mathematical optimization theory
counterpart is computationally tractable. Stability radius Minimax Minimax estimator Minimax regret Robust statistics Robust decision making Robust fuzzy
Robust_optimization
Model selection principle
sequences but differing for short ones. The 'best' (in the sense that it has a minimax optimality property) are the normalized maximum likelihood (NML) or Shtarkov
Minimum_description_length
Solution concept of a non-cooperative game
is no Nash equilibrium. On the other hand, the minimax value of the row player is 1 (R-T) and the minimax value of the column player is 1 (B-R). Hence,
Nash_equilibrium
Situation where players have only a small incentive to change strategies
players are normalized to [0,1], so this is actually a multiplicative approximation: the gain cannot be more than ε {\displaystyle \varepsilon } times the
Epsilon-equilibrium
Concept in economics and game theory
be the analogue of the 'approximation ratio' in an approximation algorithm or the 'competitive ratio' in an online algorithm. This is in the context of
Price_of_anarchy
Selection of data points in statistics
dataset in a conservative manner called minimax sampling. The minimax sampling has its origin in Anderson minimax ratio whose value is proved to be 0.5:
Sampling_(statistics)
Hungarian and American mathematician and physicist (1903–1957)
founded the field of game theory as a mathematical discipline. He proved his minimax theorem in 1928. It establishes that in zero-sum games with perfect information
John_von_Neumann
Game in algorithmic game theory
In algorithmic game theory, a succinct game or a succinctly representable game is a game which may be represented in a size much smaller than its normal
Succinct_game
Mathematical relation assigning a probability event to a cost
loss. Leonard J. Savage argued that using non-Bayesian methods such as minimax, the loss function should be based on the idea of regret, i.e., the loss
Loss_function
Fair division problem for discrete items
others. They show that the best possible approximation for MMS is 2/3, even for two agents; and present algorithms attaining this bound for 2 or 3 agents
Fair_item_allocation
Graph with tight clique-coloring relation
greater complexity for non-perfect graphs. In addition, several important minimax theorems in combinatorics, including Dilworth's theorem and Mirsky's theorem
Perfect_graph
Method of statistical inference
doi:10.1214/aoms/1177697822. Hwang, J. T. & Casella, George (1982). "Minimax Confidence Sets for the Mean of a Multivariate Normal Distribution" (PDF)
Bayesian_inference
Construct for Hermitian matrices
in eigenvalue algorithms (such as Rayleigh quotient iteration) to obtain an eigenvalue approximation from an eigenvector approximation. The range of the
Rayleigh_quotient
Multiple-winner electoral system
core.[jargon] However, it guarantees 2-approximation of the core,[jargon] which is the optimal approximation ratio that can be achieved by a rule satisfying
Proportional_approval_voting
Mathematical statistics distance measure
divergence of P from Q is the expected excess surprisal from using the approximation Q instead of P when the actual is P. While it is a measure of how different
Kullback–Leibler_divergence
Methods in artificial intelligence research
learning, and the DPLL algorithm. For adversarial search when playing games, alpha-beta pruning, branch and bound, and minimax were early contributions
Symbolic artificial intelligence
Symbolic_artificial_intelligence
von Neumann begins devising the principles of game theory and proves the minimax theorem. 1929 – Emmy Noether introduces the first general representation
Timeline_of_mathematics
Russian computer scientist (1918–2009)
computer scientist, best known for fully describing the alpha-beta pruning algorithm. From 1991 until his death he lived in Israel. Brudno developed the "mathematics/machine
Alexander_Brudno
Function in a computer game-playing program that evaluates a game position
such evaluations is usually part of a search algorithm, such as Monte Carlo tree search or a minimax algorithm like alpha–beta search. The value is presumed
Evaluation_function
Mathematical framework to model epistemic uncertainty
specified, unlike traditional Bayesian methods, which often use a symmetry (minimax error) argument to assign prior probabilities to random variables (e.g
Dempster–Shafer_theory
Study of fair cake-cutting with true valuations
Truthful cake-cutting is the study of algorithms for fair cake-cutting that are also truthful mechanisms, i.e., they incentivize the participants to reveal
Truthful_cake-cutting
Multivalued function in mathematics
and fast computation of Lambert W function by piecewise minimax rational function approximation with variable transformation. doi:10.13140/RG.2.2.30264
Lambert_W_function
Statistical method for handling multiple comparisons
1214/009053606000000074. S2CID 7581060. Donoho D, Jin J (2006). "Asymptotic minimaxity of false discovery rate thresholding for sparse exponential data". Annals
False_discovery_rate
Class of nonparametric methods
of kernel-embedding-based learning algorithms can be drastically reduced without suffering much loss in approximation accuracy. If k {\displaystyle k} is
Kernel embedding of distributions
Kernel_embedding_of_distributions
Criterion for evaluating fairness of electoral systems
computable rule that satisfies EJR. Another polytime algorithm that guarantees EJR is EJR-Exact. A simple algorithm that finds an EJR allocation is called "Greedy
Justified_representation
Branch of applied probability theory
admissible decision rules, antecedent distributions, Bayesian procedures, and minimax procedures. The phrase "decision theory" itself was used in 1950 by E.
Decision_theory
Use of approximation algorithms in voting
alternative whose social welfare is approximately optimal. The quality of approximation for a voting rule is measured by its distortion or regret, which measures
Implicit_utilitarian_voting
Analog of Pareto efficiency for situations with incomplete information
Mathematical Plays Search algorithms Alpha–beta pruning Expectiminimax Minimax Monte Carlo tree search Negamax Paranoid algorithm Principal variation search
Bayesian_efficiency
Indian inventions
paper". Parthasarathy's theorem. is a generalization of Von Neumann's minimax theorem created by Thiruvenkatachari Parthasarathy. Partial Balanced Incomplete
List of Indian inventions and discoveries
List_of_Indian_inventions_and_discoveries
Incomplete-information coordination game
illustrates the apparently paradoxical situation where arbitrarily close approximations to common knowledge lead to very different strategical implications
Electronic_mail_game
Model of humans as rational, self-interested agents
Actual usage is inconsistent. Homo economicus is a term used for an approximation or model of Homo sapiens that acts to obtain the highest possible well-being
Homo_economicus
initial investigations into strategic two-person game theory by proving the minimax theorem for two-person, zero-sum games. Oskar Morgenstern, John von Neumann
List of publications in mathematics
List_of_publications_in_mathematics
Statistical analysis where the sample size is not fixed in advance
Kenneth J. Arrow, David Blackwell and M.A. Girshick (1949). "Bayes and minimax solutions of sequential decision problems". Econometrica. 17 (3/4): 213–244
Sequential_analysis
Branch of statistics mathematics
Statistics). 45 (2): 151–163. Hilgert, N; Mas, A; Verzelen, N. (2013). "Minimax adaptive tests for the functional linear model". Annals of Statistics.
Functional_data_analysis
Mathematical modelling of phenotypic evolution
trait values may successfully invade. This follows from the linear approximation S r ( m ) ≈ S r ( r ) + S r ′ ( r ) ( m − r ) {\displaystyle S_{r}(m)\approx
Evolutionary invasion analysis
Evolutionary_invasion_analysis
Proof all ranked voting rules have spoilers
assumptions of ranked procedures more explicit by modeling them as approximations of the utilitarian rule (or score voting). In psychometrics, there is
Arrow's_impossibility_theorem
Statistical distribution for dependence between random variables
"The normal law under linear restrictions: Simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148
Copula_(statistics)
Mathematical construct in game theory
treatment of beliefs at all levels and provides a foundation for practical approximations using finite type spaces. The concept has become central in Bayesian
Hierarchy_of_beliefs
Study of rational collective decision-making
Abstract. Shoham, Yoav; Leyton-Brown, Kevin (2009). Multiagent Systems: Algorithmic, Game-Theoretic, and Logical Foundations. New York: Cambridge University
Social_choice_theory
Social choice problem
polynomial-time algorithms finding an additive approximation to the core, with a tiny multiplicative loss. With matroid constraints, the additive approximation is
Multi-issue_voting
Single-winner electoral system
polynomial-time approximation scheme for computing a Kemeny ranking, and there also exists a parameterized subexponential-time algorithm with running time
Kemeny_method
Economic Model
fixed-point theorem. This modification is similar to the generalization of the minimax theorem to the existence of Nash equilibria. The two fundamental theorems
Arrow–Debreu_model
Generalization of the one-dimensional normal distribution to higher dimensions
"The normal law under linear restrictions: simulation and estimation via minimax tilting". Journal of the Royal Statistical Society, Series B. 79: 125–148
Multivariate normal distribution
Multivariate_normal_distribution
Mixed strategy equilibria explained as the limit of pure strategy equilibria
mixed strategy of the original game emerges from the ever-improving approximations of a game which is not observed by the theorist who designed the original
Purification_theorem
Approach to optimizing robustness to failure
[min-max] worst-case analysis". Note that Ben-Haim compares info-gap to minimax, while Sniedovich considers it a case of maximin. Sniedovich has challenged
Info-gap_decision_theory
Soviet mathematician and economist
results on the convergence of spaces with a binary relation and on finite approximations. She was also among the first to publish a theorem on the existence
Olga_Bondareva
Multi-winner electoral system
party or voting bloc can take all seats in a district. The key to STV's approximation of proportionality is that each voter effectively only casts a single
Single_transferable_vote
Study of strategic interactions on networks
cooperation, and host–parasite interactions computer science - distributed algorithms, routing, and cybersecurity sociology - opinion dynamics, cultural evolution
Game_theory_on_networks
Annual session of lectures
arithmetic of curves. 1984 Paul Rabinowitz (University of Wisconsin, Madison): Minimax methods in critical point theory and applications to differential equations
Colloquium_Lectures_(AMS)
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
Girl/Female
Tamil
Manimay | மாஂநீமய
Full of jewel
Manimay | மாஂநீமய
Girl/Female
Danish, German, Nigerian
Calmness
Girl/Female
Hindu
Full of jewel
Girl/Female
Hindu, Indian
Knowledge
Girl/Female
Indian, Tamil
Sweet
Girl/Female
English, Hindu, Indian, Marathi
Small Daughter
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
Boy/Male
Sikh
Lustrous splendor of God, Has to do with happiness
Boy/Male
Hindu
Happy
Boy/Male
French American English Swedish
Prosperous protector. A FrenchOld English name Eadmund, meaning rich or happy, and protection.
Boy/Male
Hindu, Indian
Money; Russian Currency
Girl/Female
Hindu
A celestial maiden, An Angel, Most beautiful of apsaras
Girl/Female
Hindu, Indian
Sacrifice
Female
English
English name derived from the vocabulary word, summer, from Old English sumor, SUMMER means "summer," the hot season of the year.
Boy/Male
Arabic, Muslim
Servant of the All Hearing
Girl/Female
American, Australian, Christian
Crystal; Anointed; Christian; Ice
Surname or Lastname
English
English : habitational name from a place so called; there is one in Cambridgeshire and another in Northamptonshire, both named with Old English beorn ‘warrior’ (genitive plural beorna) or the Old English personal name Beorna + well(a) ‘stream’.A John Barnwell (c.1671–1724) emigrated to SC from Ireland at the end of the 17th century.
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
MINIMAX APPROXIMATION-ALGORITHM
n.
One who, or that which, approximates.
n.
The little finger; the fifth digit, or that corresponding to it, in either the manus or pes.
n.
A being of the smallest size.
a.
Resembling, or approximating to, a hemisphere in form.
n.
A value that is nearly but not exactly correct.
a.
Approaching; approximate.
n.
An approach to a correct estimate, calculation, or conception, or to a given quantity, quality, etc.
n.
One skilled in coining, or in coins; a coiner.
n.
The transient approximation of the edges of a natural opening; imperforation.
n.
The act of approximating; a drawing, advancing or being near; approach; also, the result of approximating.
p. pr. & vb. n.
of Approximate
n.
A small American bird (Empidonax minimus); the least flycatcher.
n.
A minim.
pl.
of Mintman
n.
A continual approach or coming nearer to a result; as, to solve an equation by approximation.
adv.
With approximation; so as to approximate; nearly.
n.
Anything very minute; as, the minims of existence; -- applied to animalcula; and the like.
n.
Minimum.
pl.
of Minimus
pl.
of Minimum