In mathematics, the probabilistic method is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence of a prescribed kind of mathematical object. It works by showing that if one randomly chooses objects from a specified class, the probability that the result is of the prescribed kind is strictly greater than zero. Although the proof uses probability, the final conclusion is determined for certain, without any possible error.
This method has now been applied to other areas of mathematics such as number theory, linear algebra, and real analysis, as well as in computer science (e.g. randomized rounding), and information theory.
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In mathematics, the probabilisticmethod is a nonconstructive method, primarily used in combinatorics and pioneered by Paul Erdős, for proving the existence...
action (it is not "deterministic"). It must choose an action by making a probabilistic guess and then reassess the situation to see if the action worked. In...
technique has become known as the probabilisticmethod. Erdős gave his first application of the probabilisticmethod in 1947, when he used a simple randomized...
Probabilistic argument may refer to: Probabilistic argument, any argument involving probability theory Probabilisticmethod, a method of non-constructive...
Probabilistic design is a discipline within engineering design. It deals primarily with the consideration and minimization of the effects of random variability...
In machine learning, a probabilistic classifier is a classifier that is able to predict, given an observation of an input, a probability distribution...
computer science, the method of conditional probabilities is a systematic method for converting non-constructive probabilistic existence proofs into efficient...
hand. A probabilistic proof is one in which an example is shown to exist, with certainty, by using methods of probability theory. Probabilistic proof,...
Introduced by Radford Neal in 1992, this network applies ideas from probabilistic graphical models to neural networks. A key difference is that nodes...
complexity theory, and additive combinatorics, and frequently employs the probabilisticmethod. Extremal graph theory, in its strictest sense, is a branch of graph...
American mathematician. He is a combinatorialist who has worked on probabilisticmethods in combinatorics and on Ramsey theory. He received his doctorate...
properties is greater than 0. This approach (often referred to as the probabilisticmethod) proved highly effective in applications to extremal combinatorics...
of probability topics Probabilisticmethod Probable prime Tenenbaum, Gérald (1995). Introduction to Analytic and Probabilistic Number Theory. Cambridge...
number of Kneser graphs Friendship theorem Some proofs using the probabilisticmethod Klarreich, Erica (2018-03-19). "In Search of God's Perfect Proofs"...
The probabilistic roadmap planner is a motion planning algorithm in robotics, which solves the problem of determining a path between a starting configuration...
G} in the graph, giving us a G {\displaystyle G} free graph. The probabilisticmethod can be used to prove ex ( n , G ) ≥ c n 2 − v ( G ) − 2 e ( G )...
Publications. p. 115. ISBN 9780486665214. Matoušek, J.; Vondrak, J. "The ProbabilisticMethod" (PDF). lecture notes. Archived (PDF) from the original on 2022-10-09...
Probabilistic logic (also probability logic and probabilistic reasoning) involves the use of probability and logic to deal with uncertain situations....
based on the process of natural selection, learning theory, and probabilisticmethods which helps dealing with uncertainty imprecision. Except those main...
nature,... Alon, Noga; Spencer, Joel H. (20 September 2011). The ProbabilisticMethod. John Wiley & Sons. p. 6.1. ISBN 978-1-118-21044-4. The Four Functions...
data from these individuals. The error model used in creating a probabilisticmethod for variant calling is the basis for calculating the P ( D ∣ G )...
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