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Framework for mathematical analysis of machine learning
computational learning theory, probably approximately correct (PAC) learning is a framework for mathematical analysis of machine learning. It was proposed
Probably approximately correct learning
Probably_approximately_correct_learning
Subset of artificial intelligence
theoretical viewpoint, probably approximately correct learning provides a mathematical and statistical framework for describing machine learning. Most traditional
Machine_learning
Theory of machine learning
different approaches include: Exact learning, proposed by Dana Angluin; Probably approximately correct learning (PAC learning), proposed by Leslie Valiant;
Computational_learning_theory
British American computer scientist
intractable. He created the Probably Approximately Correct or PAC model of learning that introduced the field of Computational Learning Theory and became a theoretical
Leslie_Valiant
Machine learning paradigm
subspace learning Naive Bayes classifier Maximum entropy classifier Conditional random field Nearest neighbor algorithm Probably approximately correct learning
Supervised_learning
Overview of and topical guide to machine learning
modeling Probably approximately correct learning (PAC) learning Ripple down rules, a knowledge acquisition methodology Symbolic machine learning algorithms
Outline_of_machine_learning
Ensemble learning method
algorithms that are provable boosting algorithms in the probably approximately correct learning formulation can accurately be called boosting algorithms
Boosting_(machine_learning)
Framework for analyzing machine learning algorithms
in polynomial time. An example of such a framework is probably approximately correct learning [citation needed]. The concept was introduced in E. Mark
Algorithmic_learning_theory
Paradigm in machine learning
generative models also began in the 1970s. A probably approximately correct learning bound for semi-supervised learning of a Gaussian mixture was demonstrated
Weak_supervision
Methods in artificial intelligence research
introduced Probably Approximately Correct Learning (PAC Learning), a framework for the mathematical analysis of machine learning. Symbolic machine learning encompassed
Symbolic artificial intelligence
Symbolic_artificial_intelligence
Gold. Subsequently known as Algorithmic learning theory. Probably approximately correct learning (PAC learning) proposed in 1984 by Leslie Valiant Learnability
Learnability
rule-based learning with cognitive approaches. For issues of knowledge (i.e., class) representability: Rough sets Probably approximately correct learning (PAC
Hypothesis_Theory
Overview of and topical guide to statistics
Kernel method Statistical learning theory Rademacher complexity Vapnik–Chervonenkis dimension Probably approximately correct learning Probability distribution
Outline_of_statistics
Description of limiting behavior in probabilistic algorithms
polynomial-time quantum algorithms which are correct WHP. Probably approximately correct learning: A process for machine-learning in which the learned function has
With_high_probability
Model-free reinforcement learning algorithm
implementation of the online Q-learning algorithm, with probably approximately correct (PAC) learning. Greedy GQ is a variant of Q-learning to use in combination
Q-learning
Notion in combinatorics
properties, have important applications in machine learning, in the area of probably approximately correct learning. In computational geometry, they have been
Sauer–Shelah_lemma
Computational learning model
of steps). A weaker formal model of learnability is the Probably approximately correct learning (PAC) model, introduced by Leslie Valiant in 1984. It is
Language identification in the limit
Language_identification_in_the_limit
. Machine learning Data mining Probably approximately correct learning Adversarial machine learning Valiant, L. G. (August 1985). Learning Disjunction
Error tolerance (PAC learning)
Error_tolerance_(PAC_learning)
In the theory of Probably Approximately Correct Machine Learning, the Natarajan dimension characterizes the complexity of learning a set of functions
Natarajan_dimension
Model of algorithmic learning
received training data. This is closely related to probably approximately correct (PAC) learning, where the learner is evaluated on its predictive power
Occam_learning
Interdisciplinary research area
assumptions). A natural model of passive learning is Valiant's probably approximately correct (PAC) learning. Here the learner receives random examples
Quantum_machine_learning
Code-generating large language model by OpenAI
written without having to write as much code", and that "it is not always correct, but it is just close enough". OpenAI stated that Codex could complete
OpenAI_Codex_(language_model)
AI whose outputs can be understood by humans
(XAI), generally overlapping with interpretable AI or explainable machine learning (XML), is a field of research that explores methods that provide humans
Explainable artificial intelligence
Explainable_artificial_intelligence
Process in which a first language is being acquired
and they begin to babble later on in infancy—at approximately 11 months as compared to approximately 6 months for hearing babies. Prelinguistic language
Language_acquisition
Branch of statistics
analysis. Social scientists (and, indeed, all scientists) must determine the correct model to use because different models are good at estimating different
Causal_inference
Notion in computational learning theory
between stability and consistency in ERM algorithms in the Probably Approximately Correct (PAC) setting. 2004 - Poggio et al. proved a general relationship
Stability_(learning_theory)
Technique combining machine learning and computer vision
probably approximately correct (PAC) model was applied by D. Roth (2002) to solve computer vision problem by developing a distribution-free learning theory
Geometric_feature_learning
Use of English by speakers with different native languages
languages, the correct use of prepositions in the English language is difficult to learn, and it can turn out to be quite a frustrating learning experience
English as a second or foreign language
English_as_a_second_or_foreign_language
Learning through egalitarian dialogue
Dialogic learning is learning that takes place through dialogue. It is typically the result of egalitarian dialogue; in other words, the consequence of
Dialogic_learning
Computational method in Bayesian statistics
Approximate Bayesian computation (ABC) constitutes a class of computational methods rooted in Bayesian statistics that can be used to estimate the posterior
Approximate Bayesian computation
Approximate_Bayesian_computation
Computational learning theory
computational learning theory. Concept class terminology frequently appears in model theory associated with probably approximately correct (PAC) learning. In this
Concept_class
Type of AI with wide-ranging abilities
reasoning Multi-task learning – Solving multiple machine learning tasks at the same time Neural scaling law – Statistical law in machine learning Outline of artificial
Artificial general intelligence
Artificial_general_intelligence
Faculty of mind to store and retrieve data
procedural memory is the slow and gradual learning of skills that often occurs without conscious attention to learning. Memory is not a perfect processor and
Memory
responded correctly to sequences of novel stimuli that were arranged in the same order as those previously learned. Similar sequence learning has been
Animal_cognition
Roman emperor in AD 69
from Feb. and added to August to honor him. If that is correct, Dio's math and calculus is correct. Still see other errors: Caligula ascended to the throne
Otho
understandable by a 7-year-old. The vocabulary was limited to approximately 8,000 words probably known by a 7-year-old. The stories were written by workers
Language_model_benchmark
American psychologist
research on conditioning and learning resulted in approximately 50 publications. Some of the topics within conditioning and learning that he pursued included
Winthrop_Kellogg
extant American and Chinese alligators does not consistently result in correct specific identification, and identifies invariant characters that provide
2026 in archosaur paleontology
2026_in_archosaur_paleontology
Witwicky is the human son of Spike and Carly Anderson-Witwicky. He is approximately 12 years of age in 2005, and was presumably born sometime between 1990
List of The Transformers characters
List_of_The_Transformers_characters
Topics referred to by the same term
Pointer Authentication Code, an ARM security feature Probably approximately correct, in machine learning Presentation–abstraction–control, in software architecture
PAC
Chinese characters used in Japanese writing
words or morphemes, leading to different pronunciations or "readings." The correct reading may be determined by contextual cues (such as whether the character
Kanji
Joseph, Bob (21 September 2016). "Indigenous or Aboriginal: Which is correct?". CBC News. Archived from the original on 22 September 2016. Retrieved
Indigenous peoples of the Americas
Indigenous_peoples_of_the_Americas
SpaceX satellite Internet constellation
spaceflight company SpaceX, providing broadband Internet service in approximately 160 countries and territories. It also aims to provide global mobile
Starlink
Process of learning words
successfully maps words onto the correct objects, concepts, and actions. While domain-specific accounts of word learning argue for innate constraints that
Vocabulary_development
American annual computer science prize
original on January 7, 2024. Retrieved March 4, 2024. "Fathers of the Deep Learning Revolution Receive ACM A.M. Turing Award". Association for Computing Machinery
Turing_Award
1977 film by William Friedkin
attended, knowing that his film would soon replace it. Friedkin's fears were correct; when Sorcerer debuted at the theater, it was so unsuccessful by comparison
Sorcerer_(film)
2025 legislation in the United States
experts say". The Washington Post. ISSN 0190-8286. Retrieved July 5, 2025. "Correcting the Social Security Administration About The Big Budget Bill | Tax Policy
One_Big_Beautiful_Bill_Act
legend that John Winchester knew about the gun, Samuel's version had the correct information that there were only five things that it couldn't kill rather
List of Supernatural and The Winchesters characters
List_of_Supernatural_and_The_Winchesters_characters
US government agency
falsely claimed this contract saved $8 billion, which was subsequently corrected down to $8 million. A lease for the "Allowance to Former Presidents Office"
Department of Government Efficiency
Department_of_Government_Efficiency
Method of logical reasoning
mathematical induction), where the conclusion is certain, given the premises are correct, inductive reasoning produces conclusions that are at best probable, given
Inductive_reasoning
Measures to determine proper bra fit
trying on and learning to recognize a properly fitting bra is the best way to determine a correct bra size, much like shoes. A correctly fitting bra should
Bra_size
Idiolect used by a second language learner
omitting it, before finally returning to the correct use. The period of incorrect use is sometimes seen as a learning regression. When the learners first acquired
Interlanguage
US state criminal case against president
Giuliani or the president" and said he believed it was "the clear and correct strategy". When asked if "the email speaks for itself" as he had asserted
Prosecution of Donald Trump in New York
Prosecution_of_Donald_Trump_in_New_York
a joint session of Congress was littered with false claims he's been corrected on but continued to repeat. Riley Hoffman (March 5, 2025). "Fact-checking
False or misleading statements by Donald Trump (second term)
False_or_misleading_statements_by_Donald_Trump_(second_term)
Northwest Semitic language
to a subject-verb-object ordering. Many Hebrew sentences have several correct orders of words. In Hebrew, there is no indefinite article. Hebrew sentences
Hebrew_language
Possible order of composition of Shakespeare's plays
with the palms of the vulgar"). It is unknown, however, which text is correct – Qa or Qb. E. A. J. Honigmann has suggested that the play was written
Chronology of Shakespeare's plays
Chronology_of_Shakespeare's_plays
and his "friends" will do it for her. Dirty Grandpa It takes place approximately a year later during the baptism of Dick and Lenore's baby. There is
List of films with post-credits scenes
List_of_films_with_post-credits_scenes
to give precise, logical answers, but give results that are only "probably" correct. This allowed them to solve problems that precise symbolic methods
History of artificial intelligence
History_of_artificial_intelligence
Ancient highway reorganized and rebuilt in the Achaemenid Empire
and showed that though his overall his distances in parasangs are approximately correct, his distances over the sections he describes bear no relation to
Royal_Road
that approximately 34% of photosynthesis by terrestrial plants occurs in tropical rainforests (so the Amazon rainforest would account for approximately half
List of common misconceptions about science, technology, and mathematics
List_of_common_misconceptions_about_science,_technology,_and_mathematics
Process of turning a place name/address to coordinates
attributed to the correct segment or to the correct side of the segment, nor resulting in an accurate position along that correct segment. With the geocoding
Address_geocoding
King of Wessex (871 – c. 886); King of the Anglo-Saxons (c. 886 – 899)
of his brothers, and he was probably the most open-minded. He was an early advocate for education. His desire for learning could have come from his early
Alfred_the_Great
Neurodevelopmental disorder chiefly affecting motor skills
with this area may include: Learning basic movement patterns. Developing a desired writing speed. Establishing the correct pencil grip. Handwriting that
Developmental coordination disorder
Developmental_coordination_disorder
1992 siege and shootout in Idaho, US
The standoff occurred approximately ten miles (16 km) from the nearest incorporated city of Bonners Ferry and approximately thirty miles (48 km) south
Ruby_Ridge_standoff
Outcome of the September 11 attacks
acceleration through a distance of approximately 8 stories (32 meters, or 105 feet), noting "the collapse time was approximately 40 percent longer than that
Collapse of the World Trade Center
Collapse_of_the_World_Trade_Center
Russian mathematician (1821–1894)
Chebyshov (which provides the closest pronunciation in English to the correct pronunciation in old Russian). Chebychev is an erroneous mixture between
Pafnuty_Chebyshev
Chinese mathematician (born 1968)
mathematician David Mumford and gained an introduction to "probably approximately correct" (PAC) learning under the instruction of Leslie Valiant. Zhu concluded
Song-Chun_Zhu
1966 studio album by the Beatles
with a view to how the notes would sound when the tape direction was corrected. Experimentation with backwards sounds was a key aspect of the Revolver
Revolver_(Beatles_album)
American rapper and singer-songwriter (1998–2018)
admitting that the version of events described by Onfroy and his team were correct, and that she "hope[d] that people see the video in the playful context
XXXTentacion
Attribute of machine learning models
probability at least 1 − δ {\displaystyle 1-\delta } . In probably approximately correct (PAC) learning, one is concerned with whether the sample complexity
Sample_complexity
Hybrid video game console
stick leaks gain credibility: Now that one Switch 2 leaker has been proved correct, their previous claims are being studied". Video Games Chronicle. Wikidata Q131868494
Nintendo_Switch_2
Commemorative coins of the Eurozone
structures, as well as one of the oldest religious structures. Built approximately in the 36th century BC, Ġgantija pre-dates Stonehenge and the Egyptian
2_euro_commemorative_coins
Battle between English and Normans in 1066
Godwinson, beginning the Norman Conquest of England. It took place approximately 7 mi (11 km) northwest of Hastings, close to the present-day town of
Battle_of_Hastings
Country in West Asia
figures for captives are conceivably more reliable. If 97,000 is roughly correct as a total for the war, it would mean that a huge percentage of the population
Israel
mistakenly refers to Terri as her mother, Melissa becomes hostile and sharply corrects Pam. In the sixth season premiere, Michael discovers that Stanley has been
List of The Office (American TV series) characters
List_of_The_Office_(American_TV_series)_characters
1913–1927 novel in seven volumes by Marcel Proust
had been corrected and annotated by Proust. The late changes Proust made include a small, crucial detail and the deletion of approximately 150 pages
In_Search_of_Lost_Time
"You kill people and break things for a living. You are not politically correct and don't necessarily belong always in polite society", "You might say
Domestic policy of the second Trump administration
Domestic_policy_of_the_second_Trump_administration
King of the English from 959 to 975
Æthelstan in the 930s". Four law codes have been attributed to Edgar, but the correct number is two. The Hundred Ordinance was formerly called I Edgar by historians
Edgar,_King_of_England
1493 document by Christopher Columbus
press by the State for propaganda purposes. Christopher Columbus was probably correct to send the letter from Lisbon, for shortly after, King John II of
Columbus's letter on the first voyage
Columbus's_letter_on_the_first_voyage
American serial killer (born 1945)
Without blinking an eye, Rader stopped the judge at several junctures to correct some minor detail. Unmoved by the enormity of his crimes or the responses
Dennis_Rader
American composer and pianist (1868–1917)
Connorized label show evidence of editing to correct the performance to strict rhythm and add embellishments, probably by the staff musicians at Connorized.
Scott_Joplin
Probability distribution
β·Posterior is only correct for the Haldane prior probability Beta(0,0). Specifically, for the Bayes (uniform) prior Beta(1,1) the correct interpretation would
Beta_distribution
Cast of neo-Western crime media franchise
Cousins to read to Eladio, in which he reveals Lalo's initial survival and correctly accuses Gus of having subsequently killed him. With no definitive proof
List of characters in the Breaking Bad franchise
List_of_characters_in_the_Breaking_Bad_franchise
Country in Southeast Europe
program is now underway to ensure that army units are equipped with the correct ammunition.[citation needed] Beginning in 2007, the Ministry of Defence
Bosnia_and_Herzegovina
American philosopher, psychologist, and educational reformer (1859–1952)
failures of this process, as well as how to appropriately reproduce or correct it in the future. As a result of the direct influence teachers have in
John_Dewey
distance learning. In North America, this concept is commonly denoted as a "Learning Management System" (LMS). Key terminology to describe virtual learning environments
History of virtual learning environments
History_of_virtual_learning_environments
Earliest anatomically modern humans in Europe and West Asia
compared to a bird bone flute. A section of ivory must be sawed off to the correct size, cut in half so it can be hollowed out, and then the two pieces have
Cro-Magnon
determining whether the canines of the studied specimens were correctly associated and correctly seated in tooth sockets during restoration of the skulls,
2026_in_paleomammalogy
Linear B tablet made c. 1180 BCE
1952 by the American archaeologist Carl Blegen, it has been described as "probably the most famous tablet of Linear B". The tablet catalogues tripods and
PY_Ta_641
Medical condition caused by receiving too little or too many nutrients
treat low body temperature Prevent or treat infection; Correct electrolyte imbalances Correct micronutrient deficiencies Start feeding cautiously Achieve
Malnutrition
Inability to comprehend or formulate language
is anomia, in which the affected individual has difficulty finding the correct word. With aphasia, one or more modes of communication in the brain have
Aphasia
for Nero in The Tower of Nero. After several failed attempt to find the correct remote control for Nero's bombs, he is accidentally shot in the groin by
List of characters in mythology novels by Rick Riordan
List_of_characters_in_mythology_novels_by_Rick_Riordan
Social issue
autistic young adults are more likely to be unemployed than people with learning disabilities, intellectual disabilities, or speech/language impairment
Employment_of_autistic_people
Ancient Mesopotamian goddess
According to Katz, the fact that Inanna's instructions to Ninshubur contain a correct prediction of her eventual fate, including the exact means of her rescue
Inanna
Sexual stimulation of one's own genitals
interferes in their ability to masturbate and then work with the patient to correct the problem if it is identified." The sex-positive movement argues for
Masturbation
2001 accounting scandal
restatements to its financial statements for years 1997 to 2000 were necessary to correct accounting violations. The restatements for the period reduced earnings
Enron_scandal
President of Paraguay since 2023
that the suspension favored Brazil by keeping frozen a key process to correct what they consider a historic disadvantage for Paraguay in the distribution
Santiago_Peña
Computer hardware and software capable of playing chess
reasons. First, with approximately thirty moves possible in a typical real-life position, he expected that searching the approximately 109 positions involved
Computer_chess
American politician (born 1954)
alleged errors and scientific fraud underlying the vaccine-autism claim. A corrected version of the original article was published on Rolling Stone's website
Robert_F._Kennedy_Jr.
2013 video game
shooting mechanics and cover system and reworked the driving mechanics to correct Grand Theft Auto IV's awkward vehicle controls. After an audition process
Grand_Theft_Auto_V
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
Girl/Female
Indian, Punjabi, Sikh
Correct
Girl/Female
Hindu, Indian, Kannada
Correct
Surname or Lastname
English
English : variant spelling of Corbett.
Boy/Male
Muslim
Appropriate, Correct
Boy/Male
Muslim
Correct, Accurate
Girl/Female
Arabic, Hindu, Indian, Muslim
Correct; Agreeable
Boy/Male
Tamil
Correct message
Boy/Male
Arabic, Muslim
Correct; Right
Boy/Male
Hindu
Correct message
Boy/Male
Indian
Appropriate, Correct
Male
English
English surname transferred to forename use, FORREST means "lives in or by an enclosed wood."
Girl/Female
Australian, German, Hindu, Indian
Correct
Boy/Male
Tamil
Correct
Surname or Lastname
English (Shropshire; of Norman origin)
English (Shropshire; of Norman origin) : nickname meaning ‘little crow’, ‘raven’, from Anglo-Norman French, Middle English corbet, a diminutive of corb, alluding probably to someone with dark hair or a dark complexion.Irish : see Corban.
Surname or Lastname
English
English : unexplained.Of Irish origin : unexplained; perhaps a variant of Kirrell, an Anglicized form of Ó Coirill (probably ‘descendant of Cairell’, an unexplained personal name).Americanized spelling of German Korell.
Surname or Lastname
probably Spanish
probably Spanish : unexplained. In Spain this name is mainly found in Andalusia.English : variant spelling of Paine.Southern French : from Latin paganus ‘country dweller’, hence a nickname for a country-born person, or from its later sense of ‘pagan’, ‘heathen’, given to a child not yet baptized. Compare Paine.A Payan, also called Saintonge, from the Saintonge region of France, is documented in Quebec City in 1699.
Boy/Male
Tamil
Correct
Boy/Male
Tamil
Correct message
Boy/Male
German, Hindu, Indian, Thai
Correct
Boy/Male
Hindu
Correct
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
Boy/Male
Hindu
Cloud, Ocean
Female
Spanish
Feminine form of Spanish Custodio, CUSTODIA means "guardian, keeper."
Boy/Male
Bengali, Hindu, Indian
A Serpent King
Girl/Female
Arabic, Bengali, Gujarati, Hindu, Indian, Kannada, Muslim
Beautiful; A Small Song
Girl/Female
Indian
Boy/Male
Indian
Servant of the creator, Slave of the creator
Girl/Female
French
Reads aloud.
Girl/Female
Indian
White Light
Boy/Male
Muslim
Felicities. Good fortunes.
Girl/Female
Arabic, Muslim
Beautiful One
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
PROBABLY APPROXIMATELY-CORRECT-LEARNING
n.
Fig.: A violent or rapid flow; a strong current; a flood; as, a torrent of vices; a torrent of eloquence.
a.
Approved; probable.
a.
Rendering probable; supporting, or giving ground for, belief, but not demonstrating; as, probable evidence; probable presumption.
a.
Set right, or made straight; hence, conformable to truth, rectitude, or propriety, or to a just standard; not faulty or imperfect; free from error; as, correct behavior; correct views.
n.
One who, or that which, corrects; as, a corrector of abuses; a corrector of the press; an alkali is a corrector of acids.
v. t.
To counteract the qualities of one thing by those of another; -- said of whatever is wrong or injurious; as, to correct the acidity of the stomach by alkaline preparations.
imp. & p. p.
of Correct
a.
Abounding in errors; not genuine or correct; as, the text of the manuscript is corrupt.
imp. & p. p.
of Approximate
adv.
Improbably.
a.
Incorrect.
a.
Now passing, as time; as, the current month.
adv.
With approximation; so as to approximate; nearly.
v. t.
To make right; to bring to the standard of truth, justice, or propriety; to rectify; as, to correct manners or principles.
a.
Not correct; not according to a copy or model, or to established rules; inaccurate; faulty.
v. t.
To remove or retrench the faults or errors of; to amend; to set right; as, to correct the proof (that is, to mark upon the margin the changes to be made, or to make in the type the changes so marked).
a.
Near correctness; nearly exact; not perfectly accurate; as, approximate results or values.
a.
Passing from person to person, or from hand to hand; circulating through the community; generally received; common; as, a current coin; a current report; current history.
adv.
In a probable manner; in likelihood.
adv.
In a correct manner; exactly; acurately; without fault or error.