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Mathematical method of assigning a prior probability to a given observation
In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability
Algorithmic_probability
Subfield of information theory and computer science
and the relations between them: algorithmic complexity, algorithmic randomness, and algorithmic probability. Algorithmic information theory principally
Algorithmic information theory
Algorithmic_information_theory
American inventor of algorithmic probability and artificial intelligence researcher
invented algorithmic probability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder of algorithmic information
Ray_Solomonoff
Topics referred to by the same term
game-theoretic techniques for algorithm design and analysis Algorithmic cooling, a phenomenon in quantum computation Algorithmic probability, a universal choice
Algorithmic
Monte Carlo algorithm
Metropolis–Hastings algorithm is a Markov chain Monte Carlo (MCMC) method for obtaining a sequence of random samples from a probability distribution from
Metropolis–Hastings_algorithm
Measure of algorithmic complexity
known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It
Kolmogorov_complexity
Type of randomized algorithm
Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are
Monte_Carlo_algorithm
Mathematical theory
programs from having very high probability. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. The
Solomonoff's theory of inductive inference
Solomonoff's_theory_of_inductive_inference
Method of executing orders
simple retail tools. Algorithmic trading is widely used in equities, futures, crypto, and foreign exchange markets. The term algorithmic trading is often
Algorithmic_trading
Cognitive theory
ISBN 978-2-7462-2087-4. Dessalles, J.-L. (2013). "Algorithmic simplicity and relevance". In D. L. Dowe (Ed.), Algorithmic probability and friends - LNAI 7070, 119-130
Simplicity_theory
Halting probability of a random computer program
computer science subfield of algorithmic information theory, a Chaitin constant (Chaitin omega number) or halting probability is a real number that, informally
Chaitin's_constant
Soviet-American mathematician
computing, algorithmic complexity and intractability, average-case complexity, foundations of mathematics and computer science, algorithmic probability, theory
Leonid_Levin
Distribution of an uncertain quantity
differs from Jaynes' recommendation. Priors based on notions of algorithmic probability are used in inductive inference as a basis for induction in very
Prior_probability
German computer scientist (born 1967)
Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability was published in 2005 by Springer. Also in 2005, Hutter published
Marcus_Hutter
Counterintuitive result in probability
classical probability suggests, aligning with Gregory Chaitin's modern theorem and building on algorithmic information theory and algorithmic probability by
Infinite_monkey_theorem
Hungarian-American mathematician and computer scientist
in reliable computation, randomness in computing, algorithmic complexity, algorithmic probability, and information theory. Peter Gacs attended high school
Peter_Gacs
Algorithmic selection of online media
political polarization as a side effect of optimising for user interaction. Algorithmic curation has been found to increase source diversity in some respects
Algorithmic_curation
Algorithm in mathematics
to its recursive calculation of joint probabilities. As the number of variables grows, these joint probabilities become increasingly small, leading to
Baum–Welch_algorithm
Topics referred to by the same term
The universal probability is the algorithmic probability of a universal prefix-free Turing machine, used to define a universal prior distribution. Universal
Universal probability (disambiguation)
Universal_probability_(disambiguation)
Calculation of complex statistical distributions
Monte Carlo (MCMC) is a class of algorithms used to draw samples from a probability distribution. Given a probability distribution, one can construct a
Markov_chain_Monte_Carlo
Belgian-American mathematician (1935–2014)
Belgian-American mathematician and probability theorist. He is known for contributions in algorithmic probability, stochastic processes, and queuing theory
Marcel_F._Neuts
Mathematical folklore
"No free lunch versus Occam’s razor in supervised learning." In Algorithmic Probability and Friends. Bayesian Prediction and Artificial Intelligence, pp
No_free_lunch_theorem
Apparent lack of pattern or predictability in events
randomness: Algorithmic probability Chaos theory Cryptography Game theory Information theory Pattern recognition Percolation theory Probability theory Quantum
Randomness
Branch of mathematics concerning probability
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations
Probability_theory
Quantum search algorithm
Grover's algorithm, also known as the quantum search algorithm, is a quantum algorithm for unstructured search that finds with high probability the unique
Grover's_algorithm
On constructing objects that obey a system of constraints with limited dependence
In theoretical computer science, the algorithmic Lovász local lemma gives an algorithmic way of constructing objects that obey a system of constraints
Algorithmic Lovász local lemma
Algorithmic_Lovász_local_lemma
School of thought on cognition and problem-solving
influenced by Korzybski. Solomonoff was the inventor of algorithmic probability, and founder of algorithmic information theory (a.k.a. Kolmogorov complexity)
General_semantics
Cash prize for advances in data compression
Universal Artificial Intelligence: Sequential Decisions based on Algorithmic Probability. Texts in Theoretical Computer Science an EATCS Series. Springer
Hutter_Prize
Randomized algorithm
equal probability, and keep the i-th elements. The problem is that we do not always know the exact n in advance. A simple and popular but slow algorithm, Algorithm
Reservoir_sampling
of a random number (but for a much weaker notion of algorithmic randomness). Algorithmic probability History of randomness Incompleteness theorem Inductive
Universality_probability
Scientific study of digital information
black holes, bioinformatics, and gambling. Mathematics portal Algorithmic probability Bayesian inference Communication theory Constructor theory – a
Information_theory
Philosophical problem-solving principle
"Foreword re C. S. Wallace" for the subtle distinctions between the algorithmic probability work of Solomonoff and the MML work of Chris Wallace, and see Dowe's
Occam's_razor
Random process independent of past history
generate a higher probability of transitioning from authoritarian to democratic regime. Markov chains are employed in algorithmic music composition,
Markov_chain
Model selection principle
discovery by Chaitin, Solomonoff and Kolmogorov of the concept called Algorithmic Probability which is a fundamental new theory of how to make predictions given
Minimum_description_length
Chances of card combinations in poker
the probability of each type of 5-card hand can be computed by calculating the proportion of hands of that type among all possible hands. Probability and
Poker_probability
Finds likely sequence of hidden states
Viterbi algorithm have become standard terms for the application of dynamic programming algorithms to maximization problems involving probabilities. For
Viterbi_algorithm
Technique to compress data
Huffman tree. The simplest construction algorithm uses a priority queue where the node with lowest probability is given highest priority: Create a leaf
Huffman_coding
Process of acquiring new knowledge
labeling – Cognitive process Algorithmic information theory – Subfield of information theory and computer science Algorithmic probability – Mathematical method
Learning
Mathematical function for the probability a given outcome occurs in an experiment
In probability theory and statistics, a probability distribution describes how probabilities are assigned to the possible results of a random phenomenon—more
Probability_distribution
Algorithm that employs a degree of randomness as part of its logic or procedure
found end If an ‘a’ is found, the algorithm succeeds, else the algorithm fails. After k iterations, the probability of finding an ‘a’ is: Pr [ f i n d
Randomized_algorithm
Determining the probability of future events based on past events
generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmic probability which gave
Inductive_probability
Algorithm in quantum information theory
Algorithmic cooling is an algorithmic method for transferring heat (or entropy) from some qubits to others or outside the system and into the environment
Algorithmic_cooling
Technological phenomenon with social implications
data is coded, collected, selected or used to train the algorithm. For example, algorithmic bias has been observed in search engine results and social
Algorithmic_bias
Topics referred to by the same term
phosphatase, an enzyme Axion-like particle, pseudo Nambu-Goldstone boson Algorithmic probability Association for Logic Programming IBM ALP, Assembly Language Processor
ALP
Observed value of a random variable
In probability and statistics, a realization or observation (also called observed value) of a random variable or random element is the value that is actually
Realization_(probability)
Sequence of operations for a task
aversion Algorithm engineering Algorithm characterizations Algorithmic bias Algorithmic composition Algorithmic entities Algorithmic synthesis Algorithmic technique
Algorithm
Binary sequence
Random sequences are key objects of study in algorithmic information theory. In measure-theoretic probability theory, introduced by Andrey Kolmogorov in
Algorithmically random sequence
Algorithmically_random_sequence
Philosophical thought experiment about utility
2025. De Blanc, Peter. Convergence of Expected Utilities with Algorithmic Probability Distributions (2007), arXiv:0712.4318 Kieran Marray, Dealing With
Pascal's_mugging
Probabilistic optimization technique and metaheuristic
cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution
Simulated_annealing
Family of algorithms for sampling from discrete probability distributions
computing, the alias method is a family of efficient algorithms for sampling from a discrete probability distribution, published in 1974 by Alastair J. Walker
Alias_method
Discrete probability distribution
In probability theory and statistics, the Poisson distribution (/ˈpwɑːsɒn/) is a discrete probability distribution that expresses the probability of a
Poisson_distribution
Mathematical formalism for artificial general intelligence
Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability. Texts in Theoretical Computer Science an EATCS Series. Springer
AIXI
Quantum algorithm for integer factorization
N} with very high probability of success if one uses a more advanced reduction. The goal of the quantum subroutine of Shor's algorithm is, given coprime
Shor's_algorithm
Method for stochastic equation systems
In probability theory, the Gillespie algorithm (or the Doob–Gillespie algorithm or stochastic simulation algorithm, the SSA) generates a statistically
Gillespie_algorithm
Equivalence of average-case and expected complexity
input to the algorithm Yao's principle is often used to prove limitations on the performance of randomized algorithms, by finding a probability distribution
Yao's_principle
Statistical Markov model
In probability theory, a hidden Markov model (HMM) is a Markov model in which the observations are dependent on a latent (or hidden) Markov process (referred
Hidden_Markov_model
Concept in computer science
guaranteed to run in polynomial time On any given run of the algorithm, it has a probability of at most 1/3 of giving the wrong answer, whether the answer
BPP_(complexity)
Algorithm for shuffling a finite sequence
position, as required. As for the equal probability of the permutations, it suffices to observe that the modified algorithm involves (n − 1)! distinct possible
Fisher–Yates_shuffle
Closeness of someone's association with mathematician Paul Erdős and actor Kevin Bacon
Erdős–Bacon number of 6. Mathematician Ray Solomonoff, the inventor of algorithmic probability, has an Erdős number of 3 and also appeared in the Steven Wright
Erdős–Bacon_number
Probabilistic classification algorithm
uncertainty (with naive Bayes models often producing wildly overconfident probabilities). However, they are highly scalable, requiring only one parameter for
Naive_Bayes_classifier
Formal information theory restatement of Occam's Razor
segmentation, etc. Algorithmic probability Algorithmic information theory Grammar induction Inductive inference Inductive probability Kolmogorov complexity
Minimum_message_length
Sampling algorithm
approximate integrals with respect to the target probability distribution for a given Monte Carlo error. The algorithm was originally proposed by Simon Duane,
Hamiltonian_Monte_Carlo
conditional probabilities is a systematic method for converting non-constructive probabilistic existence proofs into efficient deterministic algorithms that
Method of conditional probabilities
Method_of_conditional_probabilities
Measurement of algorithmic bias
Fairness in machine learning (ML) refers to the various attempts to correct algorithmic bias in automated decision processes based on ML models. Decisions made
Fairness_(machine_learning)
Collection of random variables
In probability theory and related fields a stochastic (/stəˈkæstɪk/) or random process is a mathematical object usually defined as a family of random
Stochastic_process
Topics referred to by the same term
result in classical mechanics for adiabatic invariants A theorem of algorithmic probability Invariant (mathematics) This disambiguation page lists articles
Invariance_theorem
Mathematical rule for inverting probabilities
conditional probabilities, allowing the probability of a cause to be found given its effect. For example, with Bayes' theorem, the probability that a patient
Bayes'_theorem
Inference algorithm for hidden Markov models
forward–backward algorithm computes a set of forward probabilities which provide, for all t ∈ { 1 , … , T } {\displaystyle t\in \{1,\dots ,T\}} , the probability of
Forward–backward_algorithm
Description of limiting behavior in probabilistic algorithms
probabilistic algorithms. For example, consider a certain probabilistic algorithm on a graph with n nodes. If the probability that the algorithm returns the
With_high_probability
Probability distribution
In probability theory and statistics, the binomial distribution with parameters n and p is the discrete probability distribution of the number of successes
Binomial_distribution
Method of logical reasoning
razor. Fundamental ingredients of the theory are the concepts of algorithmic probability and Kolmogorov complexity. Inductive inference typically considers
Inductive_reasoning
Hidden Markov model algorithm
The forward algorithm, in the context of a hidden Markov model (HMM), is used to calculate a 'belief state': the probability of a state at a certain time
Forward_algorithm
Randomized algorithm for verifying matrix multiplication
O(n^{2})} with high probability. In O ( k n 2 ) {\displaystyle O(kn^{2})} time the algorithm can verify a matrix product with probability of failure less
Freivalds'_algorithm
Randomized algorithm for minimum cuts
graph. By iterating this basic algorithm a sufficient number of times, a minimum cut can be found with high probability. A cut ( S , T ) {\displaystyle
Karger's_algorithm
Measure of similarity and diversity between sets
derives from the use of weighted minhashing algorithms that achieve this as their collision probability.) This theorem has a visual proof on three element
Jaccard_index
Conditional probability used in Bayesian statistics
The posterior probability is a type of conditional probability that results from updating the prior probability with information summarized by the likelihood
Posterior_probability
List of concepts in artificial intelligence
continuous process. algorithmic probability In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical
Glossary of artificial intelligence
Glossary_of_artificial_intelligence
Method of computing optimal strategies for last-success problems
odds algorithm applies to a class of problems called last-success problems. Formally, the objective in these problems is to maximize the probability of
Odds_algorithm
Algorithm used by Google Search to rank web pages
Marchiori, and Kleinberg in their original papers. The PageRank algorithm outputs a probability distribution used to represent the likelihood that a person
PageRank
Average uncertainty in variable's states
describe the state of the variable, considering the distribution of probabilities across all potential states. Given a discrete random variable X {\displaystyle
Entropy_(information_theory)
Overview of and topical guide to computer programming
of algorithms Empirical algorithmics Big O notation Algorithmic efficiency Algorithmic information theory Algorithmic probability Algorithmically random
Outline of computer programming
Outline_of_computer_programming
Lossless compression algorithm
is then encoded with a range encoder, using a complex model to make a probability prediction of each bit. The dictionary compressor finds matches using
LZMA
Algorithm in statistical physics
Glauber algorithm can be compared to the Metropolis–Hastings algorithm. These two differ in how a spin site is selected (step 1), and in the probability of
Glauber_dynamics
Computable number Definable number Halting probability Algorithmic information theory Algorithmic probability Data compression Advice (complexity) Amortized
List of computability and complexity topics
List_of_computability_and_complexity_topics
theory Mechanism design Algorithmic information theory – Subfield of information theory and computer science Algorithmic probability – Mathematical method
Outline of artificial intelligence
Outline_of_artificial_intelligence
Sampling technique
the same probability. It is a process of selecting a sample in a random way. In SRS, each subset of k individuals has the same probability of being chosen
Simple_random_sample
Probability distribution
In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued
Normal_distribution
Competitive algorithm for searching a problem space
parameters (adaptive genetic algorithms, AGAs) is another significant and promising variant of genetic algorithms. The probabilities of crossover (pc) and mutation
Genetic_algorithm
Variation of the minimax algorithm
Universal Artificial Intelligence: Sequential Decisions Based on Algorithmic Probability (2005) by Tom Everitt and Marcus Hutter. Bruce Ballard was the
Expectiminimax
Computational complexity class of problems
there exists a quantum algorithm (an algorithm that runs on a quantum computer) that solves the decision problem with high probability and is guaranteed to
BQP
Probability of shared birthdays
In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday
Birthday_problem
Genetic operation used to add population diversity
example of a mutation operator of a binary coded genetic algorithm (GA) involves a probability that an arbitrary bit in a genetic sequence will be flipped
Mutation (evolutionary algorithm)
Mutation_(evolutionary_algorithm)
Philosophical interpretation of the axioms of probability
word "probability" has been used in a variety of ways since it was first applied to the mathematical study of games of chance. Does probability measure
Probability_interpretations
assumption about a probability distribution on the set of all possible inputs. This assumption is then used to design an efficient algorithm or to derive the
Probabilistic analysis of algorithms
Probabilistic_analysis_of_algorithms
Algorithmic Qubits (#AQ)". IonQ. Retrieved 2025-09-19. "Algorithmic Qubits: A Better Single-Number Metric". IonQ. Retrieved 2025-09-19. "Algorithmic Qubit
Algorithmic_qubits
criterion Algebra of random variables Algebraic statistics Algorithmic inference Algorithms for calculating variance All models are wrong All-pairs testing
List_of_statistics_articles
Sequentially looking in an array
affected if the search probabilities for each element vary. Linear search is rarely practical because other search algorithms and schemes, such as the
Linear_search
Computer hardware technology that uses quantum mechanics
wave interference effects amplify the probability of the desired measurement result. The design of quantum algorithms involves creating procedures that allow
Quantum_computing
Month of 1926
Solomonoff, American mathematician known for his invention, in 1960, of algorithmic probability; in Cleveland (d.2009) Melinda Kistétényi, Hungarian composer and
July_1926
Decision rule used for minimizing the possible loss for a worst-case scenario
expected payment of more than 1/ 3 by choosing A1 with probability 1/ 6 and A2 with probability 5/ 6 : The expected payoff for A would be 3 × 1/ 6
Minimax
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
Surname or Lastname
English (Yorkshire)
English (Yorkshire) : in all probability from the Swale river in Yorkshire. (Reaney and Wilson list a 17th-century example, Swayles, with this origin.) Alternatively, it may be a metronymic from the Old Norse female personal name Svala.
Surname or Lastname
English
English : in all probability an English variant of Scottish Lachlan (see McLachlan), altered through folk etymology. However, Black cites one John sine terra (c. 1180–1214), suggesting that the surname could have arisen quite literally as a nickname for a man with no land.
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
Surname or Lastname
English
English : probably a variant of Fawley.
Girl/Female
Bengali, Gujarati, Hindu, Indian, Kannada, Malayalam, Marathi, Sindhi, Telugu
The Sky and the Earth
Girl/Female
Hindu
Art, Talent, Creativity
Surname or Lastname
English
English : variant of Tow.
Girl/Female
Indian, Telugu
From the Ocean; Spiritual
Boy/Male
Hindu, Indian, Tamil
Against Desire
Boy/Male
Hindu
Boy/Male
Arabic, Muslim
The Subduer; The Almighty
Boy/Male
Indian, Punjabi, Sikh
One who has All Treasures
Boy/Male
Hindu, Indian
Immortal
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
ALGORITHMIC PROBABILITY
a.
Based on presumption or probability; grounded on probable evidence; probable; as, presumptive proof.
n.
Probability.
n.
Likelihood; probability.
superl.
Having probability; affording probability; probable; likely.
a.
Difference in favor of one and against another; excess of one of two things or numbers over the other; inequality; advantage; superiority; hence, excess of chances; probability.
n.
Alt. of Algorithm
adv.
By presumption, or supposition grounded or probability; presumably.
n.
One who maintains that a man may do that which has a probability of being right, or which is inculcated by teachers of authority, although other opinions may seem to him still more probable.
n.
The quality or state of being verisimilar; the appearance of truth; probability; likelihood.
n.
The quality or state of being probable; appearance of reality or truth; reasonable ground of presumption; likelihood.
n.
The art of calculating by nine figures and zero.
n.
Likelihood of the occurrence of any event in the doctrine of chances, or the ratio of the number of favorable chances to the whole number of chances, favorable and unfavorable. See 1st Chance, n., 5.
adv.
In all probability; probably.
n.
That which is or appears probable; anything that has the appearance of reality or truth.
n.
Appearance of truth or reality; probability; verisimilitude.
n.
Ground for presuming; evidence probable, but not conclusive; strong probability; reasonable supposition; as, the presumption is that an event has taken place.
a.
Having probability; having or giving reason to expect; -- followed by the infinitive; as, it is likely to rain.
n.
The art of calculating with any species of notation; as, the algorithms of fractions, proportions, surds, etc.
n.
One who maintains that certainty is impossible, and that probability alone is to govern our faith and actions.
pl.
of Probability