From observer states to physics via algorithmic probability[clarification needed][1]
In algorithmic information theory, algorithmic probability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability to a given observation. It was invented by Ray Solomonoff in the 1960s.[2]
It is used in inductive inference theory and analyses of algorithms. In his general theory of inductive inference, Solomonoff uses the method together with Bayes' rule to obtain probabilities of prediction for an algorithm's future outputs.[3]
In the mathematical formalism used, the observations have the form of finite binary strings viewed as outputs of Turing machines, and the universal prior is a probability distribution over the set of finite binary strings calculated from a probability distribution over programs (that is, inputs to a universal Turing machine). The prior is universal in the
Turing-computability sense, i.e. no string has zero probability. It is not computable, but it can be approximated.[4]
Formally, the probability is not a probability and it is not computable. It is only "lower semi-computable" and a "semi-measure". By "semi-measure", it means that . That is, the "probability" does not actually sum up to one, unlike actual probabilities. This is because some inputs to the Turing machine causes it to never halt, which means the probability mass allocated to those inputs is lost. By "lower semi-computable", it means there is a Turing machine that, given an input string , can print out a sequence that converges to from below, but there is no such Turing machine that does the same from above.
^Markus Müller. Law without Law: from observer states to physics via algorithmic information theory. Quantum: the open journal for quantum science. 06 June 2020.
^Solomonoff, R., "A Preliminary Report on a General Theory of Inductive Inference", Report V-131, Zator Co., Cambridge, Ma. (Nov. 1960 revision of the Feb. 4, 1960 report).
^Li, M. and Vitanyi, P., An Introduction to Kolmogorov Complexity and Its Applications, 3rd Edition, Springer Science and Business Media, N.Y., 2008
^Hutter, M., Legg, S., and Vitanyi, P., "Algorithmic Probability", Scholarpedia, 2(8):2572, 2007.
and 27 Related for: Algorithmic probability information
In algorithmic information theory, algorithmicprobability, also known as Solomonoff probability, is a mathematical method of assigning a prior probability...
invented algorithmicprobability, his General Theory of Inductive Inference (also known as Universal Inductive Inference), and was a founder of algorithmic information...
and the relations between them: algorithmic complexity, algorithmic randomness, and algorithmicprobability. Algorithmic information theory principally...
game-theoretic techniques for algorithm design and analysis Algorithmic cooling, a phenomenon in quantum computation Algorithmicprobability, a universal choice...
differs from Jaynes' recommendation. Priors based on notions of algorithmicprobability are used in inductive inference as a basis for induction in very...
Universal Artificial Intelligence: Sequential Decisions Based on AlgorithmicProbability was published by Springer in 2005. Starting in 2000, Hutter developed...
of the first practical Causal AI approaches using Algorithmic Complexity and AlgorithmicProbability in Machine Learning. Blogger, SwissCognitive Guest...
known as algorithmic complexity, Solomonoff–Kolmogorov–Chaitin complexity, program-size complexity, descriptive complexity, or algorithmic entropy. It...
result in classical mechanics for adiabatic invariants A theorem of algorithmicprobability Invariant (mathematics) This disambiguation page lists articles...
Carlo algorithm is a randomized algorithm whose output may be incorrect with a certain (typically small) probability. Two examples of such algorithms are...
expressing algorithmic order types. The standard is called FIX Algorithmic Trading Definition Language (FIXatdl). 2010 Flash Crash Algorithmic tacit collusion...
computing, algorithmic complexity and intractability, average-case complexity, foundations of mathematics and computer science, algorithmicprobability, theory...
randomness: Algorithmicprobability Chaos theory Cryptography Game theory Information theory Pattern recognition Percolation theory Probability theory Quantum...
In probability theory and statistics, the Poisson distribution is a discrete probability distribution that expresses the probability of a given number...
is not produced by Huffman's algorithm. Given A set of symbols and their weights (usually proportional to probabilities). Find A prefix-free binary code...
criterion Algebra of random variables Algebraic statistics Algorithmic inference Algorithms for calculating variance All models are wrong All-pairs testing...
ISBN 978-2-7462-2087-4. Dessalles, J.-L. (2013). "Algorithmic simplicity and relevance". In D. L. Dowe (Ed.), Algorithmicprobability and friends - LNAI 7070, 119-130...
In probability theory and statistics, a probability distribution is the mathematical function that gives the probabilities of occurrence of different...
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...
The Viterbi algorithm is a dynamic programming algorithm for obtaining the maximum a posteriori probability estimate of the most likely sequence of hidden...
Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations...
stochastic model describing a sequence of possible events in which the probability of each event depends only on the state attained in the previous event...
cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution...
"No free lunch versus Occam’s razor in supervised learning." In AlgorithmicProbability and Friends. Bayesian Prediction and Artificial Intelligence, pp...
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...
generate new probabilities. It was unclear where these prior probabilities should come from. Ray Solomonoff developed algorithmicprobability which gave...
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...
Global Information
