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Kolmogorov Structure Function
In 1973, Andrey Kolmogorov proposed a non-probabilistic approach to statistics and model selection. Let each datum be a finite binary string and a model be a finite set of binary strings. Consider model classes consisting of models of given maximal Kolmogorov complexity. The Kolmogorov structure function of an individual data string expresses the relation between the complexity level constraint on a model class and the least log-cardinality of a model in the class containing the data. The structure function determines all stochastic properties of the individual data string: for every constrained model class it determines the individual best-fitting model in the class irrespective of whether the true model is in the model class considered or not. In the classical case we talk about a set of data with a probability distribution, and the properties are those of the expectations. In contrast, here we deal with individual data strings and the properties of the individual string focused ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Andrey Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who played a central role in the creation of modern probability theory. He also contributed to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and Analysis of algorithms, computational complexity. Biography Early life Andrey Kolmogorov was born in Tambov, about 500 kilometers southeast of Moscow, in 1903. His unmarried mother, Maria Yakovlevna Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do Russian nobility, nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been an Agronomy, agronomist. Katayev ha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Paul Vitányi
Paul Michael Béla Vitányi (born 21 July 1944) is a Dutch computer scientist, professor of computer science at the University of Amsterdam and researcher at the Dutch Centrum Wiskunde & Informatica. Biography Vitányi was born in Budapest to a Dutch mother and a Hungarian father. He received his degree of mathematical engineer from Delft University of Technology in 1971 and his Ph.D. from the Free University of Amsterdam in 1978.. Career Vitányi was appointed professor of computer science at the University of Amsterdam, and researcher at the National Research Institute for Mathematics and Computer Science in the Netherlands (Centrum Wiskunde & Informatica, CWI) where he is currently a CWI Fellow. He was guest professor at the University of Copenhagen in 1978; research associate at the Massachusetts Institute of Technology in 1985/1986; Gaikoku-Jin Kenkyuin (councilor professor) at INCOCSAT at the Tokyo Institute of Technology in 1998; visiting professor at Boston University in ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Rate Distortion
Rate or rates may refer to: Finance * Rate (company), an American residential mortgage company formerly known as Guaranteed Rate * Rates (tax), a type of taxation system in the United Kingdom used to fund local government * Exchange rate, rate at which one currency will be exchanged for another Mathematics and science * Rate (mathematics), a specific kind of ratio, in which two measurements are related to each other (often with respect to time) * Rate function, a function used to quantify the probabilities of a rare event * Reaction rate, in chemistry the speed at which reactants are converted into products Military * Naval rate, a junior enlisted member of a navy * Rating system of the Royal Navy, a former method of indicating a British warship's firepower People * Ed Rate (1899–1990), American football player * José Carlos Rates (1879–1945), General Secretary of the Portuguese Communist Party * Peter of Rates (died 60 AD), traditionally considered to be the first bisho ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Maximum Likelihood
In statistics, maximum likelihood estimation (MLE) is a method of estimating the parameters of an assumed probability distribution, given some observed data. This is achieved by maximizing a likelihood function so that, under the assumed statistical model, the observed data is most probable. The point in the parameter space that maximizes the likelihood function is called the maximum likelihood estimate. The logic of maximum likelihood is both intuitive and flexible, and as such the method has become a dominant means of statistical inference. If the likelihood function is differentiable, the derivative test for finding maxima can be applied. In some cases, the first-order conditions of the likelihood function can be solved analytically; for instance, the ordinary least squares estimator for a linear regression model maximizes the likelihood when the random errors are assumed to have normal distributions with the same variance. From the perspective of Bayesian inference, ML ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Jorma Rissanen
Jorma Johannes Rissanen (October 20, 1932 – May 9, 2020) was an information theorist, known for originating the minimum description length (MDL) principle and practical approaches to arithmetic coding for lossless data compression. His work inspired the development of the theory of stochastic chains with memory of variable length. Education and career Rissanen was born in Pielisjärvi (now Lieksa) in Finland and grew up in Kemi, a border town between Finland and Sweden. He moved to Helsinki and studied at the Helsinki University of Technology, where he obtained his Master’s degree in electrical engineering in 1956 and licentiate in control theory in 1960. He studied there under Olli Lokki and Hans Blomberg. Rissanen became an IBM researcher since 1960, first in Stockholm, Sweden, while still a Ph.D. student under Hans Blomberg. Most of his PhD work was done remotely as a result and he received his Ph.D. from the Helsinki University of Technology in 1965 with a topic ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Minimum Description Length
Minimum Description Length (MDL) is a model selection principle where the shortest description of the data is the best model. MDL methods learn through a data compression perspective and are sometimes described as mathematical applications of Occam's razor. The MDL principle can be extended to other forms of inductive inference and learning, for example to estimation and sequential prediction, without explicitly identifying a single model of the data. MDL has its origins mostly in information theory and has been further developed within the general fields of statistics, theoretical computer science and machine learning, and more narrowly computational learning theory. Historically, there are different, yet interrelated, usages of the definite noun phrase "''the'' minimum description length ''principle''" that vary in what is meant by ''description'': * Within Jorma Rissanen's theory of learning, a central concept of information theory, models are statistical hypotheses and descri ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Minimal Sufficient Statistic
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an ancillary statistic which contains no information about the model parameters, and of a complete statistic which only contains information about the parameters and no ancillary information. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of the ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Estimator
In statistics, an estimator is a rule for calculating an estimate of a given quantity based on Sample (statistics), observed data: thus the rule (the estimator), the quantity of interest (the estimand) and its result (the estimate) are distinguished. For example, the sample mean is a commonly used estimator of the population mean. There are point estimator, point and interval estimators. The point estimators yield single-valued results. This is in contrast to an interval estimator, where the result would be a range of plausible values. "Single value" does not necessarily mean "single number", but includes vector valued or function valued estimators. ''Estimation theory'' is concerned with the properties of estimators; that is, with defining properties that can be used to compare different estimators (different rules for creating estimates) for the same quantity, based on the same data. Such properties can be used to determine the best rules to use under given circumstances. Howeve ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Sufficient Statistic
In statistics, sufficiency is a property of a statistic computed on a sample dataset in relation to a parametric model of the dataset. A sufficient statistic contains all of the information that the dataset provides about the model parameters. It is closely related to the concepts of an ancillary statistic which contains no information about the model parameters, and of a complete statistic which only contains information about the parameters and no ancillary information. A related concept is that of linear sufficiency, which is weaker than ''sufficiency'' but can be applied in some cases where there is no sufficient statistic, although it is restricted to linear estimators. The Kolmogorov structure function deals with individual finite data; the related notion there is the algorithmic sufficient statistic. The concept is due to Sir Ronald Fisher in 1920. Stephen Stigler noted in 1973 that the concept of sufficiency had fallen out of favor in descriptive statistics because of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kolmogorov
Andrey Nikolaevich Kolmogorov ( rus, Андре́й Никола́евич Колмого́ров, p=ɐnˈdrʲej nʲɪkɐˈlajɪvʲɪtɕ kəlmɐˈɡorəf, a=Ru-Andrey Nikolaevich Kolmogorov.ogg, 25 April 1903 – 20 October 1987) was a Soviet mathematician who played a central role in the creation of modern probability theory. He also contributed to the mathematics of topology, intuitionistic logic, turbulence, classical mechanics, algorithmic information theory and computational complexity. Biography Early life Andrey Kolmogorov was born in Tambov, about 500 kilometers southeast of Moscow, in 1903. His unmarried mother, Maria Yakovlevna Kolmogorova, died giving birth to him. Andrey was raised by two of his aunts in Tunoshna (near Yaroslavl) at the estate of his grandfather, a well-to-do nobleman. Little is known about Andrey's father. He was supposedly named Nikolai Matveyevich Katayev and had been an agronomist. Katayev had been exiled from Saint Petersburg to the Yarosla ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Model Selection
Model selection is the task of selecting a model from among various candidates on the basis of performance criterion to choose the best one. In the context of machine learning and more generally statistical analysis, this may be the selection of a statistical model from a set of candidate models, given data. In the simplest cases, a pre-existing set of data is considered. However, the task can also involve the design of experiments such that the data collected is well-suited to the problem of model selection. Given candidate models of similar predictive or explanatory power, the simplest model is most likely to be the best choice (Occam's razor). state, "The majority of the problems in statistical inference can be considered to be problems related to statistical modeling". Relatedly, has said, "How hetranslation from subject-matter problem to statistical model is done is often the most critical part of an analysis". Model selection may also refer to the problem of selecting ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
Kolm Complexity Lect
KOLM (1520 AM, "1520 The Ticket") was a sports formatted radio station in Rochester, Minnesota, and is owned by Townsquare Media. KOLM derived a portion of its programming from Infinity Sports Network. History On August 30, 2013, a deal was announced in which Townsquare would acquire 53 Cumulus Media stations, including KOLM, for $238 million. The deal is part of Cumulus' acquisition of Dial Global; Townsquare and Dial Global are both controlled by Oaktree Capital Management Oaktree Capital Management, Inc. is an American global asset management firm specializing in alternative investment strategies. As of September 30, 2024, the company managed $205 billion for its clientele. The firm was co-founded in 1995 by a .... The sale to Townsquare was completed on November 14, 2013. As of April 1, 2025, Townsquare Media took KOLM silent, claiming changes in market economic conditions. References External linksKOLM official website Radio stations in Minnesota Radio sta ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] [Amazon] |
