Randomized machine learning: Statement, solution, applications

Popkov, Yu. S.; Dubnov, Yuri A.; Popkov, A. Yu.

doi:10.1109/is.2016.7737456

Cited by 8 publications

(5 citation statements)

References 17 publications

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“…Proof. Consider the partition of the interval [0, 1] by a grid with step η k 1 (23). At least one random value from M k = (1/η) 1/q will fall into the elementary interval with the probability η k .…”

Section: Formation Of the Monotonic Sequences Of Recordsmentioning

confidence: 99%

“…In the papers [22,23], and the book [24], a new machine learning procedure (Randomized Machine Learning, RML) was developed. The basic concept of RML is based on the use of a parameterized model with random parameters, its optimization using the conditional information entropy maximization method, and the subsequent generation of random parameters with optimized probability density functions.…”

Section: Introductionmentioning

confidence: 99%

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Reinforcement Procedure for Randomized Machine Learning

Popkov,

Dubnov,

Popkov

2023

Mathematics

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This paper is devoted to problem-oriented reinforcement methods for the numerical implementation of Randomized Machine Learning. We have developed a scheme of the reinforcement procedure based on the agent approach and Bellman’s optimality principle. This procedure ensures strictly monotonic properties of a sequence of local records in the iterative computational procedure of the learning process. The dependences of the dimensions of the neighborhood of the global minimum and the probability of its achievement on the parameters of the algorithm are determined. The convergence of the algorithm with the indicated probability to the neighborhood of the global minimum is proved.

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Section: Formation Of the Monotonic Sequences Of Recordsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Reinforcement Procedure for Randomized Machine Learning

Popkov,

Dubnov,

Popkov

2023

Mathematics

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“…Therefore, according to RML [16] general procedure, the problem of "2"-soft classification is represented as follows:…”

Section: Learningmentioning

confidence: 99%

“…Within the general concept of machine learning, its modification had been proposed: Randomized Machine Learning (RML) [16]. An idea of the randomization is expanding to data and parameters of decision rules.…”

Section: Introductionmentioning

confidence: 99%

Entropy “2”-Soft Classification of Objects

Popkov

Volkovich

Dubnov

et al. 2017

Entropy

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Abstract:A proposal for a new method of classification of objects of various nature, named "2"-soft classification, which allows for referring objects to one of two types with optimal entropy probability for available collection of learning data with consideration of additive errors therein. A decision rule of randomized parameters and probability density function (PDF) is formed, which is determined by the solution of the problem of the functional entropy linear programming. A procedure for "2"-soft classification is developed, consisting of the computer simulation of the randomized decision rule with optimal entropy PDF parameters. Examples are provided.

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“…The problem of estimating some model characteristics on real data was further developed in connection with the appearance of new machine learning methods, called randomized machine learning (RML) [20]. They are based on models with random parameters, and it is necessary to estimate the probability density functions of these parameters.…”

Section: Introductionmentioning

confidence: 99%

Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions

Popkov

2021

Mathematics

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The problem of randomized maximum entropy estimation for the probability density function of random model parameters with real data and measurement noises was formulated. This estimation procedure maximizes an information entropy functional on a set of integral equalities depending on the real data set. The technique of the Gâteaux derivatives is developed to solve this problem in analytical form. The probability density function estimates depend on Lagrange multipliers, which are obtained by balancing the model’s output with real data. A global theorem for the implicit dependence of these Lagrange multipliers on the data sample’s length is established using the rotation of homotopic vector fields. A theorem for the asymptotic efficiency of randomized maximum entropy estimate in terms of stationary Lagrange multipliers is formulated and proved. The proposed method is illustrated on the problem of forecasting of the evolution of the thermokarst lake area in Western Siberia.

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Randomized machine learning: Statement, solution, applications

Cited by 8 publications

References 17 publications

Reinforcement Procedure for Randomized Machine Learning

Reinforcement Procedure for Randomized Machine Learning

Entropy “2”-Soft Classification of Objects

Qualitative Properties of Randomized Maximum Entropy Estimates of Probability Density Functions

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