scholarly journals Optimal experimental design for machine learning using the Fisher information

2018 ◽  
Author(s):  
Tracianne B. Neilsen ◽  
David F. Van Komen ◽  
Mark K. Transtrum ◽  
Makenzie B. Allen ◽  
David P. Knobles
Keyword(s):  
Machine Learning ◽  
Experimental Design ◽  
Fisher Information ◽  
Optimal Experimental Design

Optimal experimental design for machine learning using the Fisher information matrix

2018 ◽  
Vol 144 (3) ◽  
pp. 1730-1730 ◽  
Author(s):  
Tracianne B. Neilsen ◽  
Mark K. Transtrum ◽  
David F. Van Komen ◽  
David P. Knobles
Keyword(s):  
Machine Learning ◽  
Experimental Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Optimal Experimental Design

Synthesis of optimal experiment designs under the conditions of Generalized Lambda-distribution of errors for models with errors in variables

2020 ◽  
pp. 130-141
Author(s):  
Владимир Семенович Тимофеев ◽  
Екатерина Алексеевна Хайленко
Keyword(s):  
Experimental Design ◽  
Fisher Information ◽  
Fisher Information Matrix ◽  
Information Matrix ◽  
Experimental Designs ◽  
Optimal Experimental Design ◽  
Efficiency Function ◽  
Explanatory Variables ◽  
Generalized Lambda Distribution ◽  
Optimal Experiment

Рассмотрена задача планирования эксперимента в условиях появления ошибок в объясняющих переменных. Сформулировано и доказано утверждение о способе вычисления элементов информационной матрицы Фишера с использованием обобщенного лямбда-распределения, доказано следствие о способе вычисления функции эффективности плана эксперимента. Сравнение результатов вычисления функции эффективности с использованием выведенного в следствии соотношения и с помощью известного соотношения для нормального распределения ошибок показало, что результаты совпадают. Построены оптимальные планы эксперимента для различных распределений случайных компонент. The problem of experimental design under conditions of errors in the explanatory variables is considered. The proposition of the method for calculating the Fisher information matrix elements using the Generalized Lambda-distribution is formulated and proved, the consequence of the method for calculating the efficiency function of the experimental design is proved. This method of calculating the Fisher information matrix takes into account the heterogeneity of the errors in random distribution throughout the planning area. In this paper, studies of the synthesis of optimal experimental designs using proven proposition and consequence under various conditions of computational experiments are presented. The results of calculating the efficiency function using the obtained relation and using the known relation for the normal distribution of errors are compared, it is found that the results coincide. Optimal experimental designs are constructed for various distributions of random components. The results of the synthesis of optimal experimental design showed that when function of efficiency is constant throughout the planning area then the optimal experimental design is equilibrium plan. When there are differences in the values of the efficiency function in the planning area, the optimal plan ceases to be equilibrium

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