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Abstract <p>The article is devoted to the development of methods for probability informing of machine learning models and deep neural networks in the problem of time series forecasting. In continuation of previous studies that used moments of finite mixtures of normal distributions and connected mixture components, this paper proposes a new joint approach to this type of informing: using the connected components with simultaneous modifications of the standard loss function. Weighted loss functions are considered, including approximation of the data distribution density using kernel estimators and finite normal mixtures. The experiments conducted using real datasets (geophysical and electric time series) demonstrate the possibility of significant improvement of forecasting metrics (root mean square errors, mean absolute error in percent) compared to baseline models that do not use informed models. Thus, on geophysical data, the reduction in the mean square error in short-term forecasting problems only from the modification of the loss function amounted to 15.7%, and the greatest improvement within informing was 31.8% compared to the basic methods. For the characteristics of electrical circuit elements, the improvement of metrics in the medium-term forecasting problem with modification of only the loss function amounted to 12.5%, and the combined approach increased the values by 13.6%. A reduction in the number of training epochs required to achieve similar or higher accuracy was demonstrated with a moderate change in the duration of the epoch itself—on average, no more than 3.7%. It is noted that in all cases the results of informed models exceed classical versions of algorithms.</p>

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Joint Probability-Informed Approach Based on Feature Space Expansion and Modified Loss Functions for Time Series Forecasting

  • 期刊论文

  • 发表日期：

    2025年9月1日

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  • A. K. Gorshenin,
  • A. L. Vilyaev

摘要

Abstract

The article is devoted to the development of methods for probability informing of machine learning models and deep neural networks in the problem of time series forecasting. In continuation of previous studies that used moments of finite mixtures of normal distributions and connected mixture components, this paper proposes a new joint approach to this type of informing: using the connected components with simultaneous modifications of the standard loss function. Weighted loss functions are considered, including approximation of the data distribution density using kernel estimators and finite normal mixtures. The experiments conducted using real datasets (geophysical and electric time series) demonstrate the possibility of significant improvement of forecasting metrics (root mean square errors, mean absolute error in percent) compared to baseline models that do not use informed models. Thus, on geophysical data, the reduction in the mean square error in short-term forecasting problems only from the modification of the loss function amounted to 15.7%, and the greatest improvement within informing was 31.8% compared to the basic methods. For the characteristics of electrical circuit elements, the improvement of metrics in the medium-term forecasting problem with modification of only the loss function amounted to 12.5%, and the combined approach increased the values by 13.6%. A reduction in the number of training epochs required to achieve similar or higher accuracy was demonstrated with a moderate change in the duration of the epoch itself—on average, no more than 3.7%. It is noted that in all cases the results of informed models exceed classical versions of algorithms.