error root-mean-square

简明释义

均方误差

英英释义

例句

1.A lower error root-mean-square 均方根误差 indicates a better fit of the regression line to the data points.

较低的均方根误差 error root-mean-square表示回归线与数据点的拟合更好。

2.The engineer calculated the error root-mean-square 均方根误差 to assess the accuracy of the model.

工程师计算了均方根误差 error root-mean-square以评估模型的准确性。

3.The error root-mean-square 均方根误差 value was used to compare different forecasting models.

使用均方根误差 error root-mean-square值来比较不同的预测模型。

4.In machine learning, minimizing the error root-mean-square 均方根误差 is crucial for improving prediction accuracy.

在机器学习中，最小化均方根误差 error root-mean-square对于提高预测准确性至关重要。

5.To evaluate the performance of the sensor, we measured the error root-mean-square 均方根误差 over several trials.

为了评估传感器的性能，我们在多个试验中测量了均方根误差 error root-mean-square。

作文

In the realm of data analysis and statistics, one often encounters various metrics that help in evaluating the accuracy and reliability of a model. Among these metrics, the error root-mean-square (RMSE) stands out as a crucial measure for assessing the differences between predicted values and observed values. The error root-mean-square is defined as the square root of the average of the squares of the errors, which are the differences between predicted and actual values. This mathematical formulation allows researchers and analysts to quantify the extent of deviation from the expected outcome, providing a clear picture of the model's performance.To understand the significance of the error root-mean-square, it is essential to first grasp the concept of error itself. In any predictive modeling scenario, errors occur when there is a discrepancy between what is predicted by the model and what is actually observed. These discrepancies can arise due to various factors, such as noise in the data, incorrect model assumptions, or inherent variability in the system being studied. The error root-mean-square serves to aggregate these errors into a single value, making it easier to interpret the overall accuracy of the model.The calculation of the error root-mean-square involves several steps. First, the errors are computed by subtracting the predicted values from the actual values. Next, each of these errors is squared to eliminate negative values and to give more weight to larger errors. The mean of these squared errors is then calculated, which represents the average squared error. Finally, taking the square root of this mean yields the error root-mean-square, providing a metric that is in the same units as the original data, thus facilitating interpretation.One of the key advantages of using the error root-mean-square is its sensitivity to large errors. Since the errors are squared before averaging, larger discrepancies have a disproportionately higher impact on the final RMSE value. This characteristic makes RMSE particularly useful in contexts where large errors are especially undesirable, such as in forecasting, engineering, and various scientific applications. For example, in a weather prediction model, a significant deviation from the actual temperature could lead to dire consequences, making it critical to minimize such errors. Therefore, a lower error root-mean-square indicates a better fit of the model to the observed data, highlighting its effectiveness in capturing the underlying patterns.Despite its advantages, the error root-mean-square is not without limitations. One notable drawback is that RMSE can be influenced by outliers, which may skew the results and provide a misleading representation of model performance. Consequently, it is often recommended to use RMSE in conjunction with other metrics, such as Mean Absolute Error (MAE) or R-squared, to gain a more comprehensive understanding of model accuracy. By considering multiple evaluation criteria, analysts can make more informed decisions about the suitability of a model for a particular application.In conclusion, the error root-mean-square is an invaluable tool in the field of data analysis, offering a robust measure for assessing model accuracy. Its ability to highlight discrepancies between predicted and observed values makes it an essential component of model evaluation. However, like any statistical measure, it should be used thoughtfully and in conjunction with other metrics to ensure a well-rounded assessment of model performance. Understanding and applying the error root-mean-square can significantly enhance the quality of insights derived from data, ultimately leading to better decision-making across various domains.

在数据分析和统计学领域，人们常常会遇到各种指标，这些指标有助于评估模型的准确性和可靠性。在这些指标中，误差均方根（RMSE）作为评估预测值与观察值之间差异的重要度量，显得尤为重要。误差均方根的定义是误差平方的平均值的平方根，而误差是指预测值与实际值之间的差异。这一数学公式使研究人员和分析师能够量化与预期结果的偏差程度，从而清晰地了解模型的表现。要理解误差均方根的重要性，首先需要掌握误差的概念。在任何预测建模场景中，当模型预测与实际观察之间存在差异时，就会产生误差。这些差异可能由于多种因素而产生，例如数据中的噪声、模型假设不正确或被研究系统的固有变异性。误差均方根旨在将这些误差汇总为一个单一的值，使得解释模型的整体准确性变得更加容易。误差均方根的计算涉及几个步骤。首先，通过将预测值与实际值相减来计算误差。接下来，将每个误差平方，以消除负值并对较大误差给予更多权重。然后计算这些平方误差的平均值，表示平均平方误差。最后，取这个均值的平方根得到误差均方根，提供一个与原始数据单位相同的度量，从而便于解释。使用误差均方根的一个主要优点是其对大误差的敏感性。由于在平均之前对误差进行了平方处理，因此较大的差异对最终的RMSE值有不成比例的影响。这一特性使得RMSE在大误差特别不可取的背景下特别有用，例如在预测、工程和各种科学应用中。例如，在天气预测模型中，实际温度的重大偏差可能导致严重后果，因此至关重要的是尽量减少此类误差。因此，较低的误差均方根表示模型与观察数据的拟合更好，突显了其捕捉基本模式的有效性。尽管具有优势，误差均方根也并非没有局限性。其中一个显著缺点是RMSE可能会受到离群值的影响，这可能会扭曲结果并提供误导性的模型性能表示。因此，通常建议将RMSE与其他指标（如平均绝对误差（MAE）或R平方）结合使用，以获得对模型准确性更全面的理解。通过考虑多个评估标准，分析师可以就模型在特定应用中的适用性做出更明智的决策。总之，误差均方根是数据分析领域中一项宝贵的工具，提供了评估模型准确性的强大度量。它能够突出预测值与观察值之间的差异，使其成为模型评估的基本组成部分。然而，像任何统计度量一样，它应该被谨慎使用，并与其他指标结合使用，以确保对模型性能进行全面评估。理解和应用误差均方根可以显著提高从数据中得出的洞察质量，最终在各个领域促进更好的决策。