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Ensuring It Works – How Do You Know?
Published in James Luke, David Porter, Padmanabhan Santhanam, Beyond Algorithms, 2022
James Luke, David Porter, Padmanabhan Santhanam
Three popular metrics that characterise errors in regression models are: Mean Square Error (MSE) is the error in the model captured as the sum of the squares of the difference between the prediction and the actual value in the training data, divided by the number of predictions. The goal of the modelling process is to find specific values of the model parameters that minimise this error. Obviously, smaller MSE is better.A related metric is Root Mean Square Error (RMSE) which is just the square root of the MSE. A simple interpretation of the RMSE for the linear regression model is that the prediction of the model is within ±17.839 kg of the actual for 68% of the data, when the error is normally distributed.R2 (R-Square) represents the percentage variation of the output that is explained by the input variable(s). It ranges between 0 and 1. In our example, R2 = 0.64 means, 64% of the variation in the weight is explained by the height. During the model creation activity, this metric also helps to do better feature engineering by identifying input variables (i.e. features) that do not contribute much to quality of the model and hence can be removed from the analysis.
Machine Learning Perspective in Additive Manufacturing
Published in Shwetank Avikal, Amit Raj Singh, Mangey Ram, Sustainability in Industry 4.0, 2021
Mayuresh S. Suroshe, Vaibhav S. Narwane, Rakesh D. Raut
Mean Square Error (MSE) is an average of the squares of the error between target and output values. The smaller the MSE, the closer the results are to the best fit or results with low error. Thus, a well-trained NN should have very low MSE (close to zero). In the performance plot, the best validation performance is 0.002237 at epoch 9. Out of 15 iterations of the system to classify or compare the data, the best performance is obtained at the ninth iteration. After training, the error reduces for more epochs but can start to increase instead when the network overfits the data. If validation error increases six consecutive times, then the training will stop. It takes the best training performances among all epochs with the least error. For this example, the plot indicates that the test and validation curves are not far from each other hence it signifies that the performance plot does not point out any serious problems with the training. In case some overfitting is present then the test curve will increase significantly before the validation curve. These signs indicate the presence of random error in the data. Refer Figure 8.8 for the performance plot.
Applications of Sensors to Physical Measurements
Published in Robert B. Northrop, Introduction to Instrumentation and Measurements, 2018
The root-mean squared error (RMSE) is simply the square root of the MSE. From Equation 7.156, we can illustrate the three principal error statistics used by GPS manufacturers and evaluators. CEP or circular error probable assumes that Pr(ε ≤ r) = 0,5. r = 0.83 for this to happen. This means that for large N, about half the positions determined will lie inside a circle of radius r = 0.83 × RMSE. If r = 1 RMSE, 63% of a large number of measurements will lie inside a circle of this radius. Finally, the Rayleigh probability model tells us that if r = 1,73 × RMSE, the probability is that 95% of the measurement points will lie inside a circle with this radius drawn around the known location of the receiver. One problem in evaluating GPS receiver performance is that manufacturers often just give a statement such as error = 1 m without specifying how the error is evaluated.
Reactive Black 5 Removal with Ozone on Lab-scale and Modeling
Published in Ozone: Science & Engineering, 2023
Bülent Sari, Hakan Güney, Selman Türkeş, Olcayto Keskinkan
Ghaedi et al. (2018) used the MSE value in addition to R2 in the evaluation and selection of the developed models. In the evaluation of the models developed in this study, MSE was considered as another criterion. Schluchter (2014) defined MSE as a measure of the approximation of the estimate to the observed value. MSE expresses the reliability and accuracy of the developed model as well as how much the estimate deviates systematically from the observed value and the precision (variance) of the model. On the other hand, Gadekar and Ahammed (2019) reported that the MSE value should be close to zero, and by comparing the color removal prediction algorithms they developed, they chose the algorithm with the lowest MSE value although the R2 value was low compared to other algorithms.
Prediction of Hydraulic Blockage at Culverts using Lab Scale Simulated Hydraulic Data
Published in Urban Water Journal, 2022
Umair Iqbal, Muhammad Zain Bin Riaz, Johan Barthelemy, Pascal Perez
Standard evaluation metrics such as MSE, MAE, and score were used to analyse machine learning regression models’ performance. Mean Squared Error (MSE) is a metric that indicates a model’s absolute quality of fit and is computed by dividing the sum of the squares of the prediction error (i.e. actual minus predicted) by the total number of data samples. It returns an absolute real value indicating the extent to which the projected results differ from the actual findings. MSE is well-suited for comparing various regression models and selecting the best model in comparison to the others. The mathematical expression for the MSE is given in Equation 3.
A comparative study of prediction and classification models on NCDC weather data
Published in International Journal of Computers and Applications, 2022
Ibrahim Gad, Doreswamy Hosahalli
There are various metrics used to assess the efficiency and performance of different classification and regression models. Firstly, the most commonly used metrics to evaluate the performance of regression models are R squared (R2), mean squared error (MSE), root mean squared error (RMSE) and mean absolute error (MAE). MSE is the average value of the sum of squared differences between true values and predicted. RMSE is calculated by the squared root of MSE. MAE is calculated by the average value of the sum of absolute differences between true values and predicted [31, 32]. Where is the predicted value, is the mean value and is the actual value.