Why minimize quadratic errors? Repair immediatelyJuly 15, 2020 by Logan Robertson
It is worth reading these corrective recommendations when you find out why you minimize the square error on your computer. Minimizing the smallest quadratic loss is equivalent to minimizing the variance! This explains why the slightest loss of square works for a lot of problems. The main noise due to CLT is very often Gaussian, and minimizing the squared error is correct!
In statistics, the mean square error (MSE) or standard deviation (MSD) of an estimate (a method for estimating an unobservable value) measures the mean of the squared errors, i.e. the standard deviation between the estimated values and the current value. MSE is a risk function that corresponds to the expected value of the squared error loss. The fact that ESM is almost always strictly positive (and not null) is due to the random nature or the fact that the evaluator does not take into account information that can provide a more accurate estimate. 
MSE is an indicator of the quality of the evaluator - it is not always negative, and values close to zero are better.
MSE is the second point (around the source) of the error, taking into account both the variance of the estimate (how far the estimates are distributed from the data sample to another) and its bias (how far from the average) the estimated value comes from the truth). For an undistorted assessment, MSE is the variance of the assessment. Like variance, MSE has the same units as the square of the calculated sum. Similar to standard deviation, square root from the MSE gives the standard error or standard error (RMSE or RMSD), which has the same units as the calculated value. For an undistorted estimate, the RMSE is the square root of the variance called the standard error.
Definition And Basic Properties 
MSE evaluates the quality of the population predictor (that is, a function that maps arbitrary input data to a sample of random values) or an estimate (that is, say a mathematical function that maps a sample of data to a parameter estimate) where the data comes from). The definition of MSE differs depending on whether you are describing a predictor or evaluator.
If the vector
In other words, MSE is the mean
MSE can also be calculated for q data points that were not used in the evaluation of the model, either because they were stored for this purpose, or because these data were obtained recently. In this process, known as cross-validation, MSEs are often referred to as root-mean-square errorazanias and calculate
This definition depends on an unknown parameter, but the MSE is a priori a property of the evaluator. MSE may be a function of unknown parameters. In this case, any MSE evaluator based on estimates of these parameters will be a data function and therefore a random variable. If the evaluator has
MSE can be written as the sum of the variance of the estimate and the squared bias of the estimate, which is a useful method for calculating MSE and implies that in the case of distorted estimates, the MSE and variance are equivalent. 
In regression analysis, plotting is a more natural way to show the general trend of all data. The average distance from each point to the predicted regression model can be calculated and displayed as the standard error. Squaring is necessary to reduce the complexity of negative symptoms. To minimize this, the model can be more accurate, which means that the model is close enough to the actual data. An example of linear regression using This method is the least squares method. This is a method for assessing the ability of a linear regression model to model a two-dimensional data set  , but the limitation is related to the known distribution of data.
The term rms error is sometimes used to denote an undistorted estimate of the variance of the error: the remaining sum of squares divided by the number of degrees of freedom. This definition for a known calculated quantity differs from the above definition for a calculated MSE predictor in that a different denominator is used. The denominator is the sample size, which is reduced by the number of model parameters (n-p) estimated from the same data.
- gradient descent
- average squared
- loss function
- summed squared
- neural networks
- conditional expectation
- linear regression
- least squares regression line
- squared residuals
- root mean
- unbiased estimator
- cost function
- Squared Mean Root Error
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