Details of variance, standard deviation, and mean square error, and variance error details

Details of variance, standard deviation, and mean square error, and variance error details
Variance

In Baidu encyclopedia, variance is interpreted as: (variance) a measure of the degree of discretization in the measurement of random variables or a set of data in probability theory and statistical variance. In probability theory, variance is used to measure the deviation between a random variable and its mathematical expectation (that is, the mean. The variance (sample variance) in the statistics is the mean of the Square Value of the difference between each sample value and the average of all sample values. In many practical problems, it is important to study variance, that is, deviation degree.

Variance is a measure of the difference between the source data and the expected value.

Assume that there is a set of discrete data xn = [x1, x2, x3, x4 ........ xn] "role =" presentation "> xn = [x1, x2, x3, x4 ........ xn] xn = [x1, x2, x3, x4 ........ xn]. Mean Value of data: x Kernel = Sigma 1 nxin "role =" presentation "> x Kernel kernel = Sigma n1xkernel kernel = Sigma 1 nxin, then the variance of the data is var = Σ 1n (x −x percentile) 2n "role =" presentation "> var = Σ n1 (x? X ˉ) 2 nvar = Σ 1n (x? X percentile) 2n.

Standard Deviation

Standard Deviation, also known as mean variance, is the square root of the arithmetic mean of the squared Deviation. Standard deviation is the arithmetic square root of variance. The standard deviation reflects the degree of discretization of a dataset. For two groups of data with the same mean, the standard deviation may not be the same.

Standard deviation can be used as a measurement of uncertainty. For example, in physical science, when performing repetitive measurements, the standard deviation of the set of measurements represents the accuracy of these measurements. To determine whether the measured value meets the predicted value, the standard deviation of the measured value plays a decisive role. If the difference between the measured average value and the predicted value is too far (compared with the standard deviation value), the measured value and the predicted value are considered to be in conflict. This is easy to understand, because if the measured values are out of a certain range, you can reasonably infer whether the predicted values are correct.

The standard deviation and variance have an open square relationship, that is, Delta = var "role =" presentation "> Delta = var ??? √ Delta = var

Mean Squared Error

The mean squared error (MSE) is different from the mean squared error (mean squared error). The mean squared error is the mean of the sum of the squares of distance between different data values, that is, the mean of the sum of squares of errors, expressed by σ. Mean square error can be used in loss functions in Machine Learning for prediction and regression. The mean square error formula is as follows:

σ = Σ 1n (xi −si') 2n "role =" presentation "> σ = Σ n1 (xi? Si') 2n σ = Σ 1n (xi? Si') 2n

Finally, the relationship is as follows:

1. mean variance is the standard deviation, and standard deviation is the mean variance

2. mean square error is different from mean square error

3. mean square error is the mean of the sum of the squared distance between the actual values of each data.