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We have seen in the previous post what mean squared logarithmic error (MSE) is and how it operates behind the scenes. This will be the same as what we saw in the previous article. In this piece, we will attempt to broaden our understanding of Mean Squared Error (MSE) by looking at another variant of the statistic known as the mean squared logarithmic error (MSLE) and how it operates.

When we try to forecast a very large number, we may not want to punish the model as much as we punish it based on its mean squared logarithmic error. However, there are occasions when we may run into specific regression problems. These problems can occur when the target value has a range of values.

When calculating the mean squared logarithmic error (MSLE), the first step is to take each of the expected values and find its natural logarithm.

Mean Squared Error (sometimes called Mean Squared Logarithmic Error) (MSLE).

It’s also a ratio of actual to expected numbers.

**The following is a list of some of the many advantages of using MSLE:**

The only thing that matters to MSLE is the percentage gap that exists between the log-transformed actual values and the anticipated values.

MSLE makes an effort to handle somewhat insignificant discrepancies between tiny actual and predicted values in a manner that is roughly equivalent to how it handles significantly larger disparities between large actual and anticipated values.

MSLE makes an effort to deal with both minor and significant deviations between the actual and anticipated values.

When True = 40 and Anticipated = 30, MSE = 100 and MSLE = 0.07816771. This is the case when the True value is equal to 40 and the forecasted value is equal to 30.

In a similar vein, when we compare the actual value of 4,000 to the forecasted value of 3,000. The MSE was determined to be 100000000, and the MSLE was found to be 0.08271351.

The difference in the MSEs value of these two situations is quite substantial compared to one another. And when we look at the difference in their MSLE values and see how close they are to being the same, or how little of a gap there is between them, we can say that. Consequently, when utilizing MSLE, it endeavors to treat relatively insignificant variations between relatively insignificant actual and anticipated value sets nearly the same as significant differences between relatively significant actual and predicted value sets.

The MSEs of the two different scenarios have a significant and vastly different variations between them. And if you compare the difference in their MSLE values, then we will be able to determine whether or not you are most likely the same or have only a very slight difference. MSLE treats relatively modest variations between actual and anticipated values as noteworthy.

**Underestimations are penalized more on the MSLE.**

MSLE makes an additional effort to punish students who underestimate the value more than those who overestimate the value.

- The two situations both have a true value of 20, but their expected values are 10 and 30, respectively.
- In scenario 1, we can state that the anticipated value is 10 points lower than expected, and in case 2, we can say that the forecasted value is 10 points higher than expected.
- The MSE value that we obtain for both cases is the same, which is equal to 100. However, the values that we get for MSLE are 0.07886 and 0.02861 respectively.
- We can see from this that the disparity between the two values is rather significant. Therefore, we are able to claim that the MSLE punished those who underestimated the worth more than those who overestimated it.
- MSLE has the effect of reducing the harshness of the punishment caused by significant variations in significant projected values.
- When a model is trying to predict an indirect quantity, the MSLE may be a better choice of loss measure to use.

**Applying the mean squared logarithmic error measure**

- When predicted and actual values are high, use RMSLE. This is the case when the predicted and actual values are large.
- You want to predict the restaurant’s future customer count. Because the number of future visitors is a continuous variable, we will be performing a regression analysis. As a loss function, MSLE can be used.

**Python-based implementation of the MSLE protocol**

On any regression problem, we are able to apply the mean squared logarithmic error calculation as follows:

After reading this essay, you have hopefully gained a better understanding of the significance of mean squared logarithmic error (MSLE). InsideAIML covers data science, machine learning, AI, and emerging technologies.

Thank you very much for reading…

MSLE makes an effort to handle somewhat insignificant discrepancies between tiny actual and predicted values in a manner that is roughly equivalent to how it handles significantly larger disparities between large actual and anticipated values.

MSLE makes an effort to deal with both minor and significant deviations between the actual and anticipated values.

When True = 40 and Anticipated = 30, MSE = 100 and MSLE = 0.07816771. This is the case when the True value is equal to 40 and the forecasted value is equal to 30.

In a similar vein, when we compare the actual value of 4,000 to the forecasted value of 3,000. The MSE was determined to be 100000000, and the MSLE was found to be 0.08271351.

The difference in the MSEs value of these two situations is quite substantial compared to one another. And when we look at the difference in their MSLE values and see how close they are to being the same, or how little of a gap there is between them, we can say that. Consequently, when utilizing MSLE, it endeavors to treat relatively insignificant variations between relatively insignificant actual and anticipated value sets nearly the same as significant differences between relatively significant actual and predicted value sets.