In Simple terms, log transform squashes or compresses range of large numbers and expands the range of small numbers. So if x is larger, then slower the log(x) increments.

用简单的术语来说，对数变换可以挤压或压缩大数范围，并扩大小数范围。 因此，如果x较大，则log(x)的增量会变慢。

If you closely look at the plot above, which actually talks about log transformation on values ranging from 1 to 1000. As we can see from the plot, log has transformed values from [1,1000] into [0,7] range.

如果仔细看一下上面的图，它实际上是关于从1到1000的值的对数转换。从图中可以看出，对数已将值从[1,1000]转换为[0,7]范围。

Note that how x values from 200 to 1000 get compressed into just ~5 and 7. So the larger the x, slower the log(x) increments.

请注意，如何将200到1000之间的x值压缩为仅〜5和7。因此，x越大，log(x)的增量越慢。

Log is only defined when x>0. Log 0 is undefined. It’s not a real number, let’s say Log (base 10) 0=x, so 10^x=0, if you try to solve this, you will see that no value of x raised to the power of 10 gives you zero. 10⁰ is also 1.

仅在x> 0时定义对数。 日志0未定义。 它不是一个实数 ，比方说对数(以10为底)0 = x，所以10 ^ x = 0，如果尝试解决这个问题，您会发现x的任何数值都不提高到10的幂。 10⁰也是1。

Log transform is also known as variance stabilizing transform, which is useful when dealing with heavy tailed distributions. Log transform can make highly skewed distributions less skewed. So log transform reduces or removes skewness in data.

对数变换也称为方差稳定变换，在处理重尾分布时很有用。 对数变换可以使高度偏斜的分布减少偏斜。 因此，对数变换可以减少或消除数据的偏斜。

使用对数变换作为特征工程技术： (Using Log transform as feature engineering technique:)

To reduce or remove skewness in our data distribution and make it more normal (A.K.A Gaussian distribution) we can use log transformation on our input features (X).

为了减少或消除数据分布中的偏斜并使之更正态(又称高斯分布)，我们可以对输入要素(X)使用对数变换。

We usually see heavy tailed distributions in real world data where values are right skewed(More larger values in distribution) and left skewed(More smaller values in distribution). Algorithms can be sensitive to such distribution of values and can under perform if the range is not properly normalized.

我们通常会在现实世界数据中看到重尾分布，其中值右偏(分布中的值更大)和左偏(分布中的值更小)。 算法可能对这种值的分布很敏感，如果范围未正确归一化，则算法可能会表现不佳。

It is common practice to apply a logarithmic transformation on the data so that the very large and very small values do not negatively affect the performance of a learning algorithm. Log transform reduces the range of values caused by outliers.

通常的做法是对数据应用对数转换 ，以使非常大和非常小的值都不会对学习算法的性能产生负面影响。 对数变换可减少由异常值引起的值范围。

However it is important to remember that once log transform is done, observing data in its raw form will no longer have the same original meaning, as Log transforming the data.

但是，重要的是要记住，一旦完成对数转换，以原始形式观察数据将不再具有与对数进行数据转换相同的原始含义。

Next question is: when we do linear regression and get coefficient for X (Independent variable) how do we interpret log transformed independent variables (X) coefficient (Feature importance).

下一个问题是：当我们进行线性回归并获得X(独立变量)的系数时，我们如何解释对数变换后的独立变量(X)系数(特征重要性)。

For Independent variable(X) Divide the coefficient by 100. This tells us that a 1% increase in the independent variable increases (or decreases) the dependent variable by (coefficient/100) units.

对于自变量(X)，将系数除以100。这告诉我们，自变量增加1％，因变量增加(或减少)的系数为(系数/ 100)单位。

Example: the coefficient is 0.198. 0.198/100 = 0.00198. For every 1% increase in the independent variable, our dependent variable increases by about 0.002.

示例 ：系数为0.198。 0.198 / 100 = 0.00198。 自变量每增加1％，我们的因变量将增加约0.002。

Note: I’m also attaching a link below which dives deep into interpreting log transformed features.

注意 ：我还将在下面附加一个链接，以深入了解解释日志转换的功能。

在目标变量上使用对数变换： (Using Log transform on target variable:)

For example let’s consider a machine learning problem where you want to predict price of a house based on input features like (Area, number of bed rooms,…etc).

例如，让我们考虑一个机器学习问题，您希望根据输入特征(面积，床房数量等)来预测房屋价格 。

In this problem if you choose to create a linear regression model to fit prices(y) on X(Area, number of bed rooms….) and gradient descent in optimizing the model, the dataset would have some extreme prices (higher values properties) due to which your gradient descent algorithm would focus more on optimizing higher valued properties(Due to large error) and hence would produce a bad model. So performing a log transform on target variable makes sense when your performing linear regression.More importantly linear regression can predict values that are any real number (Negative values). If your model is far off, it can produce negative values, especially when predicting some of the cheaper houses. Real world values like price, income, stock price are positive so its good to log transform it before using linear regression otherwise the linear regression would predict negative values as predictions which doesn’t make sense.

在此问题中，如果您选择创建线性回归模型以在X(面积，床位数…。)上拟合价格(y)，并在优化模型时采用梯度下降，则数据集将具有一些极端价格(较高值的属性)因此，您的梯度下降算法将更多地专注于优化更高价值的属性(由于误差较大)，因此会产生错误的模型。 因此，在执行线性回归时，对目标变量执行对数转换是有意义的。更重要的是，线性回归可以预测任何实数的值(负值)。 如果您的模型相差太远，则可能会产生负值，尤其是在预测一些较便宜的房屋时。 诸如价格，收入，股票价格等现实世界中的值都是正值，因此在使用线性回归之前最好先对其进行对数转换，否则线性回归会将负值预测为没有意义的预测。

If you look at the above example, if you chose to go with RMSE as the cost function then the model would focus more on high valued properties and would perform bad. If you chose log(Actual)-log(Predicted) value it intuitively works in optimizing the model and thereby produce a good model.

如果看上面的示例，如果选择将RMSE作为成本函数，则该模型将更多地关注高价值的房地产，并且表现不佳。 如果选择log(Actual)-log(Predicted)值，则可以直观地优化模型，从而生成一个好的模型。

Model will be under more pressure on correcting large errors due to High valued properties so using log here makes sense.

由于具有高价值的属性，模型在校正大错误时将承受更大的压力，因此在此处使用log是有意义的。

Converting to actual predictions using np.exp:But you would need actual predictions not the log of predictions, so you can always convert back to actual predictions using exponential of the value (Log(price)).

使用np.exp转换为实际预测：但是您将需要实际预测而不是预测的对数，因此您始终可以使用值的指数(Log(price))转换回实际预测。

日志损失以改善模型 (Log loss to improve models)

Logarithmic loss (related to cross-entropy) measures the performance of a classification model where the prediction input is a probability value between 0 and 1. The goal of our machine learning models is to minimize this value. A perfect model would have a log loss of 0. Log loss increases as the predicted probability diverges from the actual label. So predicting a probability of .012 when the actual observation label is 1 would be bad and result in a high log loss.

对数损失(与交叉熵有关 )用于衡量分类模型的性能，其中预测输入为0到1之间的概率值。我们的机器学习模型的目标是最小化该值。 理想模型的对数损失为0。对数损失随着预测概率与实际标签的偏离而增加。 因此，当实际观察标签为1时预测0.01的概率将很糟糕，并会导致较高的对数损失。

If you look at the above example when true value is 1 and predicted probability is 0.1, the log loss is high. Whereas when true value is 1 and predicted probability is 0.9, log loss is low.

如果看上面的示例，当true值为1且预测概率为0.1时，对数损失很高。 而当真实值为1且预测概率为0.9时，对数损失较低。

文本分类中的日志转换(自然语言处理) (Log transformation in Text Classification (Natural language processing))

We use tf-idf method to encode our text data to fit machine learning models. Tf-idf uses log transform on inverse document frequency, so the word that appears in every single document will be effectively zeroed out, and a word that appears in very few documents will have an even larger count than before.

我们使用tf-idf方法对文本数据进行编码，以适合机器学习模型。 Tf-idf对文档的逆频率使用对数变换，因此每个文档中出现的单词将被有效地清零，而在很少文档中出现的单词的计数将比以前更大。

Please share this article if it helped you understand how important log is to machine learning. Do comment if you have any questions.

如果可以帮助您了解日志对机器学习的重要性，请分享此文章。 如有任何疑问，请发表评论。

GOOD DAY!

美好的一天！

Reference:1. https://data.library.virginia.edu/interpreting-log-transformations-in-a-linear-model/#:~:text=We%20simply%20log%2Dtransform%20x.&text=To%20interpret%20the%20slope%20coefficient%20we%20divide%20it%20by%20100.&text=The%20result%20is%20multiplying%20the,variable%20by%20the%20coefficient%2F100.2. http://wiki.fast.ai/index.php/Log_Loss#:~:text=Logarithmic%20loss%20(related%20to%20cross,a%20log%20loss%20of%200.

参考： 1. https://data.library.virginia.edu/interpreting-log-transformations-in-a-linear-model/#:~:text=We%20simply%20log%2Dtransform%20x.&text=To% 20解释％20the％20slope％20coefficient％20we％20divide％20it％20by％20100。＆text =％20result％20is％20乘以％20the，可变％20by％20the％20coefficient％2F100。 2. http://wiki.fast.ai/index.php/Log_Loss#:~:text=Logarithmic%20loss%20(related%20to%20cross,a%20log%20loss%20of%200。