Which are outliers? I am in the process of solving a Machine Learning challenge, and I want to do it the right way.
I did some exploratory data analysisand I wanted to check the distribution of the data.
As displayed in the figure below, the box plots of each of the numerical continuous dataset features.
According to my understanding, several features do contain outliers, but after reading some articles, I encountered cases where outliers are mistaken for a Pareto distribution, and removing them leads to information loss.

Could you please explain which contain and which do not contain outliers?

Outliers, like beauty and much else, are often in the eye of the beholder.
Identifying outliers is often treated as if it were a matter of knowing that your data are a mix of gazelles (regular beasts) and giraffes (probably large, awkward and unwanted), so the problem is to tell which is which.  In real applications, it may not be obvious that there are two  such distinct subsets, even in abstract principle. And even if the principle is accepted, it can be hard in practice to tell them apart: imagine how you would proceed  if the variables were height, weight, and number of legs and there are known to be young giraffes in the data.
Box plots are routinely misused in this context. First of all, although box plots were (re-)introduced by John W. Tukey in the 1970s, he himself played with several different conventions, and later people haven't stopped inventing different variations -- which could be worthwhile experiment. Unfortunately users often fail to explain in reports which detailed rules their software uses -- which is not helpful.
Here I guess that the convention being followed is one Tukey introduced: plot data points individually whenever any is more than 1.5 IQR from the nearer quartile. Here IQR is interquartile range or upper quartile MINUS lower quartile. Tukey himself regarded this just as a way of identifying data points that need to be thought about, and not at all as a reliable criterion for identifying points that should be rejected. Indeed, sometimes outliers (and skewness) are a signal that data should be analysed on a transformed scale and/or that they need resistant or robust summaries. .
I won't try to say which of your data points are outliers, because

*

*The whole idea that some points are expected to be BAD outliers or problematic, and the rest GOOD, needs to be argued in each case. For example, in banking some transactions are rogue and most are honest, so there is strong concern to identify rogues, which is rarely easy. In many other fields, strongly skewed distributions are entirely expected and the larger outliers are known extremes (the Amazon, or Amazon, say).


*There are no outliers except in relation to an implicit or explicit model of what is expected. If one distribution is expected to be (roughly) normal and another (roughly) Poisson or anything else, I have quite different expectations of whether outliers are likely and how to detect them. (This is the kind of point made in the question with the example of a Pareto distribution.) Here the data are just labelled X without even a signal for whether they are versions of the same (kind of) variable or whether they are quite different.


*Box plots alone are inadequate to make the decision even if #1 and #2 are satisfied.  I'd much prefer dot or quantile plots. I'd also want to know the number of data points, which is impossible to discern precisely. But by failing to show simple patterns box plots can signal that you need another and a deeper look. Some of the box plots above are degenerate in that median and quartiles are identical, or very close, so that the box collapses to a line: in that case every other data point is plotted individually. (If the IQR is zero, every point beyond the quartiles must be plotted individually!)  Such a pattern could be anything from the quirks of small samples to some special situation: the box plots alone cannot do more than flag an oddity. Specifically X27 X31 X33 spring out as demanding careful scrutiny.


*Specifically the numerical labels for these data suggest that the data were standardized first (likely by (value MINUS mean) / SD): this pre-processing is over-valued and inhibits or prohibits reading off basic characteristics of the data, such as



*

*the data being all positive


*the data being all positive or zero


*the data being positive, zero or negative


*whether only certain values occur (e.g. discrete grades or counts that are integers). This is one of the worst problems, as box plots are often hard work with such data. Repeated values plot as one symbol or contribute to compressed boxes. X33 seems possibly an example as there are perhaps only 3 distinct values; they may even be nominal codes with no intrinsic meaning.
