Typos in the Mixed domain type Jupyter example

[yfarjoun]

The Jupyter notebook http://nbviewer.jupyter.org/github/SheffieldML/GPyOpt/blob/master/manual/GPyOpt_mixed_domain.ipynb# seems to have typos that are severe enough to make reading the example confusing.

the text says:

We will consider that variables $x_1$ and $x_2$ are continuous and defined in the interval $[-5,5]$, variable $x_3$ is takes continuous values in the interval $[-1,5]$ and the variables $x_4$ and $x_5$ are discrete and take values ${-3,0,3}$ and ${-5,-1,1,5}$ respectively. Next we define this domain to use it in GPyOpt.

and then the code says:

mixed_domain =[{'name': 'var1', 'type': 'continuous', 'domain': (-5,5),'dimensionality': 3},
{'name': 'var3', 'type': 'discrete', 'domain': (3,8,10),'dimensionality': 2},
{'name': 'var4', 'type': 'categorical', 'domain': (0,1,2),'dimensionality': 1},
{'name': 'var5', 'type': 'continuous', 'domain': (-1,2)}]

questions:

• where's the definition for $x_2$?
• what is 'dimentionality' and why does it have the values specified? (and why does 'var5' not have it?)
• is x_3 in (3,8,10) or continuous in [-1,5]?
• is x_4 categorical (-3,0,3) or (0,1,2)?
• is x_5 cetegorical (-5, -1, 1, 5) or continuous in (-1,2)?
• what is the difference between 'categorical' and 'discrete'?

If there's a difference between categorical and discrete, this is VERY interesting and deserves to be show-cased more. I have an interest in a case of integer domain with relatively large space and so if treated as categorical (with no inference from one value to the next) this is quite worse than if the geometry of integers is taken into consideration in the modeling....

Thanks for this!