Notation for features (general notation for continuous and discrete random variables)

Question

Notation for features (general notation for continuous and discrete random variables)

Yael M

2022年2月26日 16:04

I'm looking for the right notation for features from different types. Let us say that my samples as $m$ features that can be modeled with $X_1,...,X_m$. The features Don't share the same distribution (i.e. some categorical, some numerical, etc.). Therefore, while $X_i$ might be a continuous random variable, $X_j$ could be a discrete random variable.

Now, given a data sample $x=(x_1,...,x_m)$, I want to talk about the probability, for example, $P(X_k=x_k)c$. But $X_k$ might be a continuous variable (i.e. the height of a person). Therefore, $P(X_k=x_k)$ will always be zero. However, it can also be a discrete variable (i.e. categorical feature or number of kids).

I'm looking for a notation that is equivalent to $P(X_k=x_k)$ but can work for both continuous and discrete random variables.

Topic mathematics probability notation statistics

Category Data Science

Erwan · Accepted Answer · 2020年5月27日 14:16

1

Erwan answered at 2020年5月27日 14:16

Maybe relying on set notation would work?

$P(X_k \in s_k)$ where:

$s_k = \{ x_k \}$ if $X_k$ is discrete
$s_k = [ x_k-\epsilon , x_k+\epsilon]$ if $X_k$ is continuous

Valentin Calomme · Accepted Answer · 2020年5月27日 10:26

1

Valentin Calomme answered at 2020年5月27日 10:26

As far as I am concerned, there is no distinction between a continuous and a discrete variable when it comes to notation. So $P(X_k=x_k)$ is perfectly fine for either.

Notation for features (general notation for continuous and discrete random variables)

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