Lets say we have a dependent variable $Y$ with few categories and set of independent variables.  

What are the advantages of multinomial logistic regression over set of binary logistic regressions (i.e. [one-vs-rest scheme](https://en.wikipedia.org/wiki/Multiclass_classification#One-vs.-rest))? By set of binary logistic regression I mean that for each category $y_{i} \in Y$ we build separate binary logistic regression model with target=1 when $Y=y_{i}$ and 0 otherwise.