21MAY2019
Relevant Information -

1. What should be xgb dmatrix for Interval regression ?
   Ans :- Create two column for all the times
   2-column matrix representation of outputs=labels.
2. un-censored output, event is obserrved, e.g. y_i = 5. (5, 5)

survival::Surv(10, 10, type="interval2")
[1] 10

2. left-censored output, event not observed, but we know it happened some time before t_i=5. y_i = (-Inf = \underline y_i, 5=t_i=\overline y_i)

survival::Surv(-Inf, 10, type="interval2")
[1] 10-

3. Right-censored output, event not observed , but we know it happened some time after t_i =5. y_i = (5,inf)

survival::Surv(5, Inf, type="interval2")
[1] 5+

4. Interval-censored output, event not observed, but we know it happened some time in y_i = (5,10)

survival::Surv(5, 10, type="interval2")
[1] [5, 10]

There is no need for the survival object. This is more of a legacy.

2. How to handle sigma in AFT?
   Ans:- Treat as a hyperparameter.

3. What is the dimension of the predicted value of interval regression?
   Ans:- It is always one real value, not interval.

Relevant Document
https://github.com/tdhock/aft-poster/blob/master/HOCKING-AFT.pdf
http://members.cbio.mines-paristech.fr/~thocking/survival.pdf
https://bmcbioinformatics.biomedcentral.com/articles/10.1186/1471-2105-9-269

Please Check.
@tdhock, @hcho3