Disclaimer: Dieser Thread wurde aus dem alten Forum importiert. Daher werden eventuell nicht alle Formatierungen richtig angezeigt. Der ursprüngliche Thread beginnt im zweiten Post dieses Threads.
Question regarding Solution 8
Hi,
I just went through the solution for task 8.
First of (Wednesday = 0 )
I found some points rather confusing:
-
We have a primary State M_0 with which we start. This is basically f_0:0.
Because we start at 0 shouldn’t the annotations be always (0:N) because we start from 0? -
We then do our backward step after we calculated f_1:1 (or f_0:1)
But should we first calculate f_1:2 (f_0:2) so that this backward step makes sense? I thought that backward is just smoothing.
I calculated f_0:2 and then started the backward step.
I got b_2:2 = P (J_2:1|M_2) = P (|M_2) = (1,1,1)^T
After that I got to the backward solution with :
b_1:2 = T * 0_1 * b_2:2
And finally got the probability with:
P(M_1|J_1:2) = α * f_0:1 × b_1:2
The solution calculates with b_2:2 which is the should the state for Friday and not for Thursday if I am not mistaken.
I would be really glad for some feedback.
Best,
Marius Hanisch
I can only give two short answers for now. I’ll look into it more and try to figure out what the logic behind them is.
-
Both the book and the lecture notes use this kind of notation, with 0 denoting the starting time (before we have any evidence). This carries over to f_1:n. What is basically f_0:0 does not use any evidence, so this could be the reason for the notation, while f_1:1 does.
-
Confusingly enough, the smoothing formula and algorithm don’t do exactly the same thing. Let’s fix k to be the time we are interested in. The formula uses f_1:k for the time until k and then b_k+1:n to use the “future” evidence. On the other hand, the Forward-Backward algorithm performs forward updates until time n, and then moves backward.