backward: Infer the backward probabilities for all the nodes of the treeHMM

Description

backward calculates the backward probabilities for all the nodes

Usage

backward(hmm, observation, bt_seq, kn_states = NULL)

Arguments

hmm

hmm Object of class List given as output by initHMM

observation

A list consisting "k" vectors for "k" features, each vector being a character series of discrete emmision values at different nodes serially sorted by node number

bt_seq

A vector denoting the order of nodes in which the tree should be traversed in backward direction(from leaves to roots). Output of bwd_seq_gen function.

kn_states

(Optional) A (L * 2) dataframe where L is the number of training nodes where state values are known. First column should be the node number and the second column being the corresponding known state values of the nodes

Value

(N * D) matrix denoting the backward probabilites at each node of the tree, where "N" is possible no. of states and "D" is the total number of nodes in the tree

Details

The backward probability for state X and observation at node k is defined as the probability of observing the sequence of observations e_k+1, ... ,e_n under the condition that the state at node k is X. That is:b[X,k] := Prob(E_k+1 = e_k+1, ... , E_n = e_n | X_k = X) where E_1...E_n = e_1...e_n is the sequence of observed emissions and X_k is a random variable that represents the state at node k

Examples

Run this code

# NOT RUN {
tmat = matrix(c(0,0,1,0,0,0,0,1,0,0,0,0,0,1,1,0,0,0,0,0,0,0,0,0,0),
               5,5, byrow= TRUE ) #for "X" (5 nodes) shaped tree
hmmA = initHMM(c("P","N"),list(c("L","R")), tmat) #one feature with two discrete levels "L" and "R"
obsv = list(c("L","L","R","R","L")) #emissions for the one feature for the 5 nodes in order 1:5
bt_sq = bwd_seq_gen(hmmA)
kn_st = data.frame(node=c(3),state=c("P"),stringsAsFactors = FALSE) 
                   #state at node 3 is known to be "P"
BackwardProbs = backward(hmmA,obsv,bt_sq,kn_st)
# }