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

In dagHMM: Directed Acyclic Graph HMM with TAN Structured Emissions

Infer the backward probabilities for all the nodes of the dagHMM

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	Dataframe containing the discritized character values of only covariates at each node. Column names of dataframe should be same as the covariate names. Missing values should be denoted by "NA".
bt_seq	A vector denoting the order of nodes in which the DAG 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

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

Value

(2 * N) matrix denoting the backward probabilites at each node of the dag, where "N" is the total number of nodes in the dag

See Also

forward

Examples

library(bnlearn)

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 dag
states = c("P","N") #"P" represent cases(or positive) and "N" represent controls(or negative)
bnet = model2network("[A][C|A:B][D|A:C][B|A]") #A is the target variable while
                                               #B, C and D are covariates
obsvA=data.frame(list(B=c("L","H","H","L","L"),C=c("H","H","L","L","H"),D=c("L","L","L","H","H")))
hmmA = initHMM(States=states, dagmat= tmat, net=bnet, observation=obsvA)
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(hmm=hmmA,observation=obsvA,bt_seq=bt_sq,kn_states=kn_st)

dagHMM documentation built on Jan. 11, 2023, 1:13 a.m.