SNP 遺伝子型データに基づいて祖先を割り当てるための隠れマルコフ アプローチの実装について、助けを求めたいと思います。そのように生成された遷移行列があるとします。
states <- c("A1","A2","A3","A4","A5","A6","A7","A8") # Define the names of the states
A1 <- c(0.9,0.1,0.1,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A1"
A2 <- c(0.1,0.9,0.1,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A2"
A3 <- c(0.1,0.1,0.9,0.1,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A3"
A4 <- c(0.1,0.1,0.1,0.9,0.1,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A4"
A5 <- c(0.1,0.1,0.1,0.1,0.9,0.1,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A5"
A6 <- c(0.1,0.1,0.1,0.1,0.1,0.9,0.1,0.1) # Set the probabilities of switching states, where the previous state was "A6"
A7 <- c(0.1,0.1,0.1,0.1,0.1,0.1,0.9,0.1) # Set the probabilities of switching states, where the previous state was "A7"
A8 <- c(0.1,0.1,0.1,0.1,0.1,0.1,0.1,0.9) # Set the probabilities of switching states, where the previous state was "A8"
thetransitionmatrix <- matrix(c(A1,A2,A3,A4,A5,A6,A7,A8), 8, 8, byrow = TRUE) # Create an 8 x 8 matrix
rownames(thetransitionmatrix) <- states
colnames(thetransitionmatrix) <- states
thetransitionmatrix # Print out the transition matrix
A1 A2 A3 A4 A5 A6 A7 A8
A1 0.9 0.1 0.1 0.1 0.1 0.1 0.1 0.1
A2 0.1 0.9 0.1 0.1 0.1 0.1 0.1 0.1
A3 0.1 0.1 0.9 0.1 0.1 0.1 0.1 0.1
A4 0.1 0.1 0.1 0.9 0.1 0.1 0.1 0.1
A5 0.1 0.1 0.1 0.1 0.9 0.1 0.1 0.1
A6 0.1 0.1 0.1 0.1 0.1 0.9 0.1 0.1
A7 0.1 0.1 0.1 0.1 0.1 0.1 0.9 0.1
A8 0.1 0.1 0.1 0.1 0.1 0.1 0.1 0.9
発光マトリックスは n 8x4 マトリックスのリストであり、n はデータ内の SNP/行の数に等しくなります。たとえば、3 つの SNP/行にわたる 8 つのサンプル (A1 ～ A8) の次のデータがあるとします。
A1 A2 A3 A4 A5 A6 A7 A8
T T T T T T T C
T C T T T T T C
A A A G G A A A
リストの行列 1 は次のようになります。
A C G T
A1 0 0 0 1/7
A2 0 0 0 1/7
A3 0 0 0 1/7
A4 0 0 0 1/7
A5 0 0 0 1/7
A6 0 0 0 1/7
A7 0 0 0 1/7
A8 0 1 0 0
7 つのサンプルが行 1 に T を持っているため、各サンプルの確率は 1/7 です。A8 だけが C を持っているため、C を A8 に割り当てる確率は 100% です。行 3 の場合、出力は次のようになります。
A C G T
A1 1/6 0 0 0
A2 1/6 0 0 0
A3 1/6 0 0 0
A4 1/2 0 0 0
A5 1/2 0 0 0
A6 1/6 0 0 0
A7 1/6 0 0 0
A8 1/6 0 0 0
前述の遷移行列と放出行列のリストを使用して、対立遺伝子の任意のシーケンスにビタビ アルゴリズムを実装したいと考えています。私が現在持っているコードは、行ごとに異なる放出マトリックスを使用することはできません
viterbi <- function(sequence, transitionmatrix, emissionmatrix)
# This carries out the Viterbi algorithm.
# Adapted from "Applied Statistics for Bioinformatics using R" by Wim P. Krijnen, page 209
# ( cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf )
{
# Get the names of the states in the HMM:
states <- rownames(theemissionmatrix)
# Make the Viterbi matrix v:
v <- makeViterbimat(sequence, transitionmatrix, emissionmatrix)
# Go through each of the rows of the matrix v (where each row represents
# a position in the DNA sequence), and find out which column has the
# maximum value for that row (where each column represents one state of
# the HMM):
mostprobablestatepath <- apply(v, 1, function(x) which.max(x))
# Print out the most probable state path:
prevnucleotide <- sequence[1]
prevmostprobablestate <- mostprobablestatepath[1]
prevmostprobablestatename <- states[prevmostprobablestate]
startpos <- 1
for (i in 2:length(sequence))
{
nucleotide <- sequence[i]
mostprobablestate <- mostprobablestatepath[i]
mostprobablestatename <- states[mostprobablestate]
if (mostprobablestatename != prevmostprobablestatename)
{
print(paste("Positions",startpos,"-",(i-1), "Most probable state = ", prevmostprobablestatename))
startpos <- i
}
prevnucleotide <- nucleotide
prevmostprobablestatename <- mostprobablestatename
}
print(paste("Positions",startpos,"-",i, "Most probable state = ", prevmostprobablestatename))
}
# the viterbi() function requires a second function makeViterbimat():
makeViterbimat <- function(sequence, transitionmatrix, emissionmatrix)
# This makes the matrix v using the Viterbi algorithm.
# Adapted from "Applied Statistics for Bioinformatics using R" by Wim P. Krijnen, page 209
# ( cran.r-project.org/doc/contrib/Krijnen-IntroBioInfStatistics.pdf )
{
# Change the sequence to uppercase
sequence <- toupper(sequence)
# Find out how many states are in the HMM
numstates <- dim(transitionmatrix)[1]
# Make a matrix with as many rows as positions in the sequence, and as many
# columns as states in the HMM
v <- matrix(NA, nrow = length(sequence), ncol = dim(transitionmatrix)[1])
# Set the values in the first row of matrix v (representing the first position of the sequence) to 0
v[1, ] <- 0
# Set the value in the first row of matrix v, first column to 1
v[1,1] <- 1
# Fill in the matrix v:
for (i in 2:length(sequence)) # For each position in the DNA sequence:
{
for (l in 1:numstates) # For each of the states of in the HMM:
{
# Find the probabilility, if we are in state l, of choosing the nucleotide at position in the sequence
statelprobnucleotidei <- emissionmatrix[l,sequence[i]]
# v[(i-1),] gives the values of v for the (i-1)th row of v, ie. the (i-1)th position in the sequence.
# In v[(i-1),] there are values of v at the (i-1)th row of the sequence for each possible state k.
# v[(i-1),k] gives the value of v at the (i-1)th row of the sequence for a particular state k.
# transitionmatrix[l,] gives the values in the lth row of the transition matrix, xx should not be transitionmatrix[,l]?
# probabilities of changing from a previous state k to a current state l.
# max(v[(i-1),] * transitionmatrix[l,]) is the maximum probability for the nucleotide observed
# at the previous position in the sequence in state k, followed by a transition from previous
# state k to current state l at the current nucleotide position.
# Set the value in matrix v for row i (nucleotide position i), column l (state l) to be:
v[i,l] <- statelprobnucleotidei * max(v[(i-1),] * transitionmatrix[,l])
}
}
return(v)
}