在HMM中实施维特比算法，改变基因组标记的发射矩阵

Question

我想请求帮助实施基于SNP基因型数据分配祖先的隐马尔可夫方法。 鉴于我有一个生成的转换矩阵：

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

发射矩阵是n个8×4矩阵的列表，其中n等于数据中的SNP /行数。 例如，给出3个SNP /行的8个样本（A1-A8）的以下数据：

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

列表中的矩阵1将是

   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

由于7个样品在第1行中具有T，因此每个样品的概率为1/7。 由于只有A8拥有C，因此将A分配给A8的可能性为100％。 对于第3行，输出应为

   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

使用上述转换矩阵和发射矩阵列表，我希望将Viterbi算法应用于任何等位基因序列。 我目前拥有的代码无法为每一行使用不同的发射矩阵

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)
  }

Answer 1

什么阻止你简单地给函数一个预先计算的发射矩阵列表而不是一个？

makeViterbimat <- function(sequence, transitionmatrix, emissionmatrixList)
  # 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:
 {
    emissionmatrix = emissionmatrixList[[i]]
    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)
  }

或者你是如何构建这个emissionmatrixList的问题？