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Type: Package
Title: Plot Hidden Markov Models
Version: 2023.8.28
Description: Hidden Markov Models are useful for modeling sequential data. This package provides several functions implemented in C++ for explaining the algorithms used for Hidden Markov Models (forward, backward, decoding, learning).
License: GPL-2 | GPL-3 [expanded from: GPL (≥ 2)]
Imports: Rcpp (≥ 1.0.7)
LinkingTo: Rcpp, RcppArmadillo
Suggests: testthat, knitr, markdown, R.utils, covr, depmixS4, data.table, ggplot2, neuroblastoma, microbenchmark
VignetteBuilder: knitr
NeedsCompilation: yes
Packaged: 2023-09-05 04:12:33 UTC; tdhock
Author: Toby Hocking [aut, cre]
Maintainer: Toby Hocking <toby.hocking@r-project.org>
Repository: CRAN
Date/Publication: 2023-09-05 22:10:02 UTC

Backward algorithm

Description

Efficient implementation of backward algorithm in C++ code, for N data and S states.

Usage

backward_interface(
  log_emission_mat, log_transition_mat)

Arguments

log_emission_mat

N x S numeric matrix of log likelihood of observing each data point in each state.

log_transition_mat

S x S numeric matrix; log_transition_mat[i,j] is the log probability of going from state i to state j.

Value

N x S numeric matrix of backward log likelihood.

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=10)
set.seed(1)
N.data <- length(data.mean.vec)
y.vec <- rnorm(N.data, data.mean.vec)
##model.
n.states <- 3
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
state.mean.vec <- c(-1, 0, 1)*0.1
sd.param <- 1
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
plotHMM::backward_interface(log.emission.mat, log.A.mat)

Buggy data with 5 states

Description

Data was observed to error with depmixS4 and five states

Usage

data("buggy.5states")

Format

The format is a data table.

Buggy data with one state

Description

This data set was known to produce an error with depmixS4 using one state.

Usage

data("buggy.data")

Format

The format is a data table.

Log probability arithmetic

Description

Binary operators in log probability space, to avoid numerical underflow.

Usage

elnproduct(elnx, elny)
elnsum(elnx, elny)
logsumexp(exponents.vec)

Arguments

elnx, elny, exponents.vec

numeric vectors of log probabilities.

Value

Numeric vector with one (logsumexp) or more (others) log probability value(s).

Author(s)

Toby Dylan Hocking

References

http://bozeman.genome.washington.edu/compbio/mbt599_2006/hmm_scaling_revised.pdf

Examples


px <- c(0.1, 0.5, 0.9)
py <- c(0.001, 0.123, 0.999)
lx <- log(px)
ly <- log(py)
library(plotHMM)
elnproduct(lx, ly)
elnsum(lx, ly)
logsumexp(ly)

Forward algorithm

Description

Efficient implementation of forward algorithm in C++ code, for N data and S states.

Usage

forward_interface(
  log_emission_mat, log_transition_mat, log_initial_prob_vec)

Arguments

log_emission_mat

N x S numeric matrix of log likelihood of observing each data point in each state.

log_transition_mat

S x S numeric matrix; log_transition_mat[i,j] is the log probability of going from state i to state j.

log_initial_prob_vec

S numeric vector of log probabilities of observing each state at the beginning of the sequence.

Value

list with two elements

log_alpha

N x S numeric matrix of forward log likelihood at each data/state.

log_lik

numeric scalar total log likelihood of data given model parameters.

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=10)
set.seed(1)
N.data <- length(data.mean.vec)
y.vec <- rnorm(N.data, data.mean.vec)
##model.
n.states <- 3
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
state.mean.vec <- c(-1, 0, 1)*0.1
sd.param <- 1
log.pi.vec <- log(rep(1/n.states, n.states))
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
plotHMM::forward_interface(log.emission.mat, log.A.mat, log.pi.vec)

Multiply algorithm

Description

Efficient implementation of multiply algorithm in C++ code, for N data and S states.

Usage

multiply_interface(
  log_alpha_mat, log_beta_mat)

Arguments

log_alpha_mat, log_beta_mat

N x S numeric matrices of log probabilities, from forward and backward algorithms.

Value

N x S numeric matrix of overall log likelihood.

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=10)
set.seed(1)
N.data <- length(data.mean.vec)
y.vec <- rnorm(N.data, data.mean.vec)
##model.
n.states <- 3
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
state.mean.vec <- c(-1, 0, 1)*0.1
sd.param <- 1
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
log.pi.vec <- log(rep(1/n.states, n.states))
f.list <- plotHMM::forward_interface(log.emission.mat, log.A.mat, log.pi.vec)
b.mat <- plotHMM::backward_interface(log.emission.mat, log.A.mat)
log.gamma.mat <- plotHMM::multiply_interface(f.list$log_alpha, b.mat)
prob.mat <- exp(log.gamma.mat)
rowSums(prob.mat)

Pairwise algorithm

Description

Efficient implementation of pairwise algorithm in C++ code, for N data and S states.

Usage

pairwise_interface(
  log_emission_mat, log_transition_mat, log_alpha_mat, log_beta_mat)

Arguments

log_emission_mat, log_alpha_mat, log_beta_mat

N x S numeric matrices of log likelihood.

log_transition_mat

S x S numeric matrix; log_transition_mat[i,j] is the log probability of going from state i to state j.

Value

S x S x N-1 numeric array of log likelihood.

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=10)
set.seed(1)
N.data <- length(data.mean.vec)
y.vec <- rnorm(N.data, data.mean.vec)
##model.
n.states <- 3
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
state.mean.vec <- c(-1, 0, 1)*0.1
sd.param <- 1
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
log.pi.vec <- log(rep(1/n.states, n.states))
f.list <- plotHMM::forward_interface(log.emission.mat, log.A.mat, log.pi.vec)
b.mat <- plotHMM::backward_interface(log.emission.mat, log.A.mat)
log.gamma.mat <- plotHMM::multiply_interface(f.list$log_alpha, b.mat)
prob.mat <- exp(log.gamma.mat)
plotHMM::pairwise_interface(log.emission.mat, log.A.mat, f.list$log_alpha, b.mat)

Transition algorithm

Description

Efficient implementation of transition algorithm in C++ code, for T transitions and S states.

Usage

transition_interface(
  log_gamma_mat, log_xi_array)

Arguments

log_gamma_mat

T x S numeric matrix, taken by removing the last row from the log probabilities from multiply.

log_xi_array

S x S x T numeric array of log probabilities from pairwise.

Value

S x S numeric array of log probabilities (new transition matrix).

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=10)
set.seed(1)
N.data <- length(data.mean.vec)
y.vec <- rnorm(N.data, data.mean.vec)
##model.
n.states <- 3
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
state.mean.vec <- c(-1, 0, 1)*0.1
sd.param <- 1
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
log.pi.vec <- log(rep(1/n.states, n.states))
f.list <- plotHMM::forward_interface(log.emission.mat, log.A.mat, log.pi.vec)
b.mat <- plotHMM::backward_interface(log.emission.mat, log.A.mat)
log.gamma.mat <- plotHMM::multiply_interface(f.list$log_alpha, b.mat)
prob.mat <- exp(log.gamma.mat)
log.xi.array <- plotHMM::pairwise_interface(
  log.emission.mat, log.A.mat, f.list$log_alpha, b.mat)
plotHMM::transition_interface(log.gamma.mat[-N.data,], log.xi.array)

Viterbi algorithm

Description

Efficient implementation of Viterbi algorithm in C++ code, for N data and S states.

Usage

viterbi_interface(
  log_emission_mat, log_transition_mat, log_initial_prob_vec)

Arguments

log_emission_mat

N x S numeric matrix of log likelihood of observing each data point in each state.

log_transition_mat

S x S numeric matrix; log_transition_mat[i,j] is the log probability of going from state i to state j.

log_initial_prob_vec

S numeric vector of log probabilities of observing each state at the beginning of the sequence.

Value

list with elements

log_max_prob

N x S numeric matrix of max log probabilities.

best_state

N x S integer matrix. First row is fixed at zero, other rows indicate best states (from 1 to S).

state_seq

N integer vector, best overall state sequence (entries from 1 to S).

Author(s)

Toby Dylan Hocking

Examples


##simulated data.
seg.mean.vec <- c(2, 0, -1, 0)
data.mean.vec <- rep(seg.mean.vec, each=2)
N.data <- length(data.mean.vec)
sd.param <- 0.1
set.seed(1)
y.vec <- rnorm(N.data, data.mean.vec, sd.param)
##model.
state.mean.vec <- unique(seg.mean.vec)
n.states <- length(state.mean.vec)
log.A.mat <- log(matrix(1/n.states, n.states, n.states))
log.pi.vec <- log(rep(1/n.states, n.states))
log.emission.mat <- dnorm(
  y.vec,
  matrix(state.mean.vec, N.data, n.states, byrow=TRUE),
  sd.param,
  log=TRUE)
plotHMM::viterbi_interface(log.emission.mat, log.A.mat, log.pi.vec)

These binaries (installable software) and packages are in development.
They may not be fully stable and should be used with caution. We make no claims about them.
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