markovmix package

Description

markovmix package Fit mixture of Markov chains of higher orders from multiple sequences. It is also compatible with ordinary 1-component, 1-order or single-sequence Markov chains. Various utility functions are provided to derive transition patterns, transition probabilities per component and component priors. In addition, print(), predict() and component extracting/replacing methods are also defined as a convention of mixture models.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the package.

• 0.1.2 Xiurui Zhu - Update package documentation.

Author(s)

Xiurui Zhu

Extract or replace components of MarkovMix object

Description

Operators to extract or replace components of a MarkovMix object.

Usage

## S3 method for class 'MarkovMix'
x[i]

## S3 replacement method for class 'MarkovMix'
x[i] <- value

Arguments

Note

Change log:

• 0.1.1 Xiurui Zhu - Initiate the functions.

• 0.1.2 Xiurui Zhu - Update function documentation.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: get_counts(), get_order(), get_prior(), get_prob(), get_states_mat(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

MarkovMix class

Description

An object of class MarkovMix is a list containing the following components:

counts

Numeric matrix containing soft counts of sub-sequence patterns in each component. For (non-mixture) Markov chains, the matrix contains only 1 column and counts are actually integers, but they are still stored as numeric values.

order

Integer (1L) as the order of (mixture) Markov chain(s).

states

Vector as the states in the (mixture) Markov chain(s).

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the class.

Author(s)

Xiurui Zhu

Fit mixture of Markov chains

Description

fit_markov_mix fits mixture of Markov chains. It supports high-order Markov chains, multiple sequences and mixture components with cluster probabilities.

Usage

fit_markov_mix(
  seq_list,
  order. = 1L,
  states = NULL,
  clusters = NULL,
  verbose = TRUE
)

Arguments

Value

An object of class MarkovMix.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

Examples

# Generate a list of integer sequences of different lengths with 4 states
test_states <- seq_len(4L)
test_maxlen <- 10L
set.seed(1111L)
test_seq <- purrr::map(
  seq_len(100L),
  ~ sample(test_states, sample.int(test_maxlen, 1L), replace = TRUE)
)

# Fit a 1-order Markov chain
markov_fit <- fit_markov_mix(
  seq_list = test_seq,
  order. = 1L,
  states = test_states
)
print(markov_fit)

# Fit a mixture of 2-order Markov chain with 3 components
test_n_comp <- 3L
test_clusters <- matrix(
  runif(length(test_seq) * test_n_comp),
  nrow = length(test_seq),
  ncol = test_n_comp
)
markov_mix_fit <- fit_markov_mix(
  seq_list = test_seq,
  order. = 2L,
  states = test_states,
  clusters = test_clusters
)
print(markov_mix_fit)

Get transition pattern counts from MarkovFit object

Description

get_counts gets transition pattern counts from MarkovMix object.

Usage

get_counts(object, check = TRUE)

Arguments

Value

A numeric matrix indicates transition pattern (soft) counts, where each row corresponds to a transition pattern and each column corresponds to a component.

Note

Change log:

• 0.1.2 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_order(), get_prior(), get_prob(), get_states_mat(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Get the order of Markov chains

Description

get_order gets the order of Markov chains from MarkovMix object.

Usage

get_order(object, check = TRUE)

Arguments

Value

An integer as the order of Markov chains.

Note

Change log:

• 0.1.2 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_prior(), get_prob(), get_states_mat(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Get component priors from MarkovFit object

Description

get_prior gets component priors from MarkovMix object, normalized to sum up to 1.

Usage

get_prior(object, check = TRUE)

Arguments

Value

A numeric vector indicates component priors.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_order(), get_prob(), get_states_mat(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Get probability matrix from MarkovFit object

Description

get_prob gets probability matrix from MarkovMix object. It normalizes each column in the count matrix to sum up to 1.

Usage

get_prob(object, check = TRUE)

Arguments

Value

A numeric matrix indicating probabilities of each state transition pattern in each component.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_order(), get_prior(), get_states_mat(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Get the states of Markov chains

Description

get_states gets the states of Markov chains from MarkovMix object.

Usage

get_states(object, check = TRUE)

Arguments

Value

A vector as the states used in Markov chains.

Note

Change log:

• 0.1.2 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_order(), get_prior(), get_prob(), get_states_mat(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Get state transition patterns from MarkovFit object

Description

get_states_mat gets state transition patterns from MarkovMix object. The number of columns is the order of the (mixture of) Markov chain(s) plus 1 (the destination state). Each column is arranged in the ascending order of the states. The last column serves as the destination state and iterates the fastest.

Usage

get_states_mat(object, check = TRUE)

Arguments

Value

A matrix indicating the state transition patterns.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_order(), get_prior(), get_prob(), get_states(), restate()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Derive transition pattern soft counts
get_counts(object = markov_mix_ex)

# Derive the order of Markov chains
get_order(object = markov_mix_ex)

# Derive the states of Markov chains
get_states(object = markov_mix_ex)

# Derive state transition patterns
get_states_mat(markov_mix_ex)

# Derive probability matrices
get_prob(markov_mix_ex)

# Derive component priors
get_prior(markov_mix_ex)

# Combine state transition patterns and their probabilities
cbind(
  as.data.frame(get_states_mat(markov_mix_ex)),
  as.data.frame(get_prob(markov_mix_ex))
)

# Extract 1 or more components
markov_mix_ex[2L]
markov_mix_ex[c(1L, 3L)]

# Replace 1 or more components
nrow_value <- length(get_states(object = markov_mix_ex, check = FALSE))^
  (get_order(object = markov_mix_ex, check = FALSE) + 1L)
markov_mix_ex2 <- markov_mix_ex
markov_mix_ex2[2L] <- runif(nrow_value)
print(markov_mix_ex2)
markov_mix_ex3 <- markov_mix_ex
markov_mix_ex3[c(1L, 3L)] <- matrix(runif(nrow_value * 2L), ncol = 2L)
print(markov_mix_ex3)

Mixture of Markov chain example

Description

A mixture of 2-order Markov chain fit from 100 random sequences with 4 states (A, B, C, D) and 3 components.

Usage

markov_mix_ex

Format

A MarkovMix object.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the dataset.

Author(s)

Xiurui Zhu

Predict probabilities with MarkovMix object and new sequence list

Description

predict.MarkovMix predicts probabilities with MarkovMix object and new sequence list. NA values are returned for sequences with no valid sub-sequences to distinguish them from those that are truly not observed (probabilities = 0) in the transition matrices.

Usage

## S3 method for class 'MarkovMix'
predict(object, newdata, aggregate. = TRUE, ...)

Arguments

Value

For aggregate. = TRUE, a numeric vector of probabilities. For aggregate. = TRUE, a numeric matrix of probabilities from each component.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix methods: print.MarkovMix()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Generate a new list of sequences
set.seed(2222L)
new_maxlen <- 8L
new_seq_list <- purrr::map(
  seq_len(50L),
  ~ sample(get_states(object = markov_mix_ex, check = FALSE),
           sample.int(new_maxlen, 1L),
           replace = TRUE)
)

# Predict the probabilities of sequences
predict(markov_mix_ex, newdata = new_seq_list)

# Predict the probabilities of sequences from each component
predict(markov_mix_ex, newdata = new_seq_list, aggregate. = FALSE)

Print MarkovMix object

Description

print.MarkovMix prints MarkovMix object in a user-friendly form, including component priors and transition matrices.

Usage

## S3 method for class 'MarkovMix'
print(x, sep = "->", print_max = 20L, print_min = 10L, ...)

Arguments

Value

Input x, invisibly.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix methods: predict.MarkovMix()

Examples

# Generate a list of integer sequences of different lengths with 4 states
test_states <- seq_len(4L)
test_maxlen <- 10L
set.seed(1111L)
test_seq <- purrr::map(
  seq_len(100L),
  ~ sample(test_states, sample.int(test_maxlen, 1L), replace = TRUE)
)

# Fit a 1-order Markov chain
markov_fit <- fit_markov_mix(
  seq_list = test_seq,
  order. = 1L,
  states = test_states
)
print(markov_fit)

# Fit a mixture of 2-order Markov chain with 3 components
test_n_comp <- 3L
test_clusters <- matrix(
  runif(length(test_seq) * test_n_comp),
  nrow = length(test_seq),
  ncol = test_n_comp
)
markov_mix_fit <- fit_markov_mix(
  seq_list = test_seq,
  order. = 2L,
  states = test_states,
  clusters = test_clusters
)
print(markov_mix_fit)

Reorganize states in MarkovMix object

Description

restate reorganizes states in MarkovMix object with a function.

Usage

restate(.object, .fun, .check = TRUE, ...)

Arguments

Value

A MarkovMix object with modified states and count matrix.

Note

Change log:

• 0.1.0 Xiurui Zhu - Initiate the function.

Author(s)

Xiurui Zhu

See Also

Other MarkovMix utilities: Extract.MarkovMix, get_counts(), get_order(), get_prior(), get_prob(), get_states_mat(), get_states()

Examples

# Load example MarkovMix object
data("markov_mix_ex")

# Reverse states (using function)
markov_mix_new1 <- restate(
  .object = markov_mix_ex,
  .fun = forcats::fct_rev
)
print(markov_mix_new1)

# Reorder states by hand (using function name with additional arguments)
markov_mix_new2 <- restate(
  .object = markov_mix_ex,
  .fun = "levels<-",
  value = c("B", "D", "C", "A")
)
print(markov_mix_new2)

# Merge state D into C (using purrr-style lambda function)
markov_mix_new3 <- restate(
  .object = markov_mix_ex,
  .fun = ~ forcats::fct_recode(.x, "C" = "D")
)
print(markov_mix_new3)