| Title: | 'regmhmm' Fits Hidden Markov Models with Regularization |
|---|---|
| Description: | Designed for longitudinal data analysis using Hidden Markov Models (HMMs). Tailored for applications in healthcare, social sciences, and economics, the main emphasis of this package is on regularization techniques for fitting HMMs. Additionally, it provides an implementation for fitting HMMs without regularization, referencing Zucchini et al. (2017, ISBN:9781315372488). |
| Authors: | Man Chong Leong [cre, aut]
|
| Maintainer: | Man Chong Leong <[email protected]> |
| License: | GPL (>= 3) |
| Version: | 1.0.0 |
| Built: | 2024-10-30 06:56:03 UTC |
| Source: | CRAN |
Calculate the probability given parameters of a hidden Markov model utilizing the backward algorithm.
backward(delta, Y, A, B, X, family)backward(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
A matrix of size S x T that is the backward probabilities in log scale.
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) backward_C <- backward( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P" )# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) backward_C <- backward( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P" )
Calculate the posterior joint probability of hidden states given parameters of a hidden Markov model.
compute_joint_state(delta, Y, A, B, X, family)compute_joint_state(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
An array of size S x S x T that represents the posterior joint probability of hidden states.
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) compute_joint_state_get <- compute_joint_state( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) compute_joint_state_get <- compute_joint_state( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )
Calculate the log-likelihood given parameters of a hidden Markov model using the forward algorithm. This function aids in assessing the likelihood of the observed data under the specified model.
compute_loglikelihood(delta, Y, A, B, X, family)compute_loglikelihood(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
A value that is the likelihood in log scale.
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) llh_C <- compute_loglikelihood( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) llh_C <- compute_loglikelihood( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )
Calculate the posterior probability of hidden states given parameters of a hidden Markov model.
compute_state(delta, Y, A, B, X, family)compute_state(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
A matrix of size S x T that represents the posterior probability of hidden states.
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) compute_state_get <- compute_state( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P")# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) compute_state_get <- compute_state( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P")
Calculate the probability given parameters of a hidden Markov model using the forward algorithm. This function is essential for estimating the likelihood of observing a particular sequence of observations in the context of a Hidden Markov Model (HMM).
forward(delta, Y, A, B, X, family)forward(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
A matrix of size S x T that is the forward probabilities in log scale.
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) forward_C <- forward( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) dat <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) forward_C <- forward( delta = parameters_setting$init_vec, Y = dat$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = dat$X_array[, 1:4, 1], family = "P" )
Calculate the probability given parameters of a hidden Markov model using a combination of the forward and backward algorithms.
forward_backward(delta, Y, A, B, X, family)forward_backward(delta, Y, A, B, X, family)
delta |
a vector of length S specifying the initial probabilities. |
Y |
a vector of observations of size T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X |
a design matrix of size T x p. |
family |
the family of the response. |
A list object with the following slots:
log_alpha |
a matrix of size S x T that is the forward probabilities in log scale. |
log_beta |
a matrix of size S x T that is the backward probabilities in log scale. |
# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) forward_backward_C <- forward_backward( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P" )# Example usage of the function parameters_setting <- list() parameters_setting$emis_mat <- matrix(NA, nrow = 2, ncol = 4) parameters_setting$emis_mat[1, 1] <- 0.1 parameters_setting$emis_mat[1, 2] <- 0.5 parameters_setting$emis_mat[1, 3] <- -0.75 parameters_setting$emis_mat[1, 4] <- 0.75 parameters_setting$emis_mat[2, 1] <- -0.1 parameters_setting$emis_mat[2, 2] <- -0.5 parameters_setting$emis_mat[2, 3] <- 0.75 parameters_setting$emis_mat[2, 4] <- 1 parameters_setting$trans_mat <- matrix(NA, nrow = 2, ncol = 2) parameters_setting$trans_mat[1, 1] <- 0.65 parameters_setting$trans_mat[1, 2] <- 0.35 parameters_setting$trans_mat[2, 1] <- 0.2 parameters_setting$trans_mat[2, 2] <- 0.8 parameters_setting$init_vec <- c(0.65, 0.35) simulated_data <- simulate_HMM_data( seed_num = 1, p_noise = 7, N = 100, N_persub = 10, parameters_setting = parameters_setting ) forward_backward_C <- forward_backward( delta = parameters_setting$init_vec, Y = simulated_data$y_mat[1, ], A = parameters_setting$trans_mat, B = parameters_setting$emis_mat, X = simulated_data$X_array[, 1:4, 1], family = "P" )
Fit Hidden Markov Models (HMMs) to the provided data using an iterative Expectation-Maximization (EM) algorithm. This method alternates between the E-step (Expectation) and M-step (Maximization) to iteratively optimize model parameters. The algorithm ensures convergence and provides robust estimates for latent state probabilities and transition probabilities, contributing to the accurate characterization of underlying patterns in the data.
HMM(delta, Y_mat, A, B, X_cube, family, trace, ...)HMM(delta, Y_mat, A, B, X_cube, family, trace, ...)
delta |
a vector of length S specifying the initial probabilities. |
Y_mat |
a matrix of observations of size N x T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X_cube |
a design array of size T x p x N. |
family |
the family of the response. |
trace |
logical indicating if detailed output should be produced during the fitting process. |
... |
other arguments to be passed to the next method. |
A list object with the following slots:
delta_hat |
the estimate of delta. |
A_hat |
the estimate of A. |
B_hat |
the estimate of B. |
log_likelihood |
the log-likelihood of the model. |
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit <- HMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 )# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit <- HMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 )
Employ this function to fit a Hidden Markov Model (HMM) to the provided data. It iteratively estimates model parameters using the EM algorithm.
HMM_C_raw( delta, Y_mat, A, B, X_cube, family, eps = 1e-05, eps_IRLS = 1e-04, N_iter = 1000L, max_N_IRLS = 300L, trace = 0L )HMM_C_raw( delta, Y_mat, A, B, X_cube, family, eps = 1e-05, eps_IRLS = 1e-04, N_iter = 1000L, max_N_IRLS = 300L, trace = 0L )
delta |
a vector of length S specifying the initial probabilities. |
Y_mat |
a matrix of observations of size N x T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X_cube |
a design array of size T x p x N. |
family |
the family of the response. |
eps |
convergence tolerance in the EM algorithm for fitting HMM. |
eps_IRLS |
convergence tolerance in the iteratively reweighted least squares step. |
N_iter |
the maximal number of the EM algorithm for fitting HMM. |
max_N_IRLS |
the maximal number of IRLS iterations. |
trace |
logical indicating if detailed output should be produced during the fitting process. |
A list object with the following slots:
delta_hat |
the estimate of delta. |
A_hat |
the estimate of A. |
B_hat |
the estimate of B. |
log_likelihood |
the log-likelihood of the model. |
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit_raw <- HMM_C_raw(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 )# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit_raw <- HMM_C_raw(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 )
Execute a single iteration of the Expectation-Maximization (EM) algorithm tailored for fitting Hidden Markov Models (HMMs).
HMM_one_step( delta, Y_mat, A, B, X_cube, family, eps_IRLS = 1e-04, max_N_IRLS = 300L )HMM_one_step( delta, Y_mat, A, B, X_cube, family, eps_IRLS = 1e-04, max_N_IRLS = 300L )
delta |
a vector of length S specifying the initial probabilities. |
Y_mat |
a matrix of observations of size N x T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X_cube |
a design array of size T x p x N. |
family |
the family of the response. |
eps_IRLS |
convergence tolerance in the iteratively reweighted least squares step. |
max_N_IRLS |
the maximal number of IRLS iterations. |
A list object with the following slots:
delta_hat |
the estimate of delta. |
A_hat |
the estimate of A. |
B_hat |
the estimate of B. |
log_likelihood |
the log-likelihood of the model. |
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit_raw_one_step <- HMM_one_step(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P")# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit_raw_one_step <- HMM_one_step(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P")
Iterative Reweighted Least Squares algorithm for optimizing the parameters in the M-step of the EM algorithm.
IRLS_EM(X, gamma, Y, beta, family, eps_IRLS, max_N)IRLS_EM(X, gamma, Y, beta, family, eps_IRLS, max_N)
X |
A design matrix of size n x p. |
gamma |
A vector of size n specifying the posterior probability of the hidden states. |
Y |
A vector of observations of size n. |
beta |
A vector of size p + 1 specifying the GLM parameters. |
family |
The family of the response. |
eps_IRLS |
convergence tolerance in the iteratively reweighted least squares step. |
max_N |
the maximal number of IRLS iterations. |
A vector representing the estimates of beta.
## Not run: # Example usage of the function IRLS_EM_one_step <- IRLS_EM_one(X, gamma, Y, beta, family) ## End(Not run)## Not run: # Example usage of the function IRLS_EM_one_step <- IRLS_EM_one(X, gamma, Y, beta, family) ## End(Not run)
Display detailed summary outputs and relevant information derived from a Hidden Markov Model (HMM) object. This includes state-specific parameters, transition probabilities, log-likelihood, and other essential metrics, providing an overview of the fitted model.
## S3 method for class 'HMM' print(x, ...)## S3 method for class 'HMM' print(x, ...)
x |
an object used to select a method. |
... |
further arguments passed to or from other methods. |
Return a invisible copy of "HMM" object
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit <- HMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 ) print(HMM_fit)# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 10 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) HMM_fit <- HMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", eps=1e-4, trace = 0 ) print(HMM_fit)
Utilize the modified Cyclic Coordinate Descent (CCD) algorithm to effectively fit a regularized Hidden Markov Model (rHMM).
rHMM( delta, Y_mat, A, B, X_cube, family, omega_cva = sqrt(sqrt(seq(0, 1, len = 5))), N_iter = 1000, eps = 1e-07, trace = 0 )rHMM( delta, Y_mat, A, B, X_cube, family, omega_cva = sqrt(sqrt(seq(0, 1, len = 5))), N_iter = 1000, eps = 1e-07, trace = 0 )
delta |
a vector of length S specifying the initial probabilities. |
Y_mat |
a matrix of observations of size N x T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X_cube |
a design array of size T x p x N. |
family |
the family of the response. |
omega_cva |
a vector of omega values for the modified cyclical coordinate descent algorithm used for cross-validation. |
N_iter |
the maximal number of the EM algorithm for fitting HMM. |
eps |
convergence tolerance. |
trace |
logical indicating if detailed output should be produced during the fitting process. |
A list object with the following slots:
delta_hat |
the estimate of delta. |
A_hat |
the estimate of A. |
B_hat |
the estimate of B. |
log_likelihood |
the log-likelihood of the model. |
lambda |
lambda from CV. |
omega |
omega from CV. |
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) rHMM_one_step <- rHMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", omega_cva=sqrt(sqrt(seq(0, 1, len = 5))), N_iter=10, trace = 0)# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) rHMM_one_step <- rHMM(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", omega_cva=sqrt(sqrt(seq(0, 1, len = 5))), N_iter=10, trace = 0)
Execute a single iteration of the Expectation-Maximization (EM) algorithm designed for fitting a regularized Hidden Markov Model (rHMM).
rHMM_one_step( delta, Y_mat, A, B, X_cube, family, omega_cva = sqrt(sqrt(seq(0, 1, len = 5))), trace = 0 )rHMM_one_step( delta, Y_mat, A, B, X_cube, family, omega_cva = sqrt(sqrt(seq(0, 1, len = 5))), trace = 0 )
delta |
a vector of length S specifying the initial probabilities. |
Y_mat |
a matrix of observations of size N x T. |
A |
a matrix of size S x S specifying the transition probabilities. |
B |
a matrix of size S x (p + 1) specifying the GLM parameters of the emission probabilities. |
X_cube |
a design array of size T x p x N. |
family |
the family of the response. |
omega_cva |
a vector of omega values for the modified cyclical coordinate descent algorithm used for cross-validation. |
trace |
logical indicating if detailed output should be produced during the fitting process. |
A list object with the following slots:
delta_hat |
the estimate of delta. |
A_hat |
the estimate of A. |
B_hat |
the estimate of B. |
log_likelihood |
the log-likelihood of the model. |
lambda |
lambda from CV. |
omega |
omega from CV. |
# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) rHMM_one_step <- rHMM_one_step(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", omega_cva=sqrt(sqrt(seq(0, 1, len = 5))), trace = 0)# Example usage of the function seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting) init_start = c(0.5, 0.5) trans_start = matrix(c(0.5, 0.5, 0.5, 0.5), nrow = 2) emis_start = matrix(rep(1, 8), nrow = 2) rHMM_one_step <- rHMM_one_step(delta=as.matrix(init_start), Y_mat=simulated_data$y_mat, A=trans_start, B=emis_start, X_cube=simulated_data$X_array, family="P", omega_cva=sqrt(sqrt(seq(0, 1, len = 5))), trace = 0)
Generate synthetic HMM data for testing and validation purposes. This function creates a simulated dataset with specified parameters, including initial probabilities, transition probabilities, emission matrix, and noise covariates.
simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting)simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting)
seed_num |
Seed for reproducibility. |
p_noise |
Number of noise covariates. |
N |
Number of subjects. |
N_persub |
Number of time points per subject. |
parameters_setting |
A list containing the parameters for the HMM. |
A list containing the design matrix (X_array) and response variable matrix (y_mat).
seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting)seed_num <- 1 p_noise <- 2 N <- 100 N_persub <- 50 parameters_setting <- list( init_vec = c(0.5, 0.5), trans_mat = matrix(c(0.7, 0.3, 0.2, 0.8), nrow = 2, byrow = TRUE), emis_mat = matrix(c(1, 0.5, 0.5, 2), nrow = 2, byrow = TRUE) ) simulated_data <- simulate_HMM_data(seed_num, p_noise, N, N_persub, parameters_setting)