| Type: | Package |
| Title: | Computationally Efficient Maximum Likelihood Identification of Linear Dynamical Systems |
| Version: | 0.3.0 |
| Description: | Provides implementations of computationally efficient maximum likelihood parameter estimation algorithms for models representing linear dynamical systems. Currently, two such algorithms (one offline and one online) are implemented for the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence. The corresponding scientific papers are referenced in the descriptions of the functions implementing these algorithms. |
| License: | GPL-2 |
| Copyright: | Vilnius University Institute of Data Science and Digital Technologies |
| Imports: | stats |
| Encoding: | UTF-8 |
| RoxygenNote: | 7.3.2 |
| NeedsCompilation: | no |
| Packaged: | 2025-09-17 19:34:47 UTC; milis |
| Author: | Vytautas Dulskis [cre, aut], Leonidas Sakalauskas [aut] |
| Maintainer: | Vytautas Dulskis <vytautas.dulskis@gmail.com> |
| Repository: | CRAN |
| Date/Publication: | 2025-09-17 19:50:02 UTC |
calculate_likelihood
Description
Calculates the likelihood function value for given data and statistical measure values of the output-differenced version of the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence. Suitable when there are no contradictions in statistical measure values.
Usage
calculate_likelihood(dat, params)
Arguments
dat |
An (n + 1) x (m + 1) data frame of finite numeric elements (possibly except for row 1, columns 1 to m) containing observed input (columns 1 to m) and output (column m + 1) data of the original model. |
params |
A list consisting of three elements: 1) Sigma ((m + 1) x (m + 1) matrix of finite numeric elements); 2) sigma_y^2 (vector of length 1, finite numeric element); 3) mu ((m + 1) x 1 matrix of finite numeric elements). |
Value
Calculated likelihood function value (vector of length 1, numeric element).
Examples
set.seed(1)
m <- 4
k <- 2
L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)
data <- generate_data(100, L, sigma, mu)
estimated_parameters <- estimate_parameters(data, 0.00001)
calculate_likelihood(data, estimated_parameters)
estimate_parameters
Description
Calculates maximum likelihood estimates of the statistical measures of the output-differenced version of the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence.
Usage
estimate_parameters(dat, tol)
Arguments
dat |
An (n + 1) x (m + 1) data frame of finite numeric elements (possibly except for row 1, columns 1 to m) containing observed input (columns 1 to m) and output (column m + 1) data of the original model. |
tol |
A tolerance parameter of the golden section search algorithm used for minimizing the one-dimensional likelihood function (vector of length 1, finite positive numeric element). |
Value
A list consisting of three elements: 1) estimate of the covariance at lag 0 of the data that result from the output-differenced model (Sigma; (m + 1) x (m + 1) matrix of numeric elements); 2) estimate of the only non-zero element of the negative covariance at lag 1 of the data that result from the output-differenced model (sigma_y^2; vector of length 1, numeric element); 3) estimate of the mean of the data that result from the output-differenced model (mu; (m + 1) x 1 matrix of numeric elements).
References
Leonidas Sakalauskas, Vytautas Dulskis, & Darius Plikynas (2024). A Technique for Efficient Estimation of Dynamic Structural Equation Models: A Case Study. Structural Equation Modeling: A Multidisciplinary Journal, 31(4), 635-650. DOI: 10.1080/10705511.2023.2282378
Examples
set.seed(1)
m <- 4
k <- 2
L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)
data <- generate_data(100, L, sigma, mu)
estimate_parameters(data, 0.00001)
estimate_parameters_on
Description
Online maximum likelihood estimation of the statistical measures of the output-differenced version of the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence.
Usage
estimate_parameters_on(dat, s)
Arguments
dat |
An (n + 1) x (m + 1) data frame of finite numeric elements (possibly except for row 1, columns 1 to m) containing observed input (columns 1 to m) and output (column m + 1) data of the original model. |
s |
Initial value of parameter s (a vector of length 1 containing a finite numeric element that belongs to the interval [0, 1]). |
Value
A list containing n sublists, each representing a progressively larger data sample (with 1 to n observation points), where each sublist consists of three elements: 1) estimate of the covariance at lag 0 of the data that result from the output-differenced model (an (m + 1) x (m + 1) matrix of numeric elements); 2) estimate of the only non-zero element of the negative covariance at lag 1 of the data that result from the output-differenced model (a vector of length 1 containing a numeric element); 3) estimate of the mean of the data that result from the output-differenced model (an (m + 1) x 1 matrix of numeric elements).
References
Vytautas Dulskis & Leonidas Sakalauskas (2025). Toward Efficient Online Estimation of Dynamic Structural Equation Models: A Case Study. Journal of Statistical Computation and Simulation, 1-24. DOI: 10.1080/00949655.2025.2515955
Examples
set.seed(1)
m <- 4
k <- 2
L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)
data <- generate_data(100, L, sigma, mu)
estimate_parameters_on(data, 0.35)
evaluate_estimates
Description
Calculates a discrepancy-function-based metric of accuracy of the statistical measure estimates for the output-differenced version of the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence. Suitable when there are no contradictions in the factuals/estimates.
Usage
evaluate_estimates(f, e, n)
Arguments
f |
A list consisting of three elements: 1) the factual Sigma ((m + 1) x (m + 1) matrix of finite numeric elements); 2) the factual sigma_y^2 (vector of length 1, finite numeric element); 3) the factual mu ((m + 1) x 1 matrix of finite numeric elements). |
e |
Analogous to parameter f but with estimates instead of factuals. |
n |
The number of time moments used for obtaining parameter e (vector of length 1, finite positive integer). |
Value
Calculated accuracy metric value (vector of length 1, numeric element). The lower the value, the better the accuracy, with 0 indicating perfect accuracy.
Examples
set.seed(1)
m <- 4
k <- 2
L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)
n <- 100
data <- generate_data(n, L, sigma, mu)
Sigma <- L %*% t(L) + diag(sigma[1:(m + 1), ] ^ 2)
sigma_y_squared <- sigma[m + 2, ] ^ 2
Sigma[m + 1, m + 1] <- Sigma[m + 1, m + 1] + 2 * sigma_y_squared
factual_parameters <- list(Sigma, sigma_y_squared, mu)
estimated_parameters <- estimate_parameters(data, 0.00001)
evaluate_estimates(factual_parameters, estimated_parameters, n)
generate_data
Description
Generates data according to the single-output cumulative structural equation model with an additive-noise output measurement equation and assumptions of normality and independence, with given model parameter values.
Usage
generate_data(n, L, sigma, mu)
Arguments
n |
The number of time moments to generate the data for (vector of length 1, finite positive integer). |
L |
Factor loadings ((m + 1) x k matrix of finite numeric elements: the first m rows correspond to the input measurement equation; the last row corresponds to the transition equation). |
sigma |
Standard deviations of the error/noise terms ((m + 2) x 1 matrix of finite non-negative numeric elements: the first m rows correspond to the input measurement equation; the row before the last one corresponds to the transition equation; the last row corresponds to the output measurement equation). |
mu |
Intercept terms ((m + 1) x 1 matrix of finite numeric elements: the first m rows correspond to the input measurement equation; the last row corresponds to the transition equation). |
Value
An (n + 1) x (m + 1) data frame of numeric elements (except for row 1, columns 1 to m that contain NA's) containing observed input (columns 1 to m) and output (column m + 1) data.
Examples
set.seed(1)
m <- 4
k <- 2
L <- matrix(runif((m + 1) * k, min = -10, max = 10), nrow = m + 1)
sigma <- matrix(runif(m + 2, min = 0, max = 10), nrow = m + 2)
mu <- matrix(runif(m + 1, min = -10, max = 10), nrow = m + 1)
generate_data(10, L, sigma, mu)