constraint_likelihood: Title solving constraint likelihood function using the...

In wldyddl5510/SolMfd: Implementations of solution manifold algorithms

Description

Title solving constraint likelihood function using the solution manifold.

Usage

constraint_likelihood(
  nll,
  C,
  theta,
  s,
  alpha = 0.005,
  gamma = 0.005,
  Lambda = NULL,
  tol1 = 1e-07,
  tol2 = 1e-15,
  num_iter = 1e+05,
  num_iter2 = 20
)

Arguments

nll	function: negative log-likelihood
C	function: constraint
theta	vector: initial value to start
s	int output dimension for C
alpha	double gradient descent step for likelihood update
gamma	double gradient descent step for manifold converging
Lambda	matrix positive definite matrix
tol1	double tolerance for manifold convergence
tol2	double tolerance for gradient descents
num_iter	maximum iteration for gradient descent
num_iter2	maximum iteration for all process

Value

matrix (num_iter2 * length(theta)) each row is a trajactory of theta update. last row is final results

Examples

set.seed(10)
n = 100 # number of data
X = rnorm(n, mean = 1.5, sd = 3)
nll = function(theta) {return(-sum(dnorm(X, theta[[1]], theta[[2]], log = TRUE)))}
C = function(x) {return(pnorm(2, x[[1]], x[[2]]) - pnorm(-5, x[[1]], x[[2]]) - 0.5)}
theta_updated = constraint_likelihood(nll, C, c(1, 2), 1)
theta_updated[nrow(theta_updated), ] # final result
theta_tmp = theta_updated
const_val = apply(theta_tmp, 1, C) # constraint for each row for plot
plot(x = seq(1, nrow(theta_updated)), const_val, xlab = "step", ylab = "constraint", type = 'o')
theta_tmp = theta_updated
nll_val = apply(theta_tmp, 1, nll) # nll for each row for plot
plot(x = seq(1, nrow(theta_updated)), nll_val, xlab = "step", ylab = "nll", type = 'o')
plot(theta_updated, xlab = "mean", ylab = "sd", type = 'o')

wldyddl5510/SolMfd documentation built on Dec. 23, 2021, 5:18 p.m.