Standard Expectation-Maximization (EM) Algorithm for Stock Proportions

Estimates mixing proportions (theta) from a likelihood matrix using the EM algorithm.

Usage

em_algorithm(
  likelihood,
  np,
  freq = NULL,
  max_iter = 100,
  tol = 1e-06,
  verbose = FALSE,
  save_theta_path = NULL
)

Arguments

likelihood: A numeric matrix (N_rows x N_populations) where `likelihood[i, j]` is $P(Data_i | Stock_j)$ or a value proportional to it. N_rows can be N_samples (for Theta5) or N_populations (for Theta4).
np: Integer, the number of populations (stocks). Should match `ncol(likelihood)`.
freq: Optional numeric vector of frequencies/weights for each "observation" (row in `likelihood`). Length must match `nrow(likelihood)`. Defaults to `rep(1, nrow(likelihood))`.
max_iter: Integer, the maximum number of iterations for the EM algorithm.
tol: Numeric, the convergence tolerance. The algorithm stops if the maximum absolute change in any `theta` component is less than `tol`.
verbose: Logical, if TRUE, prints iteration number and current theta estimates.
save_theta_path: Optional character string. If provided, the history of theta estimates at each iteration is saved to a CSV file at this path.

Value

A numeric vector of estimated stock proportions (theta), length `np`.

Examples

# Dummy likelihood matrix (10 samples, 3 stocks)
lik <- matrix(runif(30), 10, 3)
lik <- lik / rowSums(lik) # Normalize rows

theta_em <- em_algorithm(lik, np = 3, max_iter = 20)
print(theta_em)
#> [1] 4.840631e-01 6.137913e-05 5.158755e-01