estimation_error {mtlgmm}

Caluclate the estimation error of GMM parameters under the MTL setting (the worst performance among all tasks).

Description

Caluclate the estimation error of GMM parameters under the MTL setting (the worst performance among all tasks). Euclidean norms are used.

Usage

estimation_error(
  estimated_value,
  true_value,
  parameter = c("w", "mu", "beta", "Sigma")
)

Arguments

estimated_value

estimate of GMM parameters. The form of input depends on the parameter parameter.

true_value

true values of GMM parameters. The form of input depends on the parameter parameter.

parameter

which parameter to calculate the estimation error for. Can be "w", "mu", "beta", or "Sigma".

• w: the Gaussian mixture proportions. Both estimated_value and true_value require an input of a K-dimensional vector, where K is the number of tasks. Each element in the vector is an "w" (estimate or true value) for each task.

• mu: Gaussian mean parameters. Both estimated_value and true_value require an input of a list of two p-by-K matrices, where p is the dimension of Gaussian distribution and K is the number of tasks. Each column of the matrix is a "mu1" or "mu2" (estimate or true value) for each task.

• beta: discriminant coefficients. Both estimated_value and true_value require an input of a p-by-K matrix, where p is the dimension of Gaussian distribution and K is the number of tasks. Each column of the matrix is a "beta" (estimate or true value) for each task.

• Sigma: Gaussian covariance matrices. Both estimated_value and true_value require an input of a list of K p-by-p matrices, where p is the dimension of Gaussian distribution and K is the number of tasks. Each matrix in the list is a "Sigma" (estimate or true value) for each task.

Value

the largest estimation error among all tasks.

Note

For examples, see examples in function mtlgmm.

References

Tian, Y., Weng, H., & Feng, Y. (2022). Unsupervised Multi-task and Transfer Learning on Gaussian Mixture Models. arXiv preprint arXiv:2209.15224.

See Also

mtlgmm, tlgmm, predict_gmm, data_generation, initialize, alignment, alignment_swap, misclustering_error.