| Title: | Confidence Interval for Matrix Completion via De-Biased Estimator |
|---|---|
| Description: | Implements the de-biased estimator for low-rank matrix completion and provides confidence intervals for entries of interest. See: by Chen et al. (2019) <doi:10.1073/pnas.1910053116>, Mai (2021) <arXiv:2103.11749>. |
| Authors: | The Tien Mai [aut, cre] |
| Maintainer: | The Tien Mai <[email protected]> |
| License: | GPL-2 |
| Version: | 1.0.0 |
| Built: | 2024-11-20 04:35:09 UTC |
| Source: | https://github.com/tienmt/dbmc |
This function returns a CI for an entries of interest with a significant level alpha
CI_mc(i, j, alpha = 0.05, missfrac, X.db, est_rank, sigma2 = 1)CI_mc(i, j, alpha = 0.05, missfrac, X.db, est_rank, sigma2 = 1)
i |
the row index of the interest entry X_i,j |
j |
the row index of the interest entry X_i,j |
alpha |
confidence level, default is 0.05 |
missfrac |
the missing proportion in the underlying matrix. It is the total of missing entries over total entries. |
X.db |
the de-biased estimated matrix from the 'dbmc' function. |
est_rank |
the (estimated) low-rank of the underlying matrix or the rank of the de-biased estimator. |
sigma2 |
the noise-variance level. |
CI confidence interval.
(i,j) the location of the entry at i-th row and j-th column.
v.ij the estimated variance of the limiting Gaussian distribution.
Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.
de-biased low-rank matrix completion estimator
This function compute a de-biased estimator from a rank-r matrix completion using the algorithms from the package "softImpute".
dbmc(x, ximp, entries_miss, est_rank)dbmc(x, ximp, entries_miss, est_rank)
x |
the initial matrix with missing entries |
ximp |
an imputed matrix, output from the package "softImpute". |
entries_miss |
the missing indices |
est_rank |
the rank of the matrix x, or the estimated rank from the package "softImpute". |
x.db the de-baised estimation matrix.
Chen et al (2019). Inference and uncertainty quantification for noisy matrix completion. PNAS, 116(46), 22931-22937.
# simulated data require(softImpute) n = 100 p = 100 J = 2 # the true low-rank np = n*p sig2 = 1 missfrac = 0.5 # xtrue is the underlying matrix that we do not know and want to recover it xtrue = matrix(rnorm(n*J),n,J)%*%matrix(rnorm(J*p),J,p) # generating missing entries locations imiss = sample(np,np*missfrac,replace=FALSE) # xna is the observed matrix with missing entries xna = xtrue + matrix(rnorm(np, sd = sig2),nr = n,nc = p) xna[imiss] = NA lamda = 2.5*sig2*sqrt(n*p) # note that we only have xna as our initial data # first, fit a softImpute method fit1 = softImpute(xna, type = 'als') # complete the matrix by a softImpute method ximp = complete(xna,fit1) mean((ximp - xtrue)^2);rankMatrix(ximp,.1)[1] # now, de-biased the softImpute method x.db = dbmc(x = xna, ximp = ximp, entries_miss = imiss, est_rank = 2) mean((x.db - xtrue)^2);rankMatrix(x.db,.1)[1]# simulated data require(softImpute) n = 100 p = 100 J = 2 # the true low-rank np = n*p sig2 = 1 missfrac = 0.5 # xtrue is the underlying matrix that we do not know and want to recover it xtrue = matrix(rnorm(n*J),n,J)%*%matrix(rnorm(J*p),J,p) # generating missing entries locations imiss = sample(np,np*missfrac,replace=FALSE) # xna is the observed matrix with missing entries xna = xtrue + matrix(rnorm(np, sd = sig2),nr = n,nc = p) xna[imiss] = NA lamda = 2.5*sig2*sqrt(n*p) # note that we only have xna as our initial data # first, fit a softImpute method fit1 = softImpute(xna, type = 'als') # complete the matrix by a softImpute method ximp = complete(xna,fit1) mean((ximp - xtrue)^2);rankMatrix(ximp,.1)[1] # now, de-biased the softImpute method x.db = dbmc(x = xna, ximp = ximp, entries_miss = imiss, est_rank = 2) mean((x.db - xtrue)^2);rankMatrix(x.db,.1)[1]
This function returns a matrix where the missing entries are replaced by 0 s.
P_Omega(a, entri)P_Omega(a, entri)
a |
a matrix. |
entri |
missing entries location. |
Return a matrix whose its missing entries are replaced by 0 s.